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Talk:Airship design/Ideas

Studio Lindfors
Perhaps Studio Lindfors is interested, see their cloud city and cloud skippers deisgns(http://www.studiolindfors.com/work/speculative/index.html)

Too many notes, herr Mozart.
Just a few things off the top. Hydrogen by itself is illegal for use in airships today, since an event in the 1930s where a hydrogen-filled blimp named Hindenberg ruined it for the rest of us. Granted the envelope was likewise entirely flammable, but I digress. The design of the Hindenberg, minus the flammable skin, was sound, however, with a bladder of helium, which would have extinguished any fires. Electrolysis is the process by which water is decomposed into its constituent parts by running a current of electricity through it. If you then try to use the resultant mixture (please don't call it oxyhydrogen, it just makes you look like an idiot) as a lifting gas, you've effectively turned your lifting balloons into buoyant bombs. Flywheels, also, are a great idea, unless you're trying to minimise weight, in which case it's a dumb idea. As to making the airship go up and down, why not compress your hydrogen at need and store it in a tank that also moves on a track mounted to the gondola or frame for attitude control. In short, it's like you've taken all the ideas you could fit into the idea and crammed them together. What's required is a little focus, and a little intellectual discretion. The flying camper is a great idea, though. I'll let you know when mine's done. 70.28.62.105 16:16, 1 June 2010 (UTC)

title: Talk:Airship design/Ideas


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World Cyber Cafe

Link to any subpages this page might have

== WORLD CYBER CAFE PROJECT ==

Our Collaboration Wiki

We've got a project to finish, and this site is a central point to keep track of our goals, the project schedule, and our work in progress. Add pages as necessary, brainstorm on the wiki "whiteboard" page, and use the person-to-person messaging feature to keep in touch with team members. Please use the Research page to record all of your observations on the software and gear candidates for our Virtual Cafe.

The Assignment

Project description: Project World Cyber Cafe is to research, discuss and choose the best software at low/no cost, to enable discussion over time or at time and among participants in any time zone anywhere in the world. Of course it requires a computer and other gear connected to a fast, broadband service. Our assignments are to examine the software and gear available, including email, forum, wiki, auto conferencing, video conferencing, whiteboards, chat and even Smail. We need a consistently reliable system, easy to understand, implement and administer.

Goals:

The main goals are the same as The World Cafe = connecting people whip are problem solvers, teachers and learners. Also, we need a knowledge base. Recall the saying: "If Siemens only knew what Siemens knows...." What good is knowledge if we cannot easily find it? Wiki's are a good candidate because of the combination of search engines for key words (tags), yet they lack the spontaneity of a F2F physical group around a table. So the search goes on to find a way to maintain TWC's approach to interaction.

== Open invitation: ==

You are cordially invited to join World Cyber Cafe Design Team which is designing a digital system for holding Virtual Cafes. Please look around at the WikiWebSite wihch started the first week of July, 2008. Then leave your membership information (choose membership from the table, not the upper navigation bar) and then read our postings under Research. I'll send you an invitation to vote on the pending motions listed on the DRAFT PROPOSALS page. Please record your vote on the VOTING page. Please learn to use the Wiki by editing pages, adding comments, adding a page and voting on the two pending propositions. Thanks Jim Miller

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: World Cyber Cafe


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User talk:Remi1994

remikabura@yahoo.com
==

Headline text#REDIRECT ==Italic text

title: User talk:Remi1994


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User:Guidomac

Hi. I'm an italian user and sysop on it.wiki. This account was automatically created. My user page in my Wikipedia is here.

title: User:Guidomac


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Brezhoneg Unan/Lesson 1/War an daol

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Exercises
Go to the Quiz.

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Exercises
Go to the Quiz.

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title: Brezhoneg Unan/Lesson 1/War an daol


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User:JMulqueen

I am an Economics student. I am a native English speaker and am fluent in Spanish. I am a beginner student of Portuguese

title: User:JMulqueen


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User:PandaPanda

Sweet Transvestite from Transsexual Transylvania.

title: User:PandaPanda


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User:Vailk

Who is a Technical Writer? Technical writers write

technical and software manuals handbooks technical guides application notes tutorials data sheets technical and product briefs

Technical writers also create online help. Essentially anyone who writes about technology for other people is typically referred to as a technical writer.

All professionals require some technical writing skills. In the information technology realm, project managers and analysts write a large number of technical documents that must be clear and concise. A technical writer is still looked upon as someone who explains the product to the end user.☺

Uniquely in the IT industry, women make up the majority of technical writers. Pay is good [1] and working conditions are quite agreeable. It is a mentally stimulating creative work, which requires someone who is both sociable and well read. It is not necessary that technical writers should be programmers or have more than a general understanding of the technology. But technical writers must have the ability to learn about a new product and then explain it to others. So people with training in journalism, teaching, and writing along with technical savvy can grow to be the best technical writers. Today, both technical adaptability and writing/communication skills are essential for technical writers to succeed. Recently, more companies are requiring degrees for technical writers.

Technical writers enjoy learning and reading. They find writing comfortable, though they aren’t perfect; typically revising their work many times. They are both creative and orderly. Moreover, they put themselves in the end user’s position.

As an introductory course, only the most universal and important concepts are covered here. Later courses deal in depth with areas such as business analysis, documentation management, and other advanced topics.

What do technical writers do? [edit]When technical writers approach a new piece of technology, it is their own lack of knowledge that they inwardly observe. As they interact with and learn the software, they identify the information needs of the software users. They must be able to communicate well with programmers and customers, and extract information from them in a professional and personable manner.

A technical writer's primary tool is the English language. Secondarily, they use proprietary software like Microsoft Word, FrameMaker, and RoboHelp; or—increasingly—free and open source documentation software such as DocBook and Wiki. In the course of their careers, technical writers learn dozens of other software packages and tools, and then teach them to others.

Worldwide, there is a strong demand for technical writers. Overwhelmingly, they use the English language. Software companies require technical and user documentation for their products, and will continue to do so for the foreseeable future.

For aspiring technical writers, it’s difficult to get “a foot in the door”. Most employers are looking for technical knowledge and demonstrated experience. Completing this course, and creating a project portfolio of completed work, opens doors so you can begin a career in technical communications.

back to Technical Writing Level 1

Technical Writing at Wikiversity Professional and personable. The Essential Skills of a Technical Writer [edit]There are five skills or characteristics which are "musts" for the technical writer:

1. Facility with technology

You must have the potential to grasp technology. You may have a bent towards one of the sciences, and can understand the inner workings of cells or atoms. Or you may be web savvy and know how to interpret code. Or maybe you’re just curious about how things work. You can learn technologies you don’t understand, if you have the motivation. I personally enjoy learning about complicated systems. This understanding brings a sense of achievement and knowledge that is rewarding at the end of the day.

2. Ability to write clearly

The essential skill of any technical communicator is to disambiguate. Your core job will consist of studying complicated things and explaining them in easy-to-understand ways. You can’t just pass off an explanation that even you only half understand. Writing about something, as opposed to talking about it, requires that you understand it thoroughly. Avoid passive sentences and long constructions. Define acronyms and avoid assumptions about what the user knows.

3. Talent in showing ideas graphically

Any time you can show an idea graphically, you score a hundred points with the reader. People understand better when you can communicate your ideas visually. These images go a long way toward making your writing clear.

4. Patience in problem-solving/troubleshooting

Unless you have patience, you’ll never make it. Much of the IT work consists of problem solving. It’s amazing how a seemingly impossible problem can be solved with a little patience and persistence.

5. Ability to interact with Cross-Functional Teams (CFTs)

Interacting with CFTs is one of the most overlooked skills in technical writing. You have to be part investigative reporter, part journalist. You can’t be shy about going after certain people to extract information. And you can’t be too proud to ask the “dumb technical questions” that make engineers do double-takes. A lot of this interaction can come about if you’re lucky enough to simply sit near the CFT members.

Thanks to Tom Johnson for permission to use this material. [Edited once for clarity in context.] For more, see his website I'd Rather Be Writing -Five Skills Every Technical Writer Needs

Technical Writing Basics [edit]Wikipedia defines Technical Communication as:

To create online content, you may use a proprietary program like RoboHelp for help files, or a web authoring tool for making web pages. You may also use Javadoc, Docomatic, and XML with DocBook to create online help. We recommend that you also explore how platforms such as Wiki can be used for delivering user-oriented instructions.

Technical Communication is a conversation [edit]Lindsey Robbins of Blackbaud describes technical communication as a conversation between the user and the technical writer - in the sense that the technical writer must anticipate the questions a user would ask about the software. Robbins states that:

"Sometimes, your users or constituents won't know the correct question to ask. In those situations, try to think out the questions for them and answer them in advance. Provide them with the conversation starter and they're more likely to be engaged.

And remember, people don't have an infinite amount of time. They really will only participate in the conversation long enough to get their answer. Therefore, all your communication whether it's real time or not needs to be concise, clear, and efficient. Don't provide lots of and lots of text that users will balk at when they see."

Re-published with the kind permission of Lindsey Robbins, from her article "Be Part of the Conversation"

Technical Writing Myths [edit]In a recent article on his blog, Tom Johnson explored several common myths about technical writing and the skills needed to be a technical writer. The most common myths are as follows

Technical writers spend most of their time writing. You can’t get a job in technical writing unless you have technical writing samples; but you won’t have samples until you have a job in technical writing.

A technical writer who has years of experience is more knowledgeable than one with fewer years of experience. The tools you know are more important than your industry knowledge. Be careful about having a blog, because all employers google you and will find it. Technical writing academics are disconnected with the profession and only have a tenuous idea about the actual practice of technical writing. You can’t have voice or style in technical writing. It has to be objective. And the fewer contractions, the better. Technical writers aren’t allowed to contact users directly. They should get their information through the product manager, customer support, and marketing.

You can single source your material into all the formats your audience needs, if you just learn the right tool or technology. You have to be quite tech-savvy to be a good technical writer. For Tom's full treatment of these myths, and several others, see his article "14 Widespread Myths about Technical Writing."

This material has been re-published here in an edited form, thanks to Tom Johnson for allowing us to use his articles here.

A great future [edit]Technical Writers communicate ideas. They design information, participate in the product development process, and manage complex documentation projects. Beginning software technical writers are often responsible for communications between the developers and the end-users of the software.

Business writing skills are useful for technical writers. All technical writers must write clearly, and communicate well with specialists. In fact, the field of Technical Writing is so vast it can be hard to define exactly what it is. This is why this set of lessons concentrates mostly on technical writing for the software industry.

Beginning Technical Writers produce the following types of documents:

Product brochures, web sites, and other marketing tools that explain the benefits of the software to buyers. User Guides, manuals, tutorials, and step-by-step task lists that guide new users learning the software. Installation and maintenance guides that show the administrator and experienced user how to configure and troubleshoot the software.

As you advance in your career you may find yourself writing more advanced documents:

• Requirement Specifications that document the needs, goals, and environment of the users of the software.

• Design documents that describe the workings and interactions of the system.

• Control documents that communicate project standards, configuration, schedule and work tasks.

• Test cases that detail the required functionality so the software conforms to the specifications.

Documentation management includes:

• Cost and schedule estimating.

• Complex documentation project administration.

• Setting standards and procedures.

• Information management.

As you can see, there is a lot of room to learn and grow in the profession of technical writing.

References [edit]↑ Salary Survey Report for Job: Technical Writer.

title: User:Vailk


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Circular Motion

An object moving in a circular path, such as a person on a merry-go-round or a satellite orbiting the Earth, has an interesting motion where the speed is constant but the direction is continually changing. This is accelerated motion because in any chosen direction, the speed is changing. At the high school level (without calculus), it is interesting and rewarding to find the central formula for circular motion through an experiment that can be done with no special equipment.

Circular Motion Experiment
A force is required to provide the acceleration of an object in circular motion. This force is always toward the center of the circle and is called the centripetal force. Its formula can be found in this little experiment. It requires no special equipment, but has a fairly complex analysis.

Procedure

Swing a rubber ball attached to a string in circular motion at various speeds and string lengths. Record the time for 10 complete circles, the length of the string (to the center of the ball) and the angle of the string from vertical. For larger radii, swing it around your head. For smaller radii, swing in front of you. A good way to observe the angle is to use a light in an otherwise darkened room to cast a shadow of the swinging ball and hand holding the string onto a wall or chalkboard where a partner can measure it. The angle is the largest source of error in the experiment and needs to be measured as accurately as you can.

Analysis

Two forces act on the ball (middle diagram), gravity down and the Tension force of the string. In the right diagram, the tension force has been replaced by its horizontal and vertical components. The total vertical force must be zero because the stopper does not accelerate vertically, so T*cos(A) = mg. (1) The horizontal force is the centripetal force accelerating the stopper toward the center of the circle: Fc = T*sin(A). From equation (1), T = mg/cos(A) so we have Fc = mg*sin(A)/cos(A) = mg*tan(A)

The radius is R = L*sin(A). The velocity is distance over time: v = 2πR/t

Finding the Formula

Graph Fc versus various expressions like vR, v2R, vR2 until you get a graph that appears to be a straight line. Identify the slope (use its units as well as its magnitude) as some quantity in the experiment. A straight line graph of y vs x has the formula y = mx + b where m is the slope and b the y-intercept. For the graph of Fc, you will have Fc in place of y and some quantity such as v2/R in place of x. Hopefully the y-intercept will be zero.

This part may not be essential, but it makes the experiment much more convincing. Repeat one of the trials and estimate the accuracy of the angle measurement - perhaps plus or minus 3 degrees. With one line in the table, do the calculations with 3 degrees added and again with 3 degrees subtracted to see the plus or minus variation in the Fc and in the expression that results in the best straight line. Use these variations to make error bars on the graph. Is the graph a straight line to within the accuracy of the experiment?

Conclusion

Done carefully, this experiment shows that Fc = mv2/r to within experimental error. Here m is the mass of the object in circular motion.

title: Circular Motion


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User:Wallandbored

Wallandbored
Wallandbored is a name derived from the last name "Wallenborn". And is used for usernames and email addresses by Ian Wallenborn.

Though the actual meaning of this name is nothing, It is still used because it sounds cool, and is easy to say.

Link title

title: User:Wallandbored


text:
Web Design/HTML Challenges/WebDesign Hint1

Hint!

Can't recall what word to use while searching for information on placing an email link?

Try "mailto" in the search box at www.htmldog.com or in Google.

Return to previous page.


text:
User:Egm6936.s09/A thermal problem

= The transient heat transfer =

The dimensional thermal problem
The governing equation has the following form:
 * {| style="width:100%" border="0"

$$  \displaystyle k \frac{\partial^2 u}{\partial x^2} + f(x,t) = \rho c \frac{\partial u}{\partial t} $$ where $$\displaystyle k,\, c,\, \rho$$ are material thermal conductivity, specific heat and density proportionally.
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The initial condition:
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$$\displaystyle u(x,t=0) = u_0 $$
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The boundary conditions:
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$$\displaystyle q(x=0,t) = q(x=L,t) = 0 $$
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Using the Galerkin's Finite Element Method (FEM) as appendix 1 for a transient heat transfer problem, we obtain the global equations:
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\displaystyle \left[ C \right]\left\{ {\dot U} \right\} + \left[ K \right]\left\{ U \right\} = \left\{ {F_Q } \right\} + \left\{ {F_g } \right\} $$ where vector $$\left\{ U \right\} = \left[ {\begin{array}{*{20}c} {u_1 } & \ldots  & {u_n }  \\ \end{array}} \right]^T $$ is temperature at n nodes, that obtains by solving the original differential equation (4) with the initial condition (2).
 * style="width:95%" |$$
 * style="width:95%" |$$
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 * }

We will demonstrate the above procedure through an example.

Example 1: Solving the 1D following heat equation in a cylindrical rod having diameter d and length L:
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$$  \displaystyle k \frac{\partial^2 u}{\partial x^2} + f(x,t) = \rho c \frac{\partial u}{\partial t}  \qquad 0 \le x \le L,\,\,0 \le t \le t_{end} = 30 s $$ with material parameters
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 * $$k = 230\,W/m{}^0C,\,\,\,c = 900\,J/kg{}^0C,\,\,\,\rho = 2700kg/m^3

$$ and geometric parameters
 * $$L = 0.1m,\,\,\,d = 0.012m\,

$$

Heat generation: $$f(x,t) = \begin{cases} Q = 10^7\,\,\,\,\,\,\,\,\,\,\,\left( {x,t} \right) \in \left[ {0,\frac{L}{2}} \right] \times \left[ {0,t_1 } \right] \\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise \end{cases} $$

Initial condition:
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$$\displaystyle u(x,t=0) = u_0 = 30 ^0C $$
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The boundary condition:
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$$\displaystyle q(x=0,t) = q(x=L,t) = 0 $$
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Solution

Dividing the rod into four elements, each has length $$L_e = \frac{L}{4}$$. Thus, we have five nodes with five freedom degrees: $$\left\{ U \right\} = \left[ {\begin{array}{*{20}c}{u_1 } & {u_2 } & {u_3 } & {u_4 } & {u_5 } \\ \end{array}} \right]^T $$

FEM equations for each element are given as appendix 2

Subsituting numerical values into the global equation (4) we have:
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\displaystyle \left[ K \right] = \left[ {\begin{array}{*{20}c} {1.0403} & { - 1.0403} & 0 & 0 & 0 \\   { - 1.0403} & {2.0806} & { - 1.0403} & 0 & 0  \\   0 & { - 1.0403} & {2.0806} & { - 1.0403} & 0  \\   0 & 0 & { - 1.0403} & {2.0806} & { - 1.0403}  \\   0 & 0 & 0 & { - 1.0403} & {1.0403}  \\ \end{array}} \right] $$
 * style="width:95%" |$$
 * style="width:95%" |$$
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 * }

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\displaystyle \left[ C \right] = \left[ {\begin{array}{*{20}c} {2.2898} & {1.1449} & 0 & 0 & 0 \\   {1.1449} & {4.5796} & {1.1449} & 0 & 0  \\   0 & {1.1449} & {4.5796} & {1.1449} & 0  \\   0 & 0 & {1.1449} & {4.5796} & {1.1449}  \\   0 & 0 & 0 & {1.1449} & {2.2898}  \\ \end{array}} \right] $$
 * style="width:95%" |$$
 * style="width:95%" |$$
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 * }

 * {| style="width:100%" border="0"

\displaystyle \left\{ {F_Q } \right\} = \left\{ {\begin{array}{*{20}c} {14.1345} \\   {28.2690}  \\   {14.1345}  \\   0  \\   0  \\ \end{array}} \right\} \left\{ {F_g } \right\} = \left\{ {\begin{array}{*{20}c} 0 \\   0  \\   0  \\   0  \\   0  \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

To obtain solutions for first-order ordinary differential equations, we use the finite difference method or specifically the forward difference method. This method approximate the time derivative of the nodal temperature matrix as:

\displaystyle \left\{ {\dot U} \right\} \cong \frac $$

Substituting the above equation, the global equation becomes

\displaystyle \left\{ {U(t_{i + 1} )} \right\} = \left\{ {U(t_i )} \right\} + \left[ C \right]^{ - 1} \left( {\left\{ {F_Q (t_i )} \right\} + \left\{ {F_q (t_i )} \right\} - \left[ K \right]\left\{ {U(t_i )} \right\}} \right)\Delta t,\,\,\,\left\{ {U(t_0 )} \right\} = \left\{ {U_0 } \right\} $$

In this example, this equation yields two cases:

a) From $$0 \le t \le t_1$$: heat generation is non-zero

\displaystyle \left\{ {U(t_{i + 1} )} \right\} = \left\{ {U(t_i )} \right\} + \left[ C \right]^{ - 1} \left( {\left\{ {F_Q (t_i )} \right\} - \left[ K \right]\left\{ {U(t_i )} \right\}} \right)\Delta t,\,\,\,\left\{ {U(t_0 )} \right\} = \left\{ {U_0 } \right\} $$

b) From $$t_1 \le t \le t_{end}$$: heat generation is zero

\displaystyle \left\{ {\tilde U(t_{i + 1} )} \right\} = \left\{ {\tilde U(t_i )} \right\} - \left[ C \right]^{ - 1} \left[ K \right]\left\{ {\tilde U(t_i )} \right\}\Delta t ,\,\,\,\left\{ {\tilde U(t_0 )} \right\} = \left\{ {U(t_1 )} \right\} $$

Therefore, nodal temperatures are:

\displaystyle \left\{ U \right\} = \left[ {\begin{array}{*{20}c} {U(t_0 )} & {U(\Delta t)} & \ldots  & {U(t_1 )} & {\tilde U(t_1  + \Delta t)} &  \ldots  & {\tilde U(t_{end} )}  \\ \end{array}} \right] $$

With $$t_{end} = 30\,s,\,\,t_1  = \frac{3} = 10\,s,\,\,\Delta t = 0.1\,s$$, we plot values $$\left\{ { U(t)} \right\}$$ versus $$t$$.

The nondimensional thermal problem
Now we nondimensionalize the heat transfer equation (1). For this equation, there are four fundamental units $$\left( {F_1 ,F_2 ,F_3 ,F_4 } \right) = \left( {m,s,K,W} \right)$$ and ten physical quantities which are listed below together with their corresponding dimensional formula for the unit in terms of the fundamental units:

Thus, the dimension matrix is:

\displaystyle A = \left[ {\begin{array}{*{20}c} 0 & 0 & 1 & 1 & 0 & 0 & { - 1} & { - 3} & { - 2} & { - 3} \\   0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0  \\   1 & 1 & 0 & 0 & 0 & 0 & { - 1} & { - 1} & 0 & 0  \\   0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1  \\ \end{array}} \right]_{4 \times 10} $$ It can find the nullspace of matrix $$A$$:

\displaystyle Null\left( A \right) = \left[ {\begin{array}{*{20}c} { - 1} & 0 & 0  & 0  & { - 1}  & { - 1}   \\   1 & 0  & 0  & 0  & 0  & 0   \\   0  & { - 1}  & 0  & 2  & 1  & 2   \\   0  & 1  & 0  & 0  & 0  & 0   \\   0  & 0  & { - 1}  & { - 1}  & 0  & 0   \\   0  & 0  & 1  & 0  & 0  & 0   \\   0  & 0  & 0  & { - 1}  & { - 1}  & { - 1}   \\   0  & 0  & 0  & 1  & 0  & 0   \\   0  & 0  & 0  & 0  & 1  & 0   \\   0  & 0  & 0  & 0  & 0  & 1   \\ \end{array}} \right]_{10 \times 6} $$

From the above result, we have six independent dimensionless groups of the original variables.

\displaystyle R_1 ^{ - 1} R_2^1 = \frac{U} = {\prod}_1 ,\,\,R_3 ^{ - 1} R_4^1 \, = \frac{x}{L} = {\prod}_2 ,\,\,\,R_5 ^{ - 1} R_6^1  = \frac{t} = {\prod}_3 ,\,\,\, $$

\displaystyle R_3^2 R_5 ^{ - 1} R_7 ^{ - 1} R_8^1 = \frac = {\prod}_4 ,\,\,\,R_1^{ - 1} R_3 ^1 R_7 ^{ - 1} R_9^1  = \frac = {\prod}_5 ,\,\,\,R_1^{ - 1} R_3 ^2 R_7 ^{ - 1} R_{10}^1  = \frac = {\prod}_6 $$

Alternatively we have 6 nondimensional variables which are provided as below:

\displaystyle \frac{U} = \Gamma \,\,\,\,\,\,(5) \,\,\,\,\,\,\,\, \frac{x}{L} = \xi \,\,\,\,\,\, (6) \,\,\,\,\,\,\,\, \frac{t} = \tau \,\,\,\,\,\, (7) $$

\frac = \beta \,\,\,\,\,\, (8)\,\,\,\,\,\,\,\, \frac = \varphi \left( t \right) \,\,\,\,\,\, (9) \,\,\,\,\,\, \frac = \Phi \left( {\xi ,\tau } \right) \,\,\,\,\,\, (10) $$

In terms of these nondimensional variables the simplified thermal problem can be written in the following nondimensional form (the details of nondimensionalizing the heat problem are found in appendix 3):

Heat conduction equation:

\beta \frac + \Phi \left( {\xi ,\tau } \right) = \frac \,\,\,\,\,\, (11) ,\,\,\left( {\xi ,\tau } \right) \in \left[ {0,1} \right] \times \left[ {0,1} \right] $$

Initial condition:

\displaystyle \Gamma \left( {\xi ,\tau = 0} \right) = 1 \,\,\,\,\,\, (12) $$

Boundary condition:

\displaystyle \left. { - \frac} \right|_{\xi = 0}  = \varphi _{in} ,\,\,\left. { - \frac} \right|_{\xi = 1}  = \varphi _{out} \,\,\,\,\,\, (13) $$

where

\varphi _{in} = \frac, \,\,\,\,\,\, \varphi _{out} = \frac \,\,\,\,\,\, (14) $$

The complete set of nondimensional variables needed for the problem is given in equations (5)-(10). The nondimensional temperature $$\Gamma$$ can be expressed function of the nondimensional distance $$\xi$$ and the nondimensional time $$\tau$$ as well as function of four other nondimensional parameters.

The physical interpretation of the remaining four nondimensional parameters in equations (8)-(10) is the following. $$\beta$$, the Fourier number or a nondimensional thermal diffusivity, is the ratio of the rate of heat conduction and the rate of heat storage(thermal energy storage). $$\varphi$$ is the ratio of the incident heat flux and the rate of heat conduction, or can be seen as effective heat flux. Finally, $$\Phi$$ is the ratio of the heat source and the rate of heat storage, can interpreted as effective heat source.

Example 2: Solving the problem in example 1 with the nondimensional form. Using Galerkin's FEM, similarly to dimensional form, we have the desired FEM equation for one element:

\displaystyle \left[ {K^{\left( e \right)} } \right]\left\{ {\begin{array}{*{20}c} {\Gamma _1 \left( \tau \right)}  \\ {\Gamma _2 \left( \tau \right)}  \\ \end{array}} \right\} + \left[ {C^{\left( e \right)} } \right]\left\{ {\begin{array}{*{20}c} {\dot \Gamma _1 \left( \tau \right)}  \\ {\dot \Gamma _2 \left( \tau \right)}  \\ \end{array}} \right\} = \left\{ {F_Q^{\left( e \right)} } \right\} + \left\{ {F_g^{\left( e \right)} } \right\} $$ where

\displaystyle \left[ {K^{\left( e \right)} } \right] = \frac{\beta }\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\,\,\,\,\,\,\,\,\,\,\left[ {C^{\left( e \right)} } \right] = \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] $$

\displaystyle \left\{ {F_Q^{\left( e \right)} } \right\} = \left\{ {\begin{array}{*{20}c} {\int\limits_0^{L_e } {\Phi \left( {\xi ,\tau } \right)N_1 \left( \xi \right)d\xi } }  \\ {\int\limits_0^{L_e } {\Phi \left( {\xi ,\tau } \right)N_2 \left( \xi \right)d\xi } }  \\ \end{array}} \right\} = \frac{2}\left\{ {\begin{array}{*{20}c} 1 \\   1  \\ \end{array}} \right\} \left( {if \,\,\, \Phi  = const} \right) \,\,\,\,\,\,\,\,\,\,\,\left\{ {F_g^{\left( e \right)} } \right\} = \beta \left\{ {\begin{array}{*{20}c} {\left. { - \frac} \right|_{\xi = 0} }  \\ {\left. {\frac} \right|_{\xi = 1} }  \\ \end{array}} \right\} = \beta \left\{ {\begin{array}{*{20}c} {\varphi _1 } \\ { - \varphi _2 } \\ \end{array}} \right\} $$

Using assembly procedure to obtain the global equations:

\displaystyle \left[ C \right]\left\{ {\dot \Gamma (\tau)} \right\} + \left[ K \right]\left\{ \Gamma (\tau) \right\} = \left\{ {F_Q } \right\} + \left\{ {F_g } \right\} \,\,\,\,\,\, (15) $$

Dividing the rod into four element, each element has length $$L_e = \frac{1}{4}$$, we have 5 nodes with 5 freedom degree:

\left\{ \Gamma \right\} = \left[ {\Gamma _1 } \,\,\, {\Gamma _2 } \,\,\, {\Gamma _3 } \,\,\, {\Gamma _4 } \,\,\, {\Gamma _5 } \,\,\, \right]^T \,\,\,\,and\,\,\,\left\{ {\dot \Gamma } \right\} = \left[ {\dot \Gamma _1 } \,\,\, {\dot \Gamma _2 } \,\,\, {\dot \Gamma _3 } \,\,\, {\dot \Gamma _4 } \,\,\, {\dot \Gamma _5 } \,\,\, \right]^T $$

where

\left[ K \right] = \frac{\beta }\left[ {\begin{array}{*{20}c} 1 & { - 1} & 0 & 0 & 0 \\   { - 1} & 2 & { - 1} & 0 & 0  \\   0 & { - 1} & 2 & { - 1} & 0  \\   0 & 0 & { - 1} & 2 & { - 1}  \\   0 & 0 & 0 & { - 1} & 1  \\ \end{array}} \right] \,\,\,\,\,\, (16) $$

\left[ C \right] = \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 & 0 & 0 & 0 \\   1 & 4 & 1 & 0 & 0  \\   0 & 1 & 4 & 1 & 0  \\   0 & 0 & 1 & 4 & 1  \\   0 & 0 & 0 & 1 & 2  \\ \end{array}} \right] \,\,\,\,\,\, (17) $$

\left[ F_Q \right] = \frac{2}\left\{ {\begin{array}{*{20}c} 1 \\   2  \\   1  \\   0  \\   0  \\ \end{array}} \right\} \,\,\,\,\,\, (18) \,\,\,\,\,\, \left[ F_g \right] = \beta \left\{ {\begin{array}{*{20}c} {\varphi _1 } \\ 0 \\   0  \\   0  \\   { - \varphi _5 }  \\ \end{array}} \right\} \,\,\,\,\,\, (19) $$

Substituting the values of parameters, it can easily calculate conductance and capacitance matrix, forcing function vectors as

\left[ K \right] = \left[ {\begin{array}{*{20}c} & { - {\rm{3}}{\rm{.0288}}} & 0 & 0 & 0 \\ { - {\rm{3}}{\rm{.0288}}} & & { - {\rm{3}}{\rm{.0288}}} & 0 & 0  \\ 0 & { - {\rm{3}}{\rm{.0288}}} & & { - {\rm{3}}{\rm{.0288}}} & 0  \\ 0 & 0 & { - {\rm{3}}{\rm{.0288}}} & & { - {\rm{3}}{\rm{.0288}}}  \\ 0 & 0 & 0 & { - {\rm{3}}{\rm{.0288}}} &  \\ \end{array}} \right],\,\,\,\,\,\,\,\, $$

\left[ C \right] = \left[ {\begin{array}{*{20}c} & & 0 & 0 & 0  \\    &  &  & 0 & 0  \\   0 &  &  &  & 0  \\   0 & 0 &  &  & {1.1449}  \\   0 & 0 & 0 & {1.1449} &   \\ \end{array}} \right] $$

\left\{ {F_Q } \right\} = \left\{ {\begin{array}{*{20}c} \\    \\     \\   0  \\   0  \\ \end{array}} \right\},\,\,\,\left\{ {F_g } \right\} = \beta \left\{ {\begin{array}{*{20}c} {\varphi _1 } \\ {\rm{0}} \\ {\rm{0}} \\ 0 \\   { - \varphi _5 }  \\ \end{array}} \right\} = \left\{ {\begin{array}{*{20}c} 0 \\   0  \\   0  \\   0  \\   0  \\ \end{array}} \right\} \,\,\,\,\,\, \left( {\varphi _1 = \varphi _{in}  = 0,\,\,\varphi _5  = \varphi _{out}  = 0} \right) $$

The graph of nondimensional temperature versus nondimensional time is below:

Example 3: Now we want to generate a graph that will give us the maximum value of the temperature in a rod as the example 1(max temperature over both time and space) for any value of $$\displaystyle k,c,\rho ,L,U_0 ,Q,t_1 $$ . We do this this by solving the non-dimensional equation (11)-(13) for a range of these values. It can easily find that the maximum value of the nondimensional temperature $$\displaystyle \Gamma _{\max } $$ depends on three independent nondimensional variables:
 * $$\beta = \frac, \,\,\,\,\,\, \bar Q = \frac, \,\,\,\,\,\, \tau _1  = \frac

$$. From equation (15), we can note that the maximum temperature $$\displaystyle \Gamma _{\max } $$ will be linear in $$\displaystyle \Phi = \bar Q = const$$ so that we do not need this as a parameter. To prove this conclusion, we scale the solution by changing variable:
 * $$\Lambda = \frac $$

At that time, the global equation (15) becomes:

\bar Q\left[ C \right]\left\{ {\dot \Lambda (\tau )} \right\} + \left[ K \right]\left\{ {\bar Q\Lambda (\tau ) + \left\{ 1 \right\}} \right\} = \left\{ F \right\} $$ or

\bar Q\left[ C \right]\left\{ {\dot \Lambda (\tau )} \right\} + \bar Q\left[ K \right]\left\{ {\Lambda (\tau )} \right\} = \left\{ {F_Q } \right\}\, - \left[ K \right]\left\{ 1 \right\} = \left\{ {F_Q } \right\} \,\,\,\,\,\, (because \left[ K \right]\left\{ 1 \right\} = \left\{ 0 \right\}) $$ Thus, dividing both sides of above equation to $$\bar Q \ne 0$$, we get

\left[ C \right]\left\{ {\dot \Lambda (\tau )} \right\} + \left[ K \right]\left\{ {\Lambda (\tau )} \right\} = \left\{ F \right\} $$ where $$K,\,C$$ is determined as equations (16),(17) and $$\displaystyle F = \frac{2}\left[ {1\,\,2\,\,1\,\,0\,\,0} \right]^T $$ with the initial condition $$\Lambda (0) = 0 $$

Summing up, the maximum nondimensional temperature $$\displaystyle \Gamma _{\max } $$ only depends on two independent nondimensional variables $$ \displaystyle \beta ,\tau _1 $$ The graph of $$\displaystyle \Gamma _{\max } $$ for a range of these two parameters is below:

Appendix 1: Finite element procedures for a thermal problem
Here the Galerkin's Finite Element Method (FEM) is applied for the heat transfer equation to obtain the element equations. A two-node element with linear interpolation functions is used and the temperature distribution in an element expressed as
 * {| style="width:100%" border="0"

$$  \displaystyle u(x,t) = N_1(x) u_1(t) + N_2(x) u_2(t) $$ where $$\displaystyle u_1(t) $$ and $$\displaystyle u_2(t) $$ are the temperature at nodes 1 and 2, which define the element, and the interpolation functions $$\displaystyle N_1(x) $$ and $$\displaystyle N_2(x) $$ are given by $$\displaystyle N_1(x) = (1- \frac{x}{L}) $$, $$\displaystyle N_2(x) = \frac{x}{L} $$
 * style="width:95%" |
 * style="width:95%" |
 * style= | (20)
 * }

Substitution of the discretized solution into the governing differential Equation results in the residual intergrals:
 * {| style="width:100%" border="0"

\displaystyle \int_{0}^{L} \left ( k \frac{\partial^2 u}{\partial x^2} + f(x,t) - \rho c \frac{\partial u}     {\partial t} \right ) N_i(x) A\, dx = 0 \quad i = 1,\,2 $$ where we note that the integration is over the volume of the element, that is, the domain of the problem, with $$\displaystyle dV = A dx $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (21)
 * }

or
 * {| style="width:100%" border="0"

\displaystyle k A \int_{0}^{L} N_i(x) \frac{\partial^2 u}{\partial x^2}\, dx + A \int_{0}^{L} N_i(x) f(x,t)\, dx - \rho c A \int_{0}^{L} N_i(x) \frac{\partial u}{\partial t}\, dx = 0 \quad i = 1,\,2 $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (22)
 * }

Intergratig the first term by parts and rearranging,
 * {| style="width:100%" border="0"

\displaystyle k A \int_{0}^{L} \frac{dN_i(x)}{dx} \frac{\partial u}{\partial x}\, dx  + \rho c   A \int_{0}^{L} N_i(x) \frac{\partial u}{\partial t}\, dx = A \int_{0}^{L} N_i(x) f(x,t)\, dx + \left. {kAN_i \left( x \right)\frac} \right|_{x = 0}^{x = L} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (23)
 * }

Substituting for $$\displaystyle u(x,t)$$ from (20) yields
 * {| style="width:100%" border="0"

\displaystyle k A \int_{0}^{L} \frac{dN_i(x)}{dx} \left ( \frac{dN_1(x)}{dx} u_1(t) + \frac{dN_2(x)}{dx} u_2(t)    \right )\, dx   + \rho c A \int_{0}^{L} N_i(x) \left ( N_1(x) \dot u_1(t) + N_2(x) \dot u_2(t) \right )\, dx $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

 * {| style="width:100%" border="0"

\displaystyle = A \int_{0}^{L} N_i(x) f(x,t)\, dx + \left. {kAN_i \left( x \right)\frac} \right|_{x = 0}^{x = L} \quad i = 1,\,2 $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (24)
 * }

The two equations represented by equation (24) are conveniently combined into a matrix form by rewriting as
 * {| style="width:100%" border="0"

$$  \displaystyle u(x,t) = [N_1(x) N_2(x)] \begin{Bmatrix} u_1(t) \\ u_2(t) \end{Bmatrix} $$
 * style="width:95%" |
 * style="width:95%" |
 * style= | (25)
 * }

and substituting to obtain
 * {| style="width:100%" border="0"

\displaystyle k A \int_{0}^{L} \begin{bmatrix} \dot N_1(x) \\ \dot N_2(x) \end{bmatrix} \left [ \dot N_1(x) \dot N_2(x) \right ]dx\, \begin{Bmatrix} u_1(t) \\ u_2(t) \end{Bmatrix} + \rho c A \int_{0}^{L} \begin{bmatrix} N_1(x) \\ N_2(x) \end{bmatrix} \left [ N_1(x) N_2(x) \right ]dx\, \begin{Bmatrix} \dot u_1(t) \\ \dot u_2(t) \end{Bmatrix} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

 * {| style="width:100%" border="0"

\displaystyle = A \int_{0}^{L} \begin{bmatrix} N_1(x) \\ N_2(x) \end{bmatrix} f(x,t)\, dx + k A \begin{Bmatrix} \left. { - \frac} \right|_{x = 0} \\ \left. {\frac} \right|_{^{x = L} } \end{Bmatrix} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (26)
 * }

Equation (26) is in the desired finite element form:
 * {| style="width:100%" border="0"

\displaystyle \left[ {k^{\left( e \right)} } \right]\left\{ {\begin{array}{*{20}c} {u_1 \left( t \right)} \\ {u_2 \left( t \right)} \\ \end{array}} \right\} + \left[ {c^{\left( e \right)} } \right]\left\{ {\begin{array}{*{20}c} {\dot u_1 \left( t \right)} \\ {\dot u_2 \left( t \right)} \\ \end{array}} \right\} = \left\{ {f_Q^{\left( e \right)} } \right\} + \left\{ {f_g^{\left( e \right)} } \right\} $$ where $$\left[ {k^{\left( e \right)} } \right]$$ is the conductance matrix defined as
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (27)
 * }
 * {| style="width:100%" border="0"

\displaystyle \begin{array}{l} \left[ {k^{\left( e \right)} } \right] = kA\int\limits_0^{L} {\left[ {\begin{array}{*{20}c} {\frac} \\ {\frac} \\ \end{array}} \right]} \left[ {\begin{array}{*{20}c} {\frac} & {\frac} \\ \end{array}} \right]dx = kA\int\limits_0^{L} {\left[ {\begin{array}{*{20}c} { - \frac{1}} \\ {\frac{1}} \\ \end{array}} \right]} \left[ {\begin{array}{*{20}c} { - \frac{1}} & {\frac{1}} \\ \end{array}} \right]dx \\ \,\,\,\,\,\,\,\,\,\,\,\, = \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right] \\ \end{array} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (28)
 * }

and $$\left[ {c^{\left( e \right)} } \right]$$ is the element capacitance matrix defined by
 * {| style="width:100%" border="0"

\displaystyle \begin{array}{l} \left[ {c^{\left( e \right)} } \right] = c\rho A\int_0^L {\left[ {\begin{array}{*{20}c} {N_1 } \\ {N_2 } \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {N_1 } & {N_2 } \\ \end{array}} \right]} dx = c\rho A\int_0^L {\left[ {\begin{array}{*{20}c} {1 - \frac{x}{L}} \\ {\frac{x}{L}} \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {1 - \frac{x}{L}} & {\frac{x}{L}} \\ \end{array}} \right]} dx \\ \,\,\,\,\,\,\,\,\,\,\, = c\rho AL\int_0^1 {\left[ {\begin{array}{*{20}c} {1 - \xi } \\ \xi  \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {1 - \xi } & \xi  \\ \end{array}} \right]} d\xi = \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \\ \end{array} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (29)
 * }

The forcing function vectors on the right-hand side of equation (27) include the internal heat generation and boundary flux terms. These are given by
 * {| style="width:100%" border="0"

\displaystyle \left[ {f_Q ^{\left( e \right)} } \right] = A\left\{ {\begin{array}{*{20}c} {\int_0^L {f(x,t)N_1 (x)} dx} \\ {\int_0^L {f(x,t)N_2 (x)} dx} \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (30)
 * }
 * {| style="width:100%" border="0"

\displaystyle \left[ {f_g ^{\left( e \right)} } \right] = kA\left\{ {\begin{array}{*{20}c} {\left. { - \frac} \right|_{x = 0} } \\ {\left. {\frac} \right|_{x = L} } \\ \end{array}} \right\} = A\left\{ {\begin{array}{*{20}c} {\left. q \right|_{x = 0} } \\ {\left. { - q} \right|_{x = L} } \\ \end{array}} \right\} = A\left\{ {\begin{array}{*{20}c} {q_1 } \\ { - q_2 } \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (31)
 * }

Using assembly procedure for a transient heat transfer problem, we obtain the global equations:
 * {| style="width:100%" border="0"

\displaystyle \left[ C \right]\left\{ {\dot U} \right\} + \left[ K \right]\left\{ U \right\} = \left\{ {F_Q } \right\} + \left\{ {F_g } \right\} $$ where vector $$\left\{ U \right\} = \left[ {\begin{array}{*{20}c} {u_1 } & \ldots  & {u_n }  \\ \end{array}} \right]^T $$ is temperature at n nodes, that obtains by solving the differential equation (32) with the initial condition (2).
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= | (32)
 * }

Appendix 2: Finite element implementation of a dimensional problem
FEM equations for each element are given as (27)

Element 1:

 * {| style="width:100%" border="0"

\displaystyle \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\left\{ {\begin{array}{*{20}c} {u_1 }  \\  {u_2 }  \\ \end{array}} \right\} + \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \left\{ {\begin{array}{*{20}c} {\dot u_1 } \\ {\dot u_2 } \\ \end{array}} \right\} = QA\left\{ {\begin{array}{*{20}c} {\int\limits_0^{L_e } {N_1 (x)dx} } \\ {\int\limits_0^{L_e } {N_2 (x)dx} } \\ \end{array}} \right\} + A\left\{ {\begin{array}{*{20}c} {q_1 } \\ { - q_2 } \\ \end{array}} \right\} $$ or
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }
 * {| style="width:100%" border="0"

\displaystyle \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\left\{ {\begin{array}{*{20}c} {u_1 }  \\  {u_2 }  \\ \end{array}} \right\} + \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \left\{ {\begin{array}{*{20}c} {\dot u_1 } \\ {\dot u_2 } \\ \end{array}} \right\} = \frac{Q A L_e}{2} \left\{ {\begin{array}{*{20}c} {1}  \\   {1}   \\ \end{array}} \right\} + A\left\{ {\begin{array}{*{20}c} {q_1 } \\ { - q_2 } \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

Element 2:
 * {| style="width:100%" border="0"

\displaystyle \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\left\{ {\begin{array}{*{20}c} {u_2 }  \\  {u_3 }  \\ \end{array}} \right\} + \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \left\{ {\begin{array}{*{20}c} {\dot u_2 } \\ {\dot u_3 } \\ \end{array}} \right\} = \frac{Q A L_e}{2} \left\{ {\begin{array}{*{20}c} {1}  \\   {1}   \\ \end{array}} \right\} + A\left\{ {\begin{array}{*{20}c} {q_2 } \\ { - q_3 } \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

Element 3:
 * {| style="width:100%" border="0"

\displaystyle \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\left\{ {\begin{array}{*{20}c} {u_3 }  \\  {u_4 }  \\ \end{array}} \right\} + \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \left\{ {\begin{array}{*{20}c} {\dot u_3 } \\ {\dot u_4 } \\ \end{array}} \right\} = \frac{Q A L_e}{2} \left\{ {\begin{array}{*{20}c} {1}  \\   {1}   \\ \end{array}} \right\} + A\left\{ {\begin{array}{*{20}c} {q_3 } \\ { - q_4 } \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

Element 4:
 * {| style="width:100%" border="0"

\displaystyle \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} \\   { - 1} & 1  \\ \end{array}} \right]\left\{ {\begin{array}{*{20}c} {u_4 }  \\  {u_5 }  \\ \end{array}} \right\} + \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 \\   1 & 2  \\ \end{array}} \right] \left\{ {\begin{array}{*{20}c} {\dot u_4 } \\ {\dot u_5 } \\ \end{array}} \right\} = \frac{Q A L_e}{2} \left\{ {\begin{array}{*{20}c} {1}  \\   {1}   \\ \end{array}} \right\} + A\left\{ {\begin{array}{*{20}c} {q_4 } \\ { - q_5 } \\ \end{array}} \right\} $$
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }

The global equation (4) on the system assembly is:
 * {| style="width:100%" border="0"

\displaystyle \left[ C \right]\left\{ {\dot U} \right\} + \left[ K \right]\left\{ U \right\} = \left\{ {F_Q } \right\} + \left\{ {F_g } \right\} $$ where
 * style="width:95%" |$$
 * style="width:95%" |$$
 * style= |
 * }
 * {| style="width:100%" border="0"

\displaystyle \left[ K \right] = \frac\left[ {\begin{array}{*{20}c} 1 & { - 1} & 0 & 0 & 0 \\ { - 1} & 2 & { - 1} & 0 & 0 \\ 0 & { - 1} & 2 & { - 1} & 0 \\ 0 & 0 & { - 1} & 2 & { - 1} \\ 0 & 0 & 0 & { - 1} & 1 \\ \end{array}} \right]
 * style="width:95%" |$$
 * style="width:95%" |$$

\displaystyle \left[ C \right] = \frac{6}\left[ {\begin{array}{*{20}c} 2 & 1 & 0 & 0 & 0 \\ 1 & 4 & 1 & 0 & 0 \\ 0 & 1 & 4 & 1 & 0 \\ 0 & 0 & 1 & 4 & 1 \\ 0 & 0 & 0 & 1 & 2 \\ \end{array}} \right] $$
 * style= |
 * }

 * {| style="width:100%" border="0"

\displaystyle \left\{ {F_Q } \right\} = \frac{2}\left\{ {\begin{array}{*{20}c} 1 \\ 2 \\ 1 \\ 0 \\ 0 \\ \end{array}} \right\}
 * style="width:95%" |$$
 * style="width:95%" |$$

\displaystyle \left\{ {F_g } \right\} = A\left\{ {\begin{array}{*{20}c} {q_1 } \\ 0 \\ 0 \\ 0 \\ { - q_5 } \\ \end{array}} \right\} $$
 * style= |
 * }

Appendix 3: Nondimensionalize the thermal problem
To clarify the nondimensionalizing process, we change variables:

\displaystyle U\left( {x,t} \right) = U_0 \Gamma \left( {\xi ,\tau } \right),\,\,\frac{x}{L} = \xi ,\,\,\,\frac{t} = \tau $$

Therefore:

\displaystyle \frac = U_0 \frac = U_0 \frac\frac = \frac{L}\frac $$

\displaystyle \,\frac = \frac{\partial }\left( {\frac} \right) = \frac{\partial }\left( {\frac{L}\frac} \right) = \frac{L}\frac{\partial }\left( {\frac} \right) = \frac{L}\frac{\partial }\left( {\frac} \right)\frac = \frac\frac $$

\displaystyle \frac = U_0 \frac = U_0 \frac\frac = \frac\frac $$

Substituting the above quantities into the heat transfer problem (1):

\displaystyle k\frac\frac + f\left( {x,t} \right) = \rho c\frac\frac $$ or

\displaystyle \frac\frac + \frac = \frac $$

and the final form is:

\displaystyle \beta \frac + \Phi \left( {\xi,\tau} \right) = \frac $$

where

\displaystyle \beta = \frac, \,\,\,\,\,\, \Phi \left( {\xi,\tau} \right) = \frac $$

The initial condition:

\displaystyle U\left( {x,t = 0} \right) = U_0 \Rightarrow \Gamma \left( {\xi ,\tau  = 0} \right) = 1 $$ From

q = - k\frac =  - \frac{L}\frac \Rightarrow  - \frac = \frac = \varphi $$

we have boundary conditions:

\displaystyle \left. { - \frac} \right|_{\xi = 0}  = \frac = \frac = \varphi_{in}, \,\,\,\,\,\, \left. { - \frac} \right|_{\xi = 1}  = \frac = \frac = \varphi_{out} $$

title: User:Egm6936.s09/A thermal problem


text:
KOIIA/Reflections on Hjörne & Säljö

Hjörne, Eva & Säljö, Roger (2008): To qualify in a school for all. Student health and negotiation of normalcy in Swedish schools. (Chapter 8)
Eva Hjörnes and Roger Säljös  To qualify in a school for all  was published in 2008 with the aim to " highlight issues about how children's difficulties in finding their way around the school are understood and processed by the teachers and others who have daily contact with the children " ( 2008:9 ). The book's main focus is on the so-called. elevhålsoteamens work in selected schools, and presents the results of a study in which Hjörne and Säljö followed these groups and their everyday work for five years. Student Health teams' main task is to identify, define, explain and describe children's school problems , in short : create a forum for discussions on the difficulties created by some students in the school ( 2008:72 ). As a basis for this work is the notion of [ http://www.riksdagen.se/webbnav/index.aspx?nid=3281&dok_id=GOB319 student health ] Special for student health team meetings is that they offer a joint discussion forum for people with both professional knowledge and lekmannakunskap and that the decisions made there affect the school's use of resources to some degree, which has a direct impact on children's experiences of schooling.

 To qualify in a school for all  is basically a statement of an empirical study, but it also contains a description of the relevant theoretical background , with discussions ranging from the school's progress through the ages of children / pupils and adults / teachers' specific roles within the school and education to those roles. In the book's eighth chapter discusses the empirical results and their use. The text here is focused on this chapter, entitled "To qualify in one school for all".

Hjörne and Säljö is clear to note that in all times been and will be of such children in schools that do not "fit in ", as well as there have been children who easily found at home in the student role and able to adapt to the expectations of this role carries with it. The focus of the study reported in this book is directed towards how the school chooses to relate to children belonging to the former group, and how to try to " solve problems ". The perspective of the book is a social science and educational sociology, and the processes researched described by the authors as "a concrete illustration of how some of the social selection operates on a micro- plane " ( 2008:141 ). Here I see an interesting connection to a theme that is treated before at check those two, namely intersectionality. The authors state that it is hardly random to just some kids being marginalized and that it usually is easy to find links to factors such as class, ethnicity , language, etc. . when you look at the children who have been marginalized ( 2008:142 ).

The empirical work, the authors made have largely focused on student health team meetings where conversations , sc. " Troubles talk" is the most common working method. The authors pay attention to several specific features at these talks and the rhetorical work done by them. A clear feature of the talks and the entire student health team work is that the discussions and actions that are inserted often leads to the child in question marginalized. This is paradoxical, especially considering that the official purpose of the effort is to try to "normalize " the child , such as Säljö and Hjörne describes it ( 2008:142 ).

Much of the discussion in the chapter devoted to concepts such as marginalization, personalization , categorization , known letter diagnoses and identity processes of the simple reason that these have become highly visible in the empirical material. One obvious feature of student health teams' calls is that the problems surrounding the pupil discussed from an individual point of view, that specific right for this student. This is done by including that describes the child's behavior in categorical terms, based on eg the child's intellectual ability, maturity , motivation, concentration, and so on. ( 2008:143 ) . This finding leads the authors to a conclusion that the reason why the children in the study become topic of student health teams is more about the difficulties of finding themselves in the student role than on regular learning difficulties. The problem that arises is consequently placed in this institutional practice almost always the individual, not the institution.

An interesting aspect that the authors raise is that their study, however, its results should be seen as a historical document. The results are a reflection of how you look at children in our day and how today trying to deal with problems that have always been present in the school. There are two distinct features in this : the individualization of difficulties, problems are placed primarily in the child, not the institution , and an attitude that Säljö and Hjörne call for diagnostic - technical : to find an explanation for the problem , one looks for a diagnosis. On page 144 presents a number of cases that exemplify both traits. In one of them discuss student health team of a child with terms such as  This might be some kind of ehh ... damp or letter or something  ( 2008:144 ). Säljös and Hjörnes reasoning about individualization and endeavor to diagnose as typical phenomena can I sign on, for similar reflections came unsought even to me when I read the book. It is very characteristic of modern man ( and to some degree even more characteristic also of Swedish society, I would argue ) to want a quick diagnosis or explanation for the problems originate for as soon as possible to "cure" or at least learn to deal with the problem - much like the medical diagnoses.

Another, both typical of the times and cultural characteristic feature that the reader pay attention to is the consensus -oriented culture of discussion that seems to prevail in student health advice meetings. Discussion at meetings is described as institutionalized conversations where participants are well aware of how to speak and how decisions are made ( 2008:146 ), which usually leads to speak with a " single voice " and rarely questions or are looking for alternative solutions. This despite the fact that student health teams is and should be multidisciplinary with representatives from several disciplines ( 2008:146-8 ). The collective effort to find an explanation and a solution seems interesting not only as a cultural expression, but even when set against the huge individualization that the child is exposed. One can not help but think in terms of David and Goliath, except that the child in this constellation have very few opportunities to try to assert their rights. It is also remarkable that despite the typical institutionalized feature of discussions, it is another feature that is conspicuous by its absence, namely documentation of conversations and decisions ( with pupil welfare exemption ) ( 2008:148 ).

In the current study further concludes two things that are more a reflection of the aspects mentioned above. One is the lack of explanations based on a pedagogical analysis of the children's difficulties in school and the other a lack of children 's perspective. The discussions, which are student health team's main working tool, it is no representative voice of the child. One of context inherent in the lack of educational analysis is that the teacher's role in the problem nor analyzed, but what happens in the classroom and in teaching, remain in the dimness. No concrete events are highlighted without discussion moves on a different level, a level which already jointly decided that it is the child who is / are the problem ( 2008:145 ) and where , from the outset focused on discussing possible explanations. The difference between describing and explaining is something that the authors emphasize, and for a discussion around. In their opinion, student health teams call culture is a strong emphasis on explanatory but explicit descriptions of what actually happened remains in the background. The verbal abstraction of real events is seen as problematic by the authors, especially if one agrees that the categories it uses to describe the world influences how you see it , something called loopingeffekter ( 2008:152-153 ). Then the explanations that self-fulfilling prophecies, especially when children are made aware of what categories they "belong " as adults. Hjörne and Säljö for a brief but interesting discussion of the impact this can have on children's own identity perceptions, then all those around them in school ( maybe even outside of school ) treat them with the starting point in the assigned identity (eg " ADHD child ", " dyslexic ", " weak pupil " ). Then the identity is not something that you have, but something you " get", or attributed to , and often lives up to ( 2008:155 ).

At the end of the chapter the authors list nine points for an improved and better developed work in student health team. Some of the points have already been discussed above, if not otherwise well in a reverse perspective , but for the sake of summary contrasted results and development proposals in the following table:

{ | Class = "wiki table" ! Student Health Team work today ! development Proposal ( 2008:156-158)
 * Generalising, consensus oriented , categorizing discourse
 * Emphasize concrete descriptions of explicit events, dare to call in question, utilizing the various skills of the team
 * The problems are placed in the individual
 * See the big picture, acquiring knowledge about the circumstances of the problems
 * Teachers and other authority figures are invisible
 * All actors should be made visible in the problem solution
 * The child's weak position, and none representing the child, the child becomes a subject of discussion , not involved
 * Emphasize children's rights and child perspective, making children aware of how their actions are perceived, including some representing only the interests of children
 * Insufficient documentation
 * Documentation should be developed, especially for greater legal certainty.
 * }
 * Emphasize children's rights and child perspective, making children aware of how their actions are perceived, including some representing only the interests of children
 * Insufficient documentation
 * Documentation should be developed, especially for greater legal certainty.
 * }
 * }

Finally, discuss Hjörne and Säljö ethics and epistemic responsibility in student health teamwork. Especially epistemic responsibility is emphasized as it is described as connected to the power that adults in the school in general and in student health teams especially exercises over the kids. The authors argue, quite reasonably , that the exercise of power must take responsibility for how you express yourself and that the terms used should be possible to use in public and introduces interested students and their parents ( 2008:159 ). Ethical issues are ever present in the student health team work and should be taken into account, especially when it involves children who are from the outset in a weaker position from a legal standpoint.

/ Some thoughts from Ingela /

title: KOIIA/Reflections on Hjörne & Säljö


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User:Stevenarntson/humanitiesii

This course is an advanced study in the Humanities, used in conjunction with my on the ground course. Students will engage in self-directed research, in groups, in a field that interests them. The class is divided into 10 units, which follow a scheme the logic of which is necessitated by the venue of my physical classroom in Seattle, Washington.

/assignments/ group spaces

schedule

 * 1) steve is sick.
 * 2) introductions/policies/wiki/theme
 * 3) Socratic dialectic (SPI)
 * 4) /perception/
 * 5) /monsters/
 * 6) group presentations
 * 7) field trip - folklife
 * 8) group presentations
 * 9) group presentations
 * 10) Southern Comfort
 * 11) final presentations. self assessment due on Friday.

title: User:Stevenarntson/humanitiesii


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User:Stevenarntson/humanitiesii/assignments

 *  Your grade in this class is divided into thirds: participation, group presentation, and final presentation. Also required is an ungraded self-assessment, completed at the end of the term.

Group Projects
In groups, decide on a topic you'd like to pursue that's relevant to the Humanities. Let your own interests be your guide. Your group will be responsible for filling one class period, or about three hours, and the presentation will include the following:

Reading Assignment
The week before you present, make a reading assignment for the class.

Lecture/Media
Your group will talk about what the group members researched, what they discovered—all of the interesting stuff you found out that other people are going to be fascinated to hear.

You will have some media to share. This media can take the form of a movie, an internet site, a piece of music, a book or essay, a field trip, or a combination of elements. However, don’t rely too much on media--it can get boring pretty quick.

Discussion
Part of your presentation will involve leading a class discussion. Your group should generate a few questions to ask the class, to elicit their ideas. These questions could be about issues, or about personal experiences (“has anyone ever had ____ happen?”).

The group will be responsible for facilitating the discussion. Keep it moving forward, while also letting it explore. Bring in the reading you asked the class to do.

Assignment
You will give the class an assignment. The assignment can be creative or analytical in nature. It can involve research or opinion. Keep in mind that this is a GE class. Some people here are learning how to cook, others how to record music, and others how to build chairs. Make the assignment broad enough that it will be relevant to anyone. The assignment should result in some kind of presentation a student will be able to deliver. They must find out something, or make something, or do something.

Pre-Presentation Documents
I will want 2 documents from you one week before you present.
 * 1) Your lesson plan, which should be detailed and include everything you intend to talk about, including any and all media you intend to examine.
 * 2) The assignment sheet for the assignment you plan to give the class.

Final Project
You will choose one of the assignments presented by one of the other groups to complete for your final presentation. If you were not present to hear one of the groups' presentations, you are barred from completing their assignment. Final Projects will be presented to the class during the final two weeks of the quarter.

Participation

 * Attendance, including field trips
 * Participation, including discussion and in-class assignments

Self Assessment
This is due, posted at your user page, on the final week of the quarter.


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User:Nasalover13

Hi

title: User:Nasalover13


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Talk:Cryptography/Introduction to Simple Substitution Cypher

εΘ–ΘΔδ


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Kirsten

A Swedish pioneer girl in Minnesota
This learning project is part of the History through American Girl project; based on the Kirsten books by Janet Shaw, part of the American Girls Collection:

 * 1) Meet Kirsten
 * 2) Kirsten Learns a Lesson
 * 3) Kirsten's Surprise
 * 4) Happy Birthday, Kirsten!
 * 5) Kirsten Saves the Day
 * 6) Changes for Kirsten

In the first book, the fictional characters of 9-year-old Kirsten and her family leave Sweden to try and find a better life in Minnesota in 1854. Through the rest of the series she discovers all of the trials and joys of pioneer life with her family and friends, including learning English at a new school, celebrating the 4th of July for the first time and holding on to Swedish family traditions even in a new land.

Despite the fact that these books were written for entertainment purposes, the novels are surprisingly historically accurate; which makes them the ideal vehicle for a children's history course (especially for girls). They are very popular and easy to obtain; found in most bookstores and libraries. They are short and to the point, making them easy for an educator to read aloud to a group.

Project goals
The goal of this project is to create and maintain resources pertaining to the books, including further reading lists, possible craft projects, fun games and quizzes and more. Also, each book should have a "Cliff Notes" synopsis for quick reference as well as a more detailed breakdown for educators.

title: Kirsten


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User:Jokco

A traveller.

title: User:Jokco


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User:Radhakrishna

Hi, I am RadhaKrishna, Living in Hyderabad, India. more details @ my webhome http://www.geocities.com/hellokrishna

title: User:Radhakrishna


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User:Revan Malak

My Real Name The true blue thing on my certificate is....

Yeah. Like I'm gunna tell you. I really wonder what you were thinking. Were you like, "Is this guy serious?!" or more like, "AHA! I've got this one now!!!! I'm gunna steal his identity!" Either way, the fact that you're still reading is kinda creepy. But since you've made it this far might as well read the rest.

Reasons I'm on this site

 * I was here because I missed the bus to Auto Tech and now I'm stuck at the library.
 * I want to be a game designer and I found a link to Wikiversity. I signed up and now I'm typing stuff that I'm sure no one is going to read but I do it anyways because I would like to say, "If anybody has any good tips or software references for game designing please let me know."
 * It seems like it could be a very useful site for learning and what not.

Random Current Thoughts
 * How many people use this? It didn't seem like there were that many but hey. I think I'll have a spot at the bottom of the page for anyone that looks at this page to report that they did for a study. Let's see how many we get!

 Links''' '''
 * Blender 3D WikiBooks

Are you on this page? Please help and add your name here!!
This is just to see how many people actually DO look at pages like this, nothing like stealing an identity. Just add your name/link and time and date below!!

LIST
 * !!Revan Malak!! 4/1/09 10:30am
 * ...add name...

Thanks for your contribution!

title: User:Revan Malak


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Design for the Environment/Automobile Engines III

This page is part of the Design for the Environment course

Although internal combustion engine (ICE) have been fundamental to our modern society, conventional ICE vehicles that primarily use petroleum fuels account for 15 percent of the global carbon dioxide (CO2) emissions, a major greenhouse gas (GHG), and such emissions deteriorate the environment by eroding the ozone layer, depleting natural resources, and contributing to Global Warming. With the number of passenger cars expected to rise to one billion by 2020 from 806 million today, “radical changes in automotive design” and fuel efficiency are required to curb the trend of environmental degradation. The purpose of this report is to analyse the conventional gasoline ICE vehicle using a “wells-to-wheels” approach (considering both fuel and vehicle production) and compare it with two alternative concepts: the “wood-electricity-wheels” concept of electric vehicles (EVs); and “wood-ethanol-wheels” concept of flex fuel vehicles (FFVs) that run on ethanol-fuel mixtures. This reports’ client is Toyota Canada Inc (a subsidiary of Toyota Motor Corporation), a major car manufacturer that can use the results of the report to determine the best choice of energy source for its midsize automobiles. In order to be relevant to the client, all the alternatives were assumed to have the same performance as a 2009 Toyota Camry 2.4L, 4 cylinder, 5-speed automatic vehicle with an average gas mileage of 25mpg. All three alternatives were analysed systematically using life cycle assessment methods for an eight-year life with 15,000 miles travelled annually. Conventional ICE vehicles combust gasoline and generate rotational energy to power the vehicle. Such ICEs have been using gasoline as fuel for decades, often with additives that increase its octane number and reduce damage during operation. Recently, E85 ethanol (an ethanol-fuel mixture), which uses cellulosic ethanol derived from wood waste, has been used instead of gasoline in altered ICE vehicles. These “fuel-flex vehicles” have been successfully implemented with over 6 million on the road and can reduce the nations dependancy on foreign oil. Electric vehicles that use an electric motor that runs on rechargeable Lithium-Ion batteries are an alternative solution and although they eliminate tailpipe emissions entirely, there remains substantial emissions from electricity usage and the production of the batteries. These three alternatives were carefully analysed to determine which one is able to minimize environmental impact without compromising fuel efficiency and cost.

Highlights and Recommendation
The streamlined life cycle assessment (SLCA) and economic input-output life cycle assessment (EIO-LCA) models were used to determine the environmental impact of the three alternatives. Also, functional, cost and societal analyses were conducted to supplement our environmental analysis. These analyses were essential in determining key factors that might influence car manufacturers like our client when deciding on a vehicle type to manufacture.

Functional Analysis
Through a functional analysis, it was determined that gasoline ICE vehicles best consolidate gas mileage and fuel efficiency and deliver the most reliable performance. Although EVs have the highest gas mileage relative to other alternatives, electricity used in EVs has the lowest fuel production efficiency. Conversely, FFVs have the highest fuel production efficiency and the lowest gas mileage since E85 ethanol is an efficient energy source. FFV and gasoline ICE engines are highly compatibile, whereas there are major component differences between EVs and the baseline, such as the elimination of the engine, and the installation of Lithium Ion batteries and electric motors.

Environmental Analysis
The SLCA and EIO-LCA analyses were the focus of this report and from their results FFVs were found to have the least environmental impact over the entire lifecycle. The SLCA ranked EVs and FFVs as the top two alternatives (with a one-point score difference). Gasoline ICE vehicles performed poorly in the environmental analysis because of substantial emissions during the use stages from the production of gasoline and the direct tailpipe emissions. EVs have no direct emissions though they have substantial emissions from the production of electricity. FFVs which have a manufacturing process similar to that of gasoline ICE vehicles, have lower direct emissions. Though it was unclear from the SLCA which alternative had a lower environmental impact, after analyzing the alternatives with EIO-LCA and incorporating detailed emissions data and the resource extraction of the energy source (i.e. electricity or E85 ethanol), it was found that E85 FFVs rated the best because it had the lowest energy use (since it was re-using wood waste and not investing energy in its production) and the second lowest GHG emissions. This result confirms the SLCA`s finding that FFVs have the best environmental performance (i.e. the least environmental impact). Through EIO-LCA and SLCA methods, FFVs were determined to be the best vehicle type for the environment.

Cost Analysis
A summary of the cost analysis conducted over the eight year life of each vehicle is available below.

Although gasoline ICE vehicles are the most economical, FFVs have become increasingly affordable to consumers with government incentives. EVs have the highest cost of operation due to a large capital cost and are therefore unappealing to consumers. Other factors such as variety in the market and availability of fuel are other factors that may sway consumers minds. All these cost details are essential to Toyota Canada Inc. when deciding on a vehicle to make for consumers.

Societal Analysis
Through a societal analysis, EVs have been portrayed in the media to be the most environmentally friendly (despite contradictory evidence presented in this report), while FFVs have been supported by institutions like Canada‘s ATF that provide incentives to consumers encouraging use of alternative vehicles. Conversely, gasoline and gasoline ICE vehicles are deemed harmful to the society and thus they lack longevity in an economy with depleting natural resources.

Table 1B scores the findings from our report by first scoring the vehicle types in each section out of 5 (where 5 is an outstanding performance and 0 is a poor performance) and then assigning a weight that depends on the importance of each issue. The scores can be further explained in detail in the summaries for each section below. The SLCA and EIO-LCA were the focus of this study and were assigned a weight of 25% each. Consumers today are highly conscious of the fuel economy, which is why the cost analysis was assigned a weight of 20%. Lastly, the functional and societal issues were assigned a weight of 15%.

Recommendation
We recommend Toyota Canada Inc. should pursue a fuel-flex vehicle that operates on E85 fuel. FFVs scored the highest overall because of its relatively low environmental impact and low cost. FFVs scored the lowest in the functional analysis section because of poor gas mileage. However it should be noted that cellulosic ethanol production has the highest efficiency relative to the other energy sources. FFVs can be easily adapted to Toyota‘s existing fleet with minor alterations to a conventional vehicle. Aside from its poor gas mileage, FFVs scored high in the environmental and cost analyses. Consumers that value fuel economy will appreciate the life cycle cost of owning and operating an FFV ($39,275). Finally, FFVs are being promoted by institutions such as Canada‘s Alternative Transportation Fuels which encourage consumers to purchase vehicles that operate on biofuels. FFVs offer measurable environmental improvements over conventional vehicles (2.3 MTCO2E less GWP emissions) at a small expense to the consumer (FFVs cost $146 more than conventional vehicles over an eight year lifespan.) Finally, FFVs are a possible solution to Toyota‘s ‘Aim: Zero Emissions‘ strategy that strives to reduce emissions over the vehicles entire lifecycle.

However, it should be noted that gasoline vehicles had the lowest cost and greatest functional performance making them an ideal choice for economical consumers. Conversely, EVs offer few advantages and have been found to have the most negative environmental impact and highest cost. EV technology needs to be further developed to eliminate substantial emissions from battery production and electricity generation.

Details of Functional Analysis
For the functional analysis, the following two aspects of each vehicle concept are considered: the energy source and its efficiency; the type of engine used and its ability to meet the desired function (provide rotational energy equivalent to a 2009 Toyota Camry LE). Table 2 below summarizes the research used to form our conclusions.

Gasoline ICE Vehicles
Gasoline ranks as one of the most efficient energy sources because it is relatively economical to extract gasoline from crude oil and is widely available inexpensively to all consumers via various petrol pumps, making gasoline powered vehicles affordable and convenient to use. However, gasoline is a non-renewable fossil fuel. When burnt, gasoline releases a number of toxic pollutants such as carbon dioxide, carbon monoxide, nitrogen dioxides and unburned hydrocarbons. Typically, a gallon of gasoline releases 19.4 pounds of carbon dioxide. Fuel economy in gasoline vehicles can be further improved by 30% with the addition of turbocharger and supercharger assemblies. For baseline alternative, the 2009 Toyota Camry is fitted with a a 2.4-liter DOHC 16-valve VVT-i 4-cylinder spark ignition engine. It is able to supply the car with 158hp at the rate of 5700rpm. It averages 21 miles per gallon in the city and 31 miles per gallon on the highway (average mileage is 25mpg ) making it a highly efficient gasoline engine.

Electric Vehicles
Electricity, stored in the lithium ion batteries, is the energy source used to power EVs. Wood waste from forest reserves is used to generate electricity to power the vehicle. Abundant availability of wood waste in the region of Nanticoke, Atikokan and Great Lakes Saint Lawrence (GLSL) region makes it a viable option in Ontario. However, electricity production from wood waste is the least efficient energy source in this discussion as seen from table above. A lithium ion battery and an electric motor replace the engine to supply the car with 158 horsepower, which is equivalent to the baseline alternative (i.e. gasoline ICE vehicles). A single Lithium Ion battery charge is equivalent to 4 gallons of gasoline which will take the EV for 140 miles – that is a gas mileage of 35mpg. Thus, the electric vehicle is able to meet the functional requirement of providing rotational energy to the 2009 Toyota Camry, while running solely on electricity with no direct tailpipe emissions.

Flex-Fuel Vehicles
FFVs are the only vehicles that can use E85 fuel, which represents 85% mixture of ethanol with 15% mixture of petroleum (pure ethanol is rarely used as a fuel for transportation; conventional ICE engines can only operate on low ethanol content fuel). Ethanol production from wood waste is the most efficient production process relative to the other energy sources, as seen in the table above. Furthermore ethanol is water soluble, non toxic and biodegradable because it’s composed of fewer contaminants than gasoline. Some of the drawbacks of E85 include low availability of E85 stations, low fuel efficiency (during operation), and fewer choices in vehicles. The design of an ethanol vehicle requires few alterations from the convention gasoline vehicles. The alterations include adding a larger fuel tank because ethanol produces less energy than conventional fuel and changing the material of the tank and other components which would otherwise deteriorate due to the corrosive property of ethanol. In addition, the flex fuel vehicle has an engine control unit that controls the flow rate and adjusts the spark plug ignition to allow for accurate combustion. The resulting FFV has an average gas mileage of 17mpg.

Details of Streamlined Life Cycle Assessment
Using the SLCA model, a product life cycle of the engine and fuel type was evaluated throughout all life stages of the vehicle. Only the engine, and not the entire vehicle, was considered because it was assumed that all the other elements of the vehicle were assumed to be similar and thus irrelevant. The scoring criteria outlined in the SLCA text was used to create a 5 x 6 matrix (below), where each of the 30 entries was assigned a score between 0 and 4, where the lower value signified a greater impact on the environment (which is undesirable).

Gasoline ICE Vehicles
The product lifecycle (PLC) considered while analysing gasoline ICE vehicles is available in the figure below. Pre-Production and Production: At the automotive facility, steel and aluminum metal sheets are casted and/or forged, trimmed, polished and assembled together to form the engine and suspension that is fitted into the vehicle. This stage uses highly recyclable materials resulting in a high score in the matrix due to its low negative impact on the environment.

Distribution: After factory inspections, newly assembled automotive vehicle is sent to an auto dealership via car carriers or carrier ships. The per car impact on the environment during distribution is significantly low as a large number of vehicles are transported at a time. Delivery is common for all alternatives.

Use: The emissions are largest during the use phase. When burnt, gasoline releases large amounts of Greenhouse gases and other toxins into the air, resulting in a score of 0 in the Gaseous Residues column of the matrix. Drilling of crude oil from under the surface of the earth is highly energy intensive and thus given a score of 1 in the Energy Use column.

Gasoline life cycle (During Use Stage): Crude oil is pumped out from under the surface of the earth and refined using fractional distillation to obtain gasoline. This extracted gasoline is further supplemented with additives and transported to various petrol stations via pipelines.

End of Life: The car is sent to a scrap yard for recycling. At the yard, the car is reduced to different components and then crushed, shredded and sorted into metal sheets and rubber residue. The metal is reworked and reused while the rubber residue is sent to landfills. This stage has least negative environmental impact as these processes help reclaim 90-95% (by weight) of the car body. End of life of FFVs is similar to that of gasoline.

Electric Vehicles
A brief PLC for electric vehicles is available in the figure to the right and it is used to conduct a relevant SLCA. Pre-production and production: Raw materials needed to manufacture the lithium ion batteries, electric motor, generator and other electrical components will be extracted from steel, iron and aluminum ore. Extraction of lithium involves various metallurgical processes (Alkaline fusion,Acid roasting, Calcination, Carbonation and Mining). Use of material in rare quantities results in an overall low score in this category. (Electric Motor :Dysporium) All the raw materials obtained are pre processed (Mixing, Coating, Compressing, Drying and Slitting) to form the core before being sent to the cell assembly section. All these complex processes develop a need for automation which in turn results in high amount of energy consumption which in turn correlates to high amount of solid, liquid and gaseous residues in the atmosphere. During production of battery, corrosive chemical use (e.g.slurry in battery) results in high amount of energy being utilized. Therefore average to low rating is given in this phase.

Use with EV Life Cycle: Use stage is divided into two phases: the direct use and the resource extraction of the fuel(electricity). Owing to battery`s low reactivity to environment, it will produces minimal solid, liquid and gaseous residues which explains the high scores of 4 in this category. In resource provisioning phase,forest reserves are the primary source of wood waste. Wood waste is then transported to a nearby coal fired plant, processed and used in the burner to produce steam to run the turbines generating electricity. This operation results in a prime concern of ash disposal and air polluting emissions from combustion operations. Therefore,solid and gaseous residues are a prime concern in this matter and given a low rating.

End of life: Most of the steel components present in the car are either recycled in a scrap yard or reused by Toyota. Components such as wind-shields, batteries, motor and generator are recovered before the vehicle is sent for crushing. Disposal of the lithium-ion batteries is another critical aspect due to the presence of toxic raw material(Electrolyte-LiPF6). From batteries, raw materials such as copper, iron and cobalt are recovered and reused. All these operations result in high amount of energy needed to reclaim any reusable material in the whole process.

Flex-Fuel Vehicles
The PLC for FFVs is available in the figure to the below for use in the SLCA. Pre-Production and Production: During the pre-production and production stages, the engine is manufactured in a manner similar to the gasoline alternative with minor alterations, such as disregard of materials, such as, bare aluminum, magnesium and rubber because of the corrosive behaviour of alcohol. The pre-manufacturing score is insignificantly higher because it reduces the amount and type of material extracted for fabrication.

Use with FFV Life Cycle: The use phase is subdivided into both the resource extraction of the fuel and the direct tailpipe emissions from the fuel-flex vehicle. FFV's scored between the alternatives for direct emissions and the lowest during resource extraction. The provisioning of ethanol can be broken down into three steps: the collection of bark as wood waste from pulp mills; the transportation of wood waste to biorefineries for the gasification process and utilization of steam to produce a synthetic gas (syngas), which has low amounts of CO/H ; the filtration and cleansing of the resulting fluid. E85 is not transported using the conventional pipelines because it is prone to pick up extra water and impurities during the process and is therefore transported using trucks with corrosion-resistant tanks. The direct use measures the rotary power produced using E85 to fuel the vehicle. The end of life stage of ethanol minimizes environmental impacts in the atmosphere because of its biodegradable and high-evaporative properties. The direct emissions score is significanly lower because flex fuel engine produces less CO2, where ethanol contains more oxygen atoms that facilitates the combustion process using the ECU to burn cleaner fuel.

Details of Economic Input-Output Life Cycle Assessment
The Economic Input-Output Life Cycle Assessment provides a quantitative impact analysis by computing the potential environmental impacts over the lifecycle using the online EIO-LCA database model developed by Carnegie Mellon University. For the purpose of this analysis, the entire vehicle (and not just the engine, as in SLCA) was evaluated. Since the EIO-LCA model does not have a sector specifically for emissions during the use stage (e.g. tailpipe emissions), additional literature data was used to calculate those environmental impacts. The EIO-LCA model was used to determine the global warming potential (GWP in MTCO2E) and energy use (in Joules) of all life stages of the vehicle, as seen in the figures and table in this section:

Gasoline ICE Vehicles
According to EIOLCA, we observe that Gasoline ICE vehicles have a GWP of 71.8 MTCO2E consuming 0.781 TJ of energy over the average lifetime of a car. During pre-production and production stage, the power generation and supply sector is the maximum contibutor of global warming releasing 2.57 MTCO2E of Carbon Dioxide per car produced. It also accounts for 48% of total energy consumed by the top ten sectors in this stage. This is mainly because the power mills require energy (from burining fossil fuels) to power their generators that in turn generate electricity that is supplied to other sectors/industries. Maximum emissions occur during the use phase which encapsulates emissions during resource provisioning, vehicle's use and its repair and maintenance. 0.835 MTCO2E of methane is released during the resource provisioning stage (extraction of gasoline) while 59.2 metric tons of greenhouse gases (including Carbon Dioxide) are emitted during the full fuel cycle over the average eight year period. This fuel cycle encapsulates all the direct and indirect emissions of carbon dioxide, nitrous oxide and methane during production, refining, distribution and final use of gasoline. Excluding car washes, the maintenance and repair of the vehicle averages 1.33 MTCO2E Global Warming Potential and consumes 16GJ of energy over the eight year life-span of the car. During the delivery of a 2009 Toyota Camry from a factory to the auto-dealership, we note a Global Warming Potential of 1.15 MTCO2E and energy consumption of 9 GJ. This delivery impact is common for all the remaining alternatives and will therefore not be looked into again.

Electric Vehicles
In the EIOLCA tool, custom hybrid model has to be used to asses the impact as current modifications are not incorporated directly in the Vehicles and Other transportation equipment industry sector. From the Automobile and Light Truck Manufacturing sector, the weightage of engine manufacturing is made zero as it doesn’t exist in the EV. Other three sectors (Motor and Generator Manufacturing, Storage Battery Manufacturing and Relay & Industrial Control Manufacturing) are modified accordingly. It is observed that Power Generation and Supply sector contributes the most to the GWP,GHG emissions and Energy utilization. Potential automotive parts are extracted as raw materials and processed in a manufacturing facility and then transported to automotive assembly. These facilities normally run throughout the year 24/7 and are strongly dependent on power generation and metals/non metals extraction sector. EIOLCA also encapsulated the Use phase discussing the direct and indirect emissions. For direct emissions, batteries are constantly being charged up delivering constant power to the car. Minimal/No emissions are generated in the car as no combustion takes place. For resource provisioning phase(indirect emissions), total amount of wood waste needed to run the car during its lifetime is calculated from the mileage of the car as it is found that 1050 KWh of electricity is generated using a 1000 kg of wood waste .Pulp mill or Saw Mill sector is used to determine the environmental impact associated with the use of wood waste.Deforestation is a major cause of concern for the GWP while running these mills. Removal of trees results in reduction of CO2 neutral agents (trees). Also some pulp mills use wood waste to produce steam to run the mill which also results in GHG emissions.

Flex-Fuel Vehicles
FFV's scored between the alternatives in GWP analysis and the lowest in energy use for the life cycle of the vehicle. The pre/post-production stage utlized the producer cost determined in cost analysis to observe the Automobile and light truck manufacturing sectors. The power generation and supply industry had the highest energy use with CO2 as the highest impact. Power generation and supply is a prime sector because of the energy intensive fabrication of the metal and nont metal products use highly automated machines running 365 days a year. In addition, from the high amounts of CO2 released; only half is absorbed by natural processes in the atmosphere. The indirect emissions, net cost of extracting wood waste for ethanol production was determined in cost analysis and utlized in the Vehicle Wood, Paper, and Printing industry group and pulp mills sector. The sector with the highest energy use and GWP is the Pulp Mills sector. Deforestation is the primary polluting process, releasing CO2 from trees and soil. Pulp mills use large amounts of energy to provide electricity and power immense grinders that break down the harvested wood; for this reason we observe that power generation and supply uses the second most amount of energy. Furthermore extracting wood is a very energy intensive process and requires large machinery to which the power and generation supply sector provides electricity and energy to run. The other basic organic chemical manufacturing sector is where the actual ethanol fuel is extracted and as we see it only utilizes 1% of the total energy consumed because the gasification process involves altering fluids and gases whereas the other industries processed solids, which require more powerful machinery.

Details of Cost Analysis
A cost analysis was conducted by including all direct and indirect costs involved in various vehicle types. A summary of our analysis is provided in the table below.

Gasoline ICE Vehicles
Direct costs: This includes the capital cost of the car, the fuel and its disposal. The 2009 Toyota Camry retails for USD 20,195 .Over the period of 8 years (15,000 miles annually ), the maintenance and repair cost is determined to be USD 2,697 and USD 1,467 respectively. The cost of disposing the car is calculated using the market price of disposing a car body and engine and their respective weights. Thus, the disposal cost works out to be USD 71.08. As a result, the total direct cost is determined to be USD 36,393.

Indirect costs: Health care costs of operating a 2009 Toyota Camry are observed in this section. For Gasoline, the costs are calculated to be 1.4¢/mile in rural areas 3.0¢/mile in urban areas. Assuming 45% urban driving and 55% rural driving, the health care cost is calculated to be USD 342 per year. Therefore, the average health care cost of the lifespan of the vehicle is determined to be USD 2,736.

Electric Vehicles
Direct Costs: Capital cost of the car is calculated using the retail cost of the standard 2009 Toyota Camry ($20,195 ),subtracting the engine cost($ 2000 ) and adding the cost for additional components(Storage Battery: $ 8767, Motor & Generator Manufacturing: $1,197 and Relay & Industrial Control: $1,700 ). Operational Costs are obtained by determining the amount of electricity utilized during yearly use of the vehicle (15000 Miles).This is then translated over the next 7 years using the inflation ratio and trend in electricity price fluctuation. It is also found that normal Lithium Ion battery lasts about 4-5 years. Therefore, another battery will be required after 4 years, which would add a replacement cost.Other direct costs include disposal cost at the end of life cycle.Car body is disposed of at a cost of $50.62 with the addition of separate disposal cost for the lithium ion battery which comes out to be $39.60.

Indirect costs: In order to promote green energy, Canadian Government has provided various monetary incentives in which 09 Camry Hybrid is given a rebate of $1,500. Due to minimal data available about fully EV, one can assume a similar incentive will be given in this case. Other indirect costs include health costs. In the case of EV, no health care costs are observed since the vehicle does not have any direct toxic emissions when in use.

Flex-Fuel Vehicles
Direct Costs: FFV's 8 year life cycle cost was 0.3% higher than the gasoline fuelled vehicle. The capital cost utilized in the EIOLCA is determined using the gasoline producer cost of the vehicle incorporating a fuel-flex capability cost to account for the difference in fuels. The present value of the ethanol production cost was determined utilizing the EIOLCA wood-waste resource provisioning cost with an additional facility-processing and filtration cost. The inflated price of E85 for the next 10 years was researched and then utilized to determine the life cycle cost of ethanol. Other expenses, such as, maintenance, repair and disposal was analyzed in a manner similar to that of gasoline ICE alternative.

Indirect Costs: Victoria Transport Policy Institute proclaimed that with urban and rural areas rates of $0.01/mi and $0.0005/mi respectively the health costs to drive with E85 fuel would be $930. In a hope to promote the use of clean-burning fuel, the provincial government tax incentive was researched to be available to all FFV consumers until 2010, or 2 years of the life cycle analysis. Disregarding incentives, FFVs cost $2,676 more than the conventional ICE vehicle. However, if the incentives are available, then they should consider FFVs because its only $146 more expensive.

Details of Societal Analysis
Though gasoline is an indispensible fuel source and has deep roots in the transportation sector, alternative fuels are a prominent topic in the industry. There are insufficient supplies of petroleum and fossil fuels to develop gasoline, which means our society cannot support conventional gasoline ICE vehicles indefinitely; a solution to this energy crisis needs to be found. Alternative fuels such as E85 and similar biofuel mixtures, which combine environmental friendly fuels with gasoline, are able to consolidate gasoline’s energy with biofuels environmental friendliness. However, as discussed above, E85 is currently in low availability in North America, and especially Canada, and therefore cannot be a permanent substitute for gasoline. EVs that run on electricity have also been proposed as a viable alternative to enginebased vehicles that rely on fuels. Government initiatives such as the AFA attempt to promote energy efficient vehicles such as EVs and E85 FFVs to lower and middle class families to encourage environmentally friendly vehicles in the mainstream. Popularity of EVs in the media (and conversely, the poor image of gasoline-powered vehicles) confuse customer‘s decisions regardless of the vehicles overall environmental and societal impact. Therefore, the automotive sector needs to consider public perception of the fuel choice when develop an energy efficient vehicle.


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User:Stevenarntson/Literature/Introduction

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