A Akbarinia
email: a.akbarinia@item.uni-bremen.de

Morteza Abdolzadeh

R Laur

Critical Investigation of Heat Transfer Enhancement Using Nanofluids in Microchannels with Slip and Non-Slip Flow Regimes

The Reynolds number in nanofluids studies depends on the inlet velocity and the kinematic viscosity of nanofluid. The nanofluid kinematic viscosity increases with an increasing in nanoparticles volume fraction while the inlet velocity should be increased to keep the Reynolds number constant. Therefore, it is not clear that either increasing the nanoparticles volume fraction or increasing the inlet velocity has major role on heat transfer enhancement in nanofluids flow studies which are done at constant Reynolds numbers. In this study, forced convection Al 2 O 3 -water nanofluid flows in two-dimensional rectangular microchannels have been investigated to study heat transfer enhancement due to addition of the nanoparticles to the base fluid especially in microchannels at low Reynolds number. Three

different cases are examined to evaluate proportion impact of increasing nanoparticles volume fraction (φ) and the inlet velocity (u in ) on heat transfer enhancement. Two-dimensional Navier-Stokes and energy equations accompany with the slip velocity and the jump temperature boundary conditions expressions have been discretized using the Finite Volume Method (FVM). The Brownian motions of nanoparticles have been considered to determine the thermal conductivity of nanofluids. The calculated results show good agreement with the previous numerical and analytical data. It is found that at a given Reynolds number, the major enhancement in the Nusselt number is not due to increasing the nanoparticle concentrations but it is due to the increasing the inlet velocity to reach a constant Re. Constant Reynolds number studies of nanofluids are not sufficient approach to evaluate the heat transfer and the skin friction factor due to the nanofluids usage. requires an infinitely high frequency of collisions between the fluid and the solid surface [START_REF] Gad-El-Hak | The Fluid Mechanics of Microdevices: The Freeman Scholar Lecture[END_REF][START_REF] Beskok | Simulation of Heat and Momentum Transfer in Complex Micro-Geometries[END_REF]. In practice, the no-slip/no-jump condition leads to fairly accurate predictions as long as Kn < 0.001. Beyond that, flow in devices shows significant slip since characteristic length is on the order of the mean free path of the fluid or gas molecules. It means that the collision frequency is simply not high enough to ensure equilibrium and a certain degree of tangential velocity slip and temperature jump must be appeared. Slip velocity at the wall is the most important feature in micro/nano scale that differs from conventional internal flow. Therefore, the slip flow characteristics are very important for designing and optimizing the micro/nano systems. On the other hand, the optimization of microchannels design is affected significantly by their reliability and thermal performance. It is found that the temperature jump effects are very important and should be included in the modeling of the slip flow heat transfer problems, and neglecting these effects leads to a significant overestimate of heat transfer coefficient [START_REF] Larrodé | Slip-flow heat transfer in circular tubes[END_REF][START_REF] Sun | A numerical study of single-phase convective heat transfer in microtubes for slip flow[END_REF].

In experimental studies that the nanofluids have high thermal conductivities and abilities to increase the heat transfer [START_REF] Pak | Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles[END_REF][START_REF] Xuan | Investigation on convective heat transfer and flow features of nanofluids[END_REF][START_REF] Akbarinia | Numerical Study of Laminar Mixed Convection of a Nanofluid in Horizontal Curved Tubes[END_REF][START_REF] Akbarinia | Investigation the Diameter of solid Particles affects on a Laminar Nanofluid Flow in a Curved Tube Using a Two Phase Approach[END_REF]. The major attempts have been done to investigate the effective thermal conductivity of nanofluids and the effective dynamic viscosity for predicting the thermal conductivity and dynamic viscosity of nanofluids [START_REF] Murshed | Thermophysical and electrokinetic properties of nanofluids -A critical review[END_REF]. The most of papers have reported an enhancement in the heat transfer due to increasing the nanoparticle concentration which are done at constant Reynolds number. But some researchers have reported an uncertainty in heat transfer enhancement of nanofluids flow [START_REF] Akbarinia | Impacts of Nanofluid Flow on Skin Friction Factor and Nusselt Number in Curved Tubes with Constant Mass flow[END_REF][START_REF] Nguyen | Viscosity data for Al 2 O 3 -water nanofluid-hysteresis:is heat transfer enhancement using nanofluids reliable?[END_REF]. Akbarinia [START_REF] Akbarinia | Impacts of Nanofluid Flow on Skin Friction Factor and Nusselt Number in Curved Tubes with Constant Mass flow[END_REF] have investigated heat transfer in the nanofluids flow with constant mass flow rate and reported a reducing in heat transfer with increasing nanoparticles volume fraction.

Recently, the nanofluids utilization in microchannel has been received a great interest amongst researchers. Koo and Kleinstreuer [START_REF] Koo | Laminar nanofluid flow in microheat-sinks[END_REF], Jang and Choi [START_REF] Jang | Cooling performance of a microchannel heat sink with nanofluids[END_REF] and Chein and Huang [START_REF] Chein | Analysis of microchannel heat sink performance using nanofluids[END_REF] have studied experimentally improving thermal performance of the nanofluids flow in microchannel with different nanofluid such as CuO-water or Al 2 O 3 -water. The thermal performance of microchannels using nanofluids base on different models for effective thermal conductivity also has been investigated numerically by [START_REF] Abbassi | Evaluation of heat transfer augmentation in a nanofluidcooled microchannel heat sink[END_REF][START_REF] Tsai | Performance analysis of nanofluid-cooled microchannel heat sinks[END_REF][START_REF] Li | Thermal performance of nanofluid flow in microchannels[END_REF][START_REF] Chein | Experimental microchannel heat sink performance studies using nanofluids[END_REF][START_REF] Jung | Forced convective heat transfer of nanofluids in microchannels[END_REF][START_REF] Ho | An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3-water nanofluid[END_REF]. They have evaluated the impacts of parameters such as microchannel geometry, Reynolds number and nanoparticles volume fraction on the thermal performance of nanofluid flow in microchannels. They have reported higher heat transfer performance of nanofluids flow compare to the base fluids in microchannels at constant Reynolds number. However, all of them have used the non-slip flow regimes in their numerical research works.

To the best knowledge of the authors, the major of previous numerical and experimental

Analysis

Governing equations

The schematic of the channel and coordinate system are shown in Continuity equation:

0 = ∂ ∂ j j x u (1)
Momentum equations:

i j i j nf j i j nf x p x u x u u x ∂ ∂ -         ∂ ∂ ∂ ∂ = ∂ ∂ ) ( ) ( µ ρ (2)
Fluid energy equation:

( )         ∂ ∂ ∂ ∂ = ∂ ∂ i i nf i i nf p x T x k T u x C ) (ρ (3)
Where i=1, 2 and u i =(u x , u y ) are velocity vectors.

The continuity, momentum and fluid energy equations are non-dimensionalized using following dimensionless parameters:

h i i D x X = , in i i u u U = , 2 in nf u p P ρ = and in wall in T T T T - - = θ (4) Where W D h 2 ≈ .
Therefore, the non-dimensionalized governing equation becomes as follow:

Continuity equation:

0 = ∂ ∂ j j X U (5)
Momentum equations:

i j i nf j i j X P X U U U X ∂ ∂ - ∂ ∂ = ∂ ∂ ) ( Re 1 ) ( 2 2 (6)
Fluid energy equation:

( ) i nf i i X Pe U X ∂ ∂ = ∂ ∂ θ θ 2 1 (7)
Where

nf nf nf Pe Pr Re = , nf h in nf nf D u µ ρ = Re and nf nf p nf nf k C ) ( Pr µ =
are the Peclet number, the Reynolds number and the Prandtl number, respectively.

Nanofluid properties

The physical properties of nanofluid containing water-Al 2 O 3 can be calculated as follow:

Density:

( )

s f nf φρ ρ φ ρ + - = 1 (8)
Heat capacitance:

( ) ( )( ) ( ) s p f p nf p C C C ρ φ ρ φ ρ + - = 1 (9)
The presented expression for dynamic viscosity by Maiga et al. [START_REF] Maiga | Heat transfer behaviors of nanofluids in a uniformly heated tube[END_REF] which was determined based on available experimental results for water-Al 2 O 3 is given as:

f nf µ φ φ µ ) 1 3 . 7 123 ( 2 + + = (10)
The thermal conductivity of water-Al 2 O 3 nanofluid has been determined from Chon et al. [START_REF] Chon | Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement[END_REF] correlation which considers the Brownian motion and mean diameter of the nanoparticles as follow:

f f f s s f f nf k k d d k k                 + = φ (11)
Where Pr f and Re f in Eq.( 11) are defined as:

f f f α ρ µ = Pr ( 12
) f B f T k λ η π ρ 2 3 Re = ( 13
)
Where λ f is mean free path of water molecular (λ f =0.17nm), k B is Boltzmann constant (k B =1.3807×10 -23 j/k) and η has been calculated by the following equation:

C T B A - ⋅ = 10 η , A=2.414×10 -5 , B=247.8, C=140 (14)

Slip velocity and jump temperature

The second order non-dimensionalized velocity slip condition is expressed as [START_REF] Gad-El-Hak | The MEMS Handbook, MEMS: Introduction and Fundamentals, Second Edition[END_REF]:

( ) wall wall V V X Ec Kn Y U Kn U ∂ ∂ - + ∂ ∂         - = θ γ γ π σ σ Re 1 2 3 2 2 (15) Here Ec is Eckert number ( T C U Ec p ∆ = 2
). The second term can be negligible if

X Y ∂ ∂ >> ∂ ∂ at
the wall and also due to fact that it is second order in the Knudsen number. Similar arguments can be applied to the jump temperature boundary condition, and the resulting from Taylor series leads in dimensionless form [START_REF] Gad-El-Hak | The MEMS Handbook, MEMS: Introduction and Fundamentals, Second Edition[END_REF]:

        +         ∂ ∂ +         ∂ ∂         +         - = - ... ! 2 Pr 1 1 2 2 2 2 2 wall wall T T wall Y Kn Y Kn θ θ γ γ σ σ θ θ (16)
Values of the thermal and momentum accommodation coefficients ( V σ , T σ ) are near unity for most engineering applications and they are taken as unity in the present study.

After simplifying, the non-dimensional forms of the slip flow velocity and jump temperature boundary conditions are given by:

wall wall N Y U Kn U U ∂ ∂ = - ( 17
) wall wall N Y Kn ∂ ∂ = - θ β θ θ (18) Where         + = γ γ β 2 1
Pr ,

θ wall =1 and U wall =0 (19)

Boundary conditions

These set of nonlinear elliptical governing equations have been solved subject to following boundary conditions:

• At the channel inlet: the nanofluid velocity and the temperature profiles are assumed uniform and constant (X=0, 0≤Y≤0.5: U=1, θ=0).

• At the fluid-solid interface: The velocity in y direction is zero while the slip velocity and the jump temperature of the nanofluid flow adjacent to the wall is proportional to normal velocity and the temperature gradients at the fluid-wall interface (Equations ( 17) and ( 18)). A constant temperature (θ wall =1) at the wall is also applied.

• At the channel outlet: the diffusion flux in the direction normal to the exit is assumed to be zero for the velocity and the temperature while a zero pressure is assigned at the flow exit.

(X=10, 0≤Y≤0.5:

0 = ∂ ∂ = ∂ ∂ X X U θ , P=0)

Numerical methods and validations

The sets of coupled non-linear differential equations were discretized using the Finite Volume Method (FVM). The power law scheme was used for the convective and diffusive terms while the SIMPLER procedure was introduced to couple the velocity-pressure as described by Patankar [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. The slip velocity and the jump temperature boundary conditions expressions are discretized and employed in the discretization equations.

A structured non uniform grid distribution has been used for the computational domain. It is finer near the microchannel entrance and near the wall where the velocity and the temperature gradients are high. Channel lengths are set to a value greater than the estimated entrance lengths to ensure that fully developed conditions are achieved at the exit. Several different grid distributions have been tested to ensure that the calculated results are grid independent.

As it is shown in Fig. 2 increasing the quantity of nodes more than 60 nodes in y direction and 160 nodes in x direction do not change the velocity significantly. Therefore, the selected grid for the present calculations consisted of 160×60 nodes in the x and y directions respectively.

The solution is assumed converged when (

)

6 1 1 10 - + + ≤ Φ Φ - Φ n n n
is satisfied for all independent variables. After solving the governing equations for velocity, pressure and temperature other useful quantities such as Nusselt number and Poiseuille number can be determined.

The local Poiseuille number (fRe x ) can be obtained by:

h wall x D u y u f ∂ ∂ = 2 Re ( 20
)
After using dimensionless parameters, it becomes as follow:

wall X Y U f ∂ ∂ = 2 Re ( 21
)
By submitting the term wall Y U ∂ ∂ from Eq.( 17) into Eq.( 21), the local Poiseuille number for the slip flow regimes can be expressed as:

N X U Kn f 2 Re = (22)
The local Nusselt number (Nu x ) can be obtained by:

k D h Nu h x x = (23)
Where:

( ) b wall x T T q h - = " and wall y T k q ∂ ∂ - = " ( 24
)
After normalizing and combination of Eq.( 23) and Eq.( 24), the local Nusselt number for the case of uniform wall temperature can be calculated from:

wall b wall X Y Nu θ θ θ - ∂ ∂ = (25)
Where the bulk temperature can be calculated from: Ameel [START_REF] Yu | Slip flow heat transfer in rectangular microchannels[END_REF] for Kn=0.04, β=10 and infinity aspect ratio. As seen from this figure a significant agreement between the calculated and numerical results are observed.

∫ ∫ = h h D W D L b dX dY Y X U dX dY Y X U Y X X / 0 / 0 ) , ( ) , ( ) , ( ) ( θ θ

Results and discussion

Numerical simulations have been done for three different cases to evaluate the impact of the the first case (I), the second case (II) and the third case (III) are presented in Table 2, Table 3 and Table 4, respectively.

Velocity field

The velocity profiles for different nanoparticles volume fraction (φ ) at Re=10 and Kn=0.01 are shown in Fig. 5. The non-dimensional momentum equation (Eq.( 6)) is only depend on the Reynolds number. Therefore, at a given Re the solid volume fraction does not have any effect on the non-dimensional velocity which is illustrated in Fig. 5a and5b. However at a given Re, the inlet velocity should be increased with increasing the solid volume fraction to keep Re constant. Consequently, the velocity in any cross section increase which is presented in Fig. 5c and 5d. As it is shown in Table 2, the kinematic viscosity (υ nf = µ nf /ρ nf ) of nanofluid increases with increasing the nanoparticle volume fraction in a given Re, therefore the inlet velocity should be increased. In the previous works which are done with constant Reynolds numbers, it is not clear that the reported effects of nanofluid on heat transfer and friction factor are due to either the adding the solid nanoparticles to the base fluid or increasing the inlet velocity.

Skin friction factor

The local Poiseuille number at differentφ , Kn and Re is presented in Fig. 6 for the first case (Ι)

and second case (Π). The nanoparticle volume fraction does not have any effect on the nondimensional velocity at a given Re (see Fig. 5a and5b). Consequently, it does not have any effect on the Poiseuille number in the micro or macro (Kn=0) scale for the first case (Ι) as depicted in Fig. 6a and6b, respectively. The Fig. 6c and6d show that for the second case (Π) because of small variation in the Reynolds numbers, fRe does not change significantly when the nanoparticles volume fraction increases.

Temperature filed

The non-dimensional temperature and non-dimensional bulk temperature for three cases are presented in Fig. 7. Increasing φ for the first case (I) decreases the temperature and bulk temperature at any cross section at a given Re. Is the reduction due to either increasing the nanoparticles volume fraction or increasing the inlet velocity?

Figures of second case (II) show that increasing inlet velocity also reduces the temperature and the bulk temperature at any cross section like the first case (I). But increasing the nanoparticles volume fraction without increasing the inlet velocity does not have any significant effect on the temperature which is illustrated in Fig. 7 third row (third case (III)).

Nusselt number

Variations of the local Nusselt number in three cases are shown in Fig. 8. As it is reported by previous researcher, increasing the nanoparticles volume fraction increases the local Nusselt number in the non-slip and slip flow regimes for the first case (I) at a given Re. For the second case (II), increasing the inlet velocity also increases the local Nusselt number as well as increasing φ for the first case (I).

With considering the third case (III) in Fig. 7, Fig. 8 and Table3 it is obvious that adding solid volume nanoparticles to the base fluid increases the thermal conductivity and Prandtl number while the Reynolds number reduces. As a result, the Peclet number does not change significantly when the solid nanoparticles volume fraction increases. Consequently, increasing φ without increasing the inlet velocity does not have any significant effect on the local Nusselt number at the third case (III). This behavior also have been observed by Santra et al.

[27] at low Reynolds number (Re<100) in which the Copper (with very high thermal conductivity K s =386) nanoparticles volume fraction does not have any notable effect on the average Nusselt number (Fig. 7 in [START_REF] Santra | Study of heat transfer due to laminar flow of copper-water nanofluid through two isothermally heated parallel plates[END_REF]) in isothermally heated parallel plates.

Conclusions

The Reynolds number in nanofluids studies depends on the inlet velocity and kinematic viscosity of nanofluid. The nanofluid kinematic viscosity increases with an increasing in nanoparticles volume fraction while the inlet velocity should be increased to keep the Reynolds number constant. Therefore, it is not clear that either increasing the nanoparticles volume fraction or increasing the inlet velocity has major role on heat transfer enhancement in nanofluids studies which are done at constant Reynolds numbers. • Results clearly show that at a given Reynolds number (Re), the non-dimensional velocity is not affected by the volume fraction of nanoparticles but the inlet velocity should be increased to keep Re constant.

• The nanoparticles concentration has not any notable effect on the Poiseuille number (fRe) at any Re.

• At a given Reynolds number, the temperature decreasing is not due to increasing the nanoparticles concentration, but it is due to increasing the inlet velocity.

• It is shown that at a given Re, the major enhancement in the Nusselt number is not due to increasing the nanoparticle concentrations but it is due to the increasing the inlet velocity to reach a constant Re. Increasing the nanoparticle concentration does not change the Peclet number significantly, therefore it does not have any significant effect on the heat transfer at a constant inlet velocity.

• Increasing the nanoparticles volume fraction increases density and dynamics viscosity which could increases pumping power. On the other hand, increasing inlet velocity increases pumping power at a given Re. It has been shown that the same heat transfer enhancement could be reached only with the same increasing in inlet velocity without employing nanofluids.

• Constant Reynolds number studies of nanofluids are not sufficient to evaluate the heat transfer and the skin friction factor due to the nanofluids usage.

Further numerical and experimental investigations are needed to develop an appropriate method such as constant pumping powers for investigation heat transfer due to the nanofluids application where could clearly answer to this question "Is nanofluids application useful and economic?"

List of Table

Table 1. Thermophysical Properties of nanoparticles and base fluid at 27 0 C. Table 2. Calculated values for the first case (I) at a constant Reynolds number.

Table 3. Calculated values for the second case (II) at φ=0 and the corresponding inlet velocity values in the first case (I).

Table 4. Calculated values for the third case (III) at a constant inlet velocity and differentφ.

List of Figures

Figure1. Schematic Ameel [START_REF] Yu | Slip flow heat transfer in rectangular microchannels[END_REF] for Kn=0.04 and β=10 with infinity aspect ratio. Fig. 3 Compare the fully developed Poiseuille number with the previous numerical results by Renksizbulut et al. [25] and also with analytical results.

Keywords:

  Nanofluid, Microfluidic, Heat transfer, Slip flow, Rarefaction, Microchannel. constant (=1.3807×10 -23 j/k) Kn Knudsen number ( λ/D h ) L length of microchannel (m) Nu x local Nusselt number, ( in Eq. (19)

  υ nf = µ nf /ρ nf )With the development of science and technology, people begin to realize that with the size decreasing the system will own many advantages that do not appear in conventional size, including compact size, disposability, and increased functionality[START_REF] Gad-El-Hak | The Fluid Mechanics of Microdevices: The Freeman Scholar Lecture[END_REF]. Microchannels, however, are the basic structures in these systems. Based on the Knudsen number (Kn), the flow in microchannels have been classified into four flow regimes: continuum flow regime (Kn ≤0.001), slip flow regime (0.001 < Kn ≤0.1), transition flow regime (0.1 < Kn ≤ 10) and free molecular flow regime (Kn>10). The flow in most application of these systems, such as Micro Gyroscope, Accelerometer, Flow Sensors, Micro Nozzles, Micro Valves, is in slip flow regime, which is characterized by slip flow at wall. Traditionally, the no-slip condition at wall is enforced in the momentum equations and an analogous no-temperature-jump condition is applied in the energy equation. Strictly speaking, no-slip/no-jump boundary conditions are valid only if the fluid flow adjacent to the surface is in thermodynamic equilibrium. This

  most of the previous research, low thermal conductivity base fluids such as air or water have been employed to study the fluid flow in microchannel. The heat transfer of fluids flow is limited base on thermal properties of fluids. However, demanding for increasing the heat transfer in microchannel needs to improve thermal properties of base fluids. One of the presented solutions for this problem is adding solid nanoparticles with high thermal conductivity such as Al 2 O 3 , Cu or CuO to the base fluid which are called nanofluids. During the past two decades, scientists and researchers have been attempting to develop nanofluids, which can offer better heating and cooling performance for variety of thermal systems compared to traditional heat transfer fluids. It is found by numerous numerical and

  studies on nanofluids flow and heat transfer have been done with constant Reynolds number. The Reynolds number in nanofluids studies depend on the inlet velocity and the kinematic viscosity of nanofluid. The nanofluid kinematic viscosity increases with an increasing in nanoparticles volume fraction while the inlet velocity should be increased to keep the Reynolds number constant. Therefore, it is not clear that either increasing the nanoparticles volume fraction or increasing the inlet velocity has major role on heat transfer enhancement in nanofluids studies which are done at constant Reynolds numbers.The objective of the present paper is to study the proportion impact of nanoparticle volume fraction (φ) and the inlet velocity (u in ) on heat transfer of nanofluids flow at constant Reynolds numbers especially in microchannels with low Reynolds numbers and answer to this question " Does the nanofluid increase heat transfer?". To aim to this purpose, laminar forced convection slip and non-slip Al 2 O 3 -water nanofluid flow in a rectangular microchannel have been investigated, employing the slip velocity and the jump temperature boundary conditions at the fluid-wall interface. Three different cases are examined to evaluate proportion impact of increasing nanoparticles volume fraction (φ) and the inlet velocity (u in ) on heat transfer enhancement. Simultaneous effects of the inlet velocity and the nanoparticles volume fraction on heat transfer augmentation are studied. The axial velocity, Poiseuille number, temperature and Nusselt number profiles are presented and discussed. Although the study is done in a microchannel with slip flow regimes, but results are also presented for the case no-slip flow (Kn=0) which could cover for the macro scale.

Fig. 1 .

 1 The flow is considered along the x-axis and the channel length is chosen 20 time width in order to achieve hydrodynamically developed flow at the outlet.The Al 2 O 3 -water nanofluid flow and the heat transfer in rectangular microchannels have been considered. The nanofluid flow is laminar, steady state and incompressible with constant properties while dissipation, pressure work and body forces are neglected. The used properties of base fluid (water) and solid nanoparticles (Al 2 O 3 ) are presented in Table1. The rarefaction effects set the slip velocity and the jump temperature at the fluid-wall interface. Therefore, the steady state governing equations describing the fluid flow and the heat transfer in the microchannel in the Cartesian coordinate and in the tensors form are as follows:

  [START_REF] Chein | Experimental microchannel heat sink performance studies using nanofluids[END_REF] into Eq. (25), the local Nusselt number for the slip flow regimes can be expressed as: demonstrate the validity and also precision of the model assumptions and the numerical analysis, fully developed values of the Poiseuille numbers are compared with available numerical and analytical solutions at Re=100 for different Kn. The calculated Poiseuille numbers in Fig.3show a good agreement with numerical results by M.Renksizbulut et al.[START_REF] Renksizbulut | Slip-flow and heat transfer in rectangular microchannels with constant wall temperature[END_REF] and analytical values, which vary with Kn according to are presented in Fig.4and are compared also with the results byYu and

Al 2 O 3

 23 nanoparticle volume fraction and the inlet velocity on heat transfer enhancement in the non-slip and slip nanofluid flow regimes. The first case (I) is done with a constant Reynolds number where the inlet velocity increases with increasing φ in order to keep Re constant. The second case (II) is done for the pure fluid (φ =0) where only the inlet velocity increases according to the used inlet velocity in the first case (I) for differentφ . The third case (III) is done with a constant inlet velocity (u in =0.0502 m/s according to the used inlet velocity for φ =0 in the first case (I)) where only the nanoparticles volume fraction increases without keeping Re constant. Hence the major fluid flows in the microchannels are laminar flow with low Reynolds numbers, for this study low Reynolds numbers (7≤Re≤15) are chosen. The non-slip and slip flow simulations for these three cases have been also presented. The nanoparticles volume fraction varies from 0 to 5%, because most published paper have also done in this range. The used values for the inlet velocity and other calculated values of two φ (φ =0 and φ =5%) for

Forced convection Al 2 O 3 -

 23 water nanofluid flows in two-dimensional rectangular microchannels have been investigated to study heat transfer enhancement due to application of the nanoparticles to the base fluid. Three different cases are examined to evaluate the proportion impact of increasing the nanoparticles volume fraction (φ) and the inlet velocity (u in ) on heat transfer enhancement. Two-dimensional Navier-Stokes and energy equations accompany with the slip velocity and the jump temperature boundary conditions expressions have been discretized using the finite volume technique. The Brownian motions of nanoparticles have been considered to determine the thermal conductivity of nanofluids. The following conclusions are obtained:

  Figure1. Schematic diagram of two-dimension rectangular microchannel.

Figure. 2

 2 Figure.2 Grid independent test a) in x direction b) in y direction.

Figure. 3

 3 Figure.3 Compare the fully developed Poiseuille number with the previous numerical results

Figure. 4

 4 Figure.[START_REF] Sun | A numerical study of single-phase convective heat transfer in microtubes for slip flow[END_REF] Compare the local Nusselt number with the previous numerical results byYu and

Figure. 5

 5 Figure.5 Variation of the non-dimensional velocity (a,b) and dimensional velocity profile

Figure. 6

 6 Figure.6 The local Poiseuille number profiles for first case (I) and second case (II) at Re=10 and different φ for a) slip flow regime (Kn=0.01) and b) non-slip flow regimes

Figure. 7 a

 7 Figure.7 a) the non-dimensional temperature at the outlet and b) the non-dimensional bulk

Figure. 8

 8 Figure.[START_REF] Akbarinia | Investigation the Diameter of solid Particles affects on a Laminar Nanofluid Flow in a Curved Tube Using a Two Phase Approach[END_REF] The local Nusselt number profiles for first case (I), second case (II) and third case

Fig. 2

 2 Fig.2 Grid independent test a) in x direction b) in y direction.

Fig. 4 Fig. 5

 45 Fig.4Compare the local Nusselt number with the previous numerical results byYu and Ameel

Fig. 6

 6 Fig.6 The local Poiseuille number profiles for first case (I) and second case (II) at Re=10 and different φ for a) slip flow regime (Kn=0.01) and b) non-slip flow regimes (Kn=0).

Fig. 7 aFig. 8

 78 Fig.7 a) the non-dimensional temperature at the outlet and b) the non-dimensional bulk

Table 1 .

 1 Thermophysical Properties of nanoparticles and base fluid at 27 0 C

	Properties	Water	Nanoparticle(Al 2 O 3 )
	Density ρ(kg/m 3 )	998.2	3890
	Heat capacitance C p (J/kg.K)	4240	880
	Thermal conductivity k (W/mK)	0.608	35

Table 2 .

 2 Calculated values for the first case (I) at a constant Reynolds number.

	Re	φ	u in	µ nf /ρ nf	C p	k nf	Pr	Pe
	10	0	0.0502	1.0048e-006	4242	0.608	7	70
	10	5%	0.0734	1.4679e-006	4203	0.687	10.3	103

Table 3 .

 3 Calculated values for the second case (II) at φ=0 and the corresponding inlet velocity values in the first case (I).

	u in	φ	Re	Pr	Pe
	0.0502	0	10	7	70
	0.0734	0	14.6	7	102.2

Table 4 .

 4 Calculated values for the third case (III) at a constant inlet velocity and differentφ.

	φ	u in	µ nf /ρ nf	C p	k nf	Re	Pr	Pe
	0	0.0502	1.0048e-006	4242	0.608	10	7	70
	5%	0.0502	1.4679e-006	4203	0.687	6.9	10.3	71.1


W C Wang

R K Calay
email: r.k.calay@herts.ac.uk

Y K Chen

Experimental study of an energy efficient hybrid system for surface drying

Keywords: Dehumidification, Drying, Desiccant wheel, Heat recovery

Rapid surface drying is an important and energy intensive process in food and beverage packaging industry. Usually these products are dried at low dew point temperatures (DPT) -10 ~ -20°C and low dry ball temperatures (DBT) 20 ~ 30°C for product quality optimization. The conveyor moves at very high speeds and it is necessary to expose as much of the drying surface to the drying effect in a shortest time possible. Re-condensation is a big problem in these systems and a good drying system is that preserves the quality of the product and is energy efficient. This paper presents a feasibility study to obtain the design parameters of a hybrid dryer suited for rapid drying applications. Drying process of a recirculation heat pump is integrated with rotary dehumidifier (desiccant wheel) system. The system employed a refrigerant circuit in conjunction with a heat reactivated desiccant wheel to provide efficient drying capability and supply low DPT conditions. To increase the economic practicality of such a hybrid system, the combined system utilises the heat dissipated by the condenser in regenerating the desiccant wheel. The study shows that the proposed hybrid system can deliver supply air at much lower DPT compared to the single refrigerant circuit and a desiccant wheel. By operating the combined system in tandem, greater amount of dehumidification could be realised due to the improved ratio of latent to total load at the hybrid. Up to 60% heat energy can be saved in rapid surface drying applications by using the proposed hybrid system.

Drying process is an energy intensive activity and plays a significant role in many industrial applications such as food, textile and paper and in many other processing industries. Rapid surface drying is a special form of drying which is widely used in food and beverage packaging industry such as bottles, cans and food packets and pouches. Usually these products are dried at low dew point temperatures (DPT) -10 ~ -20°C and low dry ball temperatures (DBT) 20 ~ 30°C for product quality optimisation. The big issue in these applications is re-condensation and the moisture interference with the drying processes which adversely affects the product quality and reduces production process speeds. For example, when the cider is bottled cold it quickly causes condensation to form on the neck and body of the bottles' surface. This moisture must be completely removed prior to labeling, coating, date stamps or the label can easily slip out of alignment and water can collect under the foil wrap around the neck presenting possible hygiene concerns to customers. Drying is very rapid; compressed air is blown over the bottle on the conveyor belt, which moves at very high speeds (e.g. up to 2000 bottles per minute). Therefore, firstly it is necessary to expose as much of the drying surface to the drying effect in a shortest time possible. Secondly, energy consumption is a concern for all industries. Typically the energy efficiency for various drying applications is between 20 and 60% depending on the type of dryer and product used for drying [START_REF] Mujumdar Arun | Handbook of Industrial Drying[END_REF]. The excessive energy consumption is not acceptable when the nonreplenish able resources such as gas and oil are used. Use of hydrocarbon fuels also has problems such as CO 2 emission. For drying industry there are economic implications due to rising cost of energy. Therefore innovative methods are sought to develop low energy or efficient drying systems. A drying process involves heat and mass transfer in a dynamic process and how to achieve proper drying conditions is an important research field. The optimized drying time and energy consumption would result in an ideal drying condition. Table .1 shows the most promising options for energy savings that can then be selected [START_REF] Baker | Energy Usage for Drying in Selected U.K. Industrial Sectors[END_REF]. This study investigates a feasibility of using a hybrid dryer suited for rapid drying applications. Analytical and experimental studies were performed to obtain the design parameters for the proposed hybrid system. A combination of a dehumidifier with a heat pump is a possible energy efficient alternative method that can be applied for drying and dehumidification. The dehumidification method dries a surface by cooling the air below its dew point and causing it to condense out the water vapor. Alternatively a desiccant adsorption system such as a rotary dehumidifier can be used. Both technologies have wide application in building service applications for air conditioning system [START_REF] Dhar | Studies on solid desiccant based hybrid air-conditioning systems[END_REF][START_REF] Renato | A new heat pump desiccant dehumidifier for supermarket application[END_REF][START_REF] Subramanyam | Application of desiccant wheel to control humidity in air-conditioning systems[END_REF][START_REF] Subramanyam | Parametric studies on a desiccant assisted air-conditioner[END_REF][START_REF] Ghali | Energy consumption and feasibility study of a hybrid desiccant dehumidification air conditioning system on Beirut[END_REF]. The use of regeneration heating in desiccant rotary dryers has a limitations in energy saving. But waste heat energy could be useful normal energy source if it were used so that electrical heating with its implications of use of natural resources may not be necessary.

The role of heat pump desiccant dehumidifier is to turn up the heat recovery by the heat pump cycle. In general, the moist air with a certain temperature at the outlet of the dryer is not discharged to the outside but circulated through heat exchangers such as the evaporator. The evaporator recovers the sensible and latent heat from the moist air by condensing water vapor. The recovered energy utilises the heat dissipated by the condenser in regenerating the desiccant wheel. The desiccant wheel, which removes water vapour from the air by desiccant material, is analogous to water vapor condensing on evaporator surface. The latent heat corresponding to the extracted water liberated into the surrounding air is analogous to energy recovery through the condenser of a heat pump dryer.

The surface drying plays essential role in food packaging, labeling of bottles and cans. The aim of the current paper is to introduce a hybrid system for surface drying consisting of heat pump desiccant dehumidifier. The heat pump cycle and desiccant dehumidification was developed and investigated for the thermal and drying performance of wet surface bottles. A surface drying process is controlled by three variables, temperature, humidity rate and direction of air flow rate from external conditions. Thus, the values of these three variables should be optimized to obtain the maximum efficiency and drying performance [START_REF] Kong | Investigation on Drying Performance and Energy Savings of the Batch-Type Heat Pump Dryer[END_REF]. Design parameters of the proposed dryer were obtained by simulating the heat pump cycle and drying process.

The refrigerant R134a is used in the heat pump system. In order to examine the performance, the COP of the heat pump cycle, the specific moisture extraction rate (SMER) of the drying process, the dehydration rate in the evaporator and desiccant, the temperature and relative humidity (RH) of drying air are estimated and compared for given conditions. The thermal properties of the moist air used in the analysis are obtained from the wet surface bottles on high speed conveyor line as the test material in the surface drying process.

Hybrid system descriptions

Fig. 1. shows a heat pump desiccant dehumidifier proposed in this study. The system utilises a refrigerant circuit in conjunction with a heat reactivated desiccant wheel to provide efficient drying capability. Due to the capabilities of the desiccant wheel, the unit can continue to provide substantial capacity and low supply DPT conditions. Process air dehumidification can be achieved by two steps: cooling the air below its dew point and removing moisture by condensation from evaporator and adsorption by a desiccant material [START_REF] Ahmad | A Review of Desiccant Dehumidification Technology[END_REF].

The heat pump desiccant dehumidifier is used and the simple analysis using the drying efficiency model is employed in the drying process. The steady-state drying process can be assumed in the looptype dryer due to their continuous process, but the steady state cannot be obtained in an open-type dryer such as a conveyer dryer. During the constant rate period, the drying process might be steady state in the open-type dryer. In the present study a steady state is assumed. The variables used in the analysis such as temperature, relative humidity, enthalpy, are the averaged values in a given state. The local variations of the variables are not considered in the heat exchangers, pipes, air flows with a pressure-enthalpy (p-h) diagram. For process air side a fan provides the evaporation air flow from the space air at state 1. The moist space air from the dryer enters the evaporator where the air is dehydrated as the moist condense on the surface of the evaporator. Thus, the latent heat of condensation is recovered from the moist air in the evaporator. At the evaporator outlet at state 2 the air temperature is nearly saturated but is also very cool and low humidity ratio. Then the air through desiccant material comes into contact with the desiccant wheel, and exits the dehumidifier hot and dry at state 3. The wheel is then rotated so that the desiccant portion that has picked up moisture is exposed to hot reactivation air and its moisture removed.

A fan is also necessary to provide the coolant air flow from the ambient air 4 into the condenser. The air at the condenser outlet is at high temperature and low RH. The air passing through the condenser is related only to sensible heat transfer, the absolute humidity is kept to be constant while the air is heated in the condenser. Hot and relatively dry air at approximately ambient pressure is supplied to the desiccant regenerator at state 5. The air gains moisture in a nearly isenthalpic process and exits more humid state 6. There is also a slight increase in the entropy of the air due to the moisture addition. The moist air exiting the regenerator desiccant is still relatively hot and nearly at ambient pressure. Fig. 2. shows that heat pump desiccant dehumidifier drying process on the psychrometric chart.

As the desiccant removes the moisture from the air, desiccant releases heat and warms the air, i.e., latent heat becomes sensible heat. To re-use the desiccant, it must be regenerated or reactivated through a process in which moisture is driven off by heat from condenser waste heat. The dried warm air can obtain desirable condition by sensible condenser.

To increase the economic practicality of such a hybrid system, the combined system utilises the waste heat from the condenser coil to drive moisture off of the desiccant wheel, no extra energy is required to provide increased dehumidification performance. By using the exhaust airstream to remove all heat rejected by the refrigeration system, no additional condenser fans or remote condensers are required. The location of the compressor and expansion valve in the cycle tends to enhance this heat recovery by creating relatively large temperature differences.

Humidity Ratio

Dry Bulb Temperature

Experimental test system and measurements

By employing the mathematical model developed by N. Subramanyam et al [START_REF] Subramanyam | Application of desiccant wheel to control humidity in air-conditioning systems[END_REF][START_REF] Subramanyam | Parametric studies on a desiccant assisted air-conditioner[END_REF]. It is known that system performance is mainly governed by the design and operating parameters of heat pump and desiccant wheel. The other parameters of primary importance are inlet process air DBT, RH, and process air flow rate. An optimal choice of these parameters will reduce the regeneration heat required a given load and operation in terms of minimizing air flow rate in process sides. The refrigerant R134a is used in the heat pump system. In order to examine the performance, the input energy of the heat pump cycle, the SMER of the dehumidification process, the dehumidify rate in the evaporator and desiccant, the DPT and of dehumidification air are estimated and compared for given conditions. The thermal properties of the moist air used in the analysis are obtained from the moisture air space in the dehumidification process. The photo of the hybrid system experimental equipment is shown Fig. 3.

A model of a heat pump system of the refrigerant cycle is generated in order to simulate the process close to the real one. The modelling is done using the adiabatic efficiency applied to the isentropic compression process. The given operating conditions are used to design the heat pump cycle. The pressure, temperature, quality, and enthalpy at each cycle point are determined from the modeling. Then the compressor power, the heat transfer rate of the condenser and evaporator, and the air flow rate of process drying air are worked out.

As the refrigerant passes through the evaporator, heat transfer from the refrigerated space results in the vaporization of the refrigerant [START_REF] Pal | Calculation Steps for the Design of Different Components of Heat Pump Dryers Under Constant Drying Rate Condition[END_REF] Blower Evaporator Compressor Desiccant wheel Condenser Fig. 3 The photo of the hybrid system experimental equipment [START_REF] Mujumdar Arun | Handbook of Industrial Drying[END_REF] The cooling capacity of process drying air [START_REF] Carpinlioglu | A methodology for the performance evaluation of an experimental desiccant cooling system[END_REF] (2) Moisture removal capacity of process air in heat pump integrated desiccant wheel is

The refrigerant passes through the condenser, where the refrigerant condenses and there is heat transfer from the refrigerant to the cooler surroundings

The heat release rate in heat pump of the condenser of regeneration air [START_REF] Subramanyam | Application of desiccant wheel to control humidity in air-conditioning systems[END_REF] Fig. 4. shows the heat pump cycle p-h diagrams. The system was designed to have a refrigeration capacity of about 3.5 kW in the compressor, obtained with the conditions such as the heat release rate of the condenser of 12kW, heat rate at the evaporator 7.5 kW. The average condensing temperature 60°C, average evaporating temperature 7°C, superheating at 1l°C, the sub cooling at 5°C and the COP of the heat pump cycle is 3.43.

Results and conclusion

Figure .5. shows the schematic of the hybrid system and the sample results. The states of the drying air are determined with psychrometric relations illustrated in Fig. 2. The air conditions used in the analysis of the drying process are the DBT of 19.3°C and RH of 54.2% at the evaporator inlet, sensible heat ration (SHR) 0.7, air flow rate of 1300 m 3 /h, and the air is dehydrated and cooled down in the evaporator. Then the air enters the desiccant at DBT of 8.5 °C and RH increases to 81.1% and due to the temperature rise in desiccant, leaves the desiccant at DBT of 26.2 °C and at very low RH of 14.2%. The volumetric flow rate of the air varies slightly due to the density change with temperature, but the mass flow rate is kept constant because the air flow system is assumed to be closed. On the other side, ambient air conditions DBT of 23.2 °C and RH of 46.4% inlet the condenser, then only sensible reheat to DBT of 44.1 °C before passing through the desiccant wheel, in which desiccant material pickup moisture from the process air and transports to the hot regenerated air. The air leaving the desiccant wheel is DBT of 43.8 °C and RH of 34.3% exhausted to the ambient, the humidity ratio of regeneration air is increased and its temperature decreases.

Effect of inlet air temperature

Comparisons between single refrigerant circuit system, single desiccant wheel system and hybrid system operating in tandem are shown in Fig. 6. These three systems are tested at the following conditions, air flow rate 1300m 3 /h, RH = 60% and outlet air DPT keep at 5.6°C. The variation in input energy required for each system with respect to inlet air DBT from 20°C to 30°C is plotted. It shows that the input energy required for all systems increases with the inlet air temperature due to increased driving potential for mass transfer. However the energy demand for the hybrid system is less than the other two single systems at all inlet temperatures. It is clear that the energy requirement is reduced can be saved via the hybrid system. It is suggested that this improvement in heat recovery may be associated with the greater heat transfer area for heat transferring with the drying air and that the evaporator undertook a part of the cooling duty to cool the air to dew-point temperature. Therefore, the desiccant could dedicate more of its surface for latent heat recovery. In a physical sense, the hybrid system may be equivalent to have enlarged the mechanical boundaries for heat recovery in a drying air cycle. Fig. 6. also shows that the SMER of the refrigerant circuit system is more than that of the desiccant wheel system but less than that of hybrid system throughout the range of inlet air temperature as the hybrid system was gradually activated. The addition of desiccant wheel improved the system performance in terms of SMER. It is evident that an introduction of the desiccant wheel not only gained moist air from evaporator but also provided additional sensible heating to the air without an auxiliary heater. The gradual activation of the hybrid system improved SMER in the range of 37-42%. The additional advantage gained in terms of system performance is by employing both dehumidification and regeneration. It is suggested that this outcome may be attributed to the finite rate of heat transfer in the heat exchangers as the air interacted with more heat exchangers. Fig. 6. Effect of inlet air temperature on input energy required and SMER Fig. 7. shows the hybrid system integrated refrigerant circuit and desiccant wheel are driven by the same refrigerant circuit load 7.5 kW cooling capacity. The supply air DPT increases with the inlet temperature rate due to increased driving potential for mass transfer. Further, the supply air DPT of the hybrid system is lower than that of the refrigerant circuit and desiccant wheel at all inlet temperature rates. This is because the hybrid system decreased the sensible and latent load on the cooling coil, resulting in reheat and dehumidification on desiccant wheel. In other words, the potential for sensible heat transfer is reduced, while the potential for moisture transfer is increased. It is observed that supply air DTB of the hybrid system is lowered by about -20 °C compared to that the refrigerant circuit and desiccant wheel, which enables to maintain low humidity in the dryer. Fig. 7. also shows that the supply air DBT of the hybrid system is more than that of refrigerant circuit but less than that of desiccant wheel throughout the range of inlet air temperature rate. The hybrid system basically converts the latent load to sensible load by absorbing moisture and releasing heat to air. Hence its supply air temperature is always more by about 20 °C throughout the range. However, it is less by about 13 °C compared to that of the desiccant wheel. Thus the hybrid system is far better than single refrigerant circuit in providing low humidity, while the single desiccant wheel cannot provide low humidity at all.

Effect of air flow rate

It is well known that the air flow rate of the drying air is a key parameter in a drying system [START_REF] Ghali | Energy consumption and feasibility study of a hybrid desiccant dehumidification air conditioning system on Beirut[END_REF]. The flow rate uses the air flow and is closely related to the air velocity in the drying process. Although the high air velocity results in a fast evaporation of water, the quality of the products might be degraded. The low air velocity causes the drying rate to decrease so that the productivity will decrease. Therefore, the appropriate flow rate for a dryer operation in the optimised conditions should be determined in order to achieve a requested high efficiency. In this section, experiments were conducted to study the effect of regulating the process air flow rate by the control damper. The three system were tested at the following conditions, process air flow rate from 1000m 3 /h to1500m 3 /h, inlet air DBT fixed at 25°C, RH = 60% and outlet air DPT kept at 5.6°C. Fig. 8. illustrates that in all three systems the input power energy increase significantly with air flow rate. However the rate of increase in input energy in the hybrid system is significantly less when compared to the rate of increase in input energy for the desiccant wheel but when compared with the refrigerant circuit system the rate of increase is similar. However the input energy for hybrid system is the least of all the systems. This is because condenser heat release is more than the heat recovered by evaporator. There is no change in the SMER when the air flow rate is increased though all three systems. This is because as the airflow rate increases the input power energy also increases in the system to meet the change in the humidity ratio (Fig. 8). The variation in DPT with respect to air flow rate is compared in Fig. 9 for the three systems. The DPT increases with the increasing air flow rate in all three systems, which is attributed to a short residence time. The hybrid system integrated refrigerant circuit and desiccant wheel are driven by same refrigerant circuit load 7.5 kW cooling capacity. In the case of hybrid system, the integrated desiccant wheel further dehumidifies the DPT is lowered by about -3.7 °C compared to that of refrigerant circuit and desiccant wheel signifying the effectiveness of the former for achieving low humidity air. Fig. 9. also depicts correlations between the air flow rate and the supply air DBT. It can be seen that the supply DBT of the hybrid system is more than that of the refrigerant circuit but less than that of desiccant wheel throughout the range of air flow rate.

SHR 1 Space air inlet or refrigerant outlet at evaporator 2 3 Process air outlet at desiccant wheel 4

 1234 Mass flow rate of air (kg/s) h Enthalpy of air (kJ/kg dry air) fg h Latent heat of vaporization (kJ/kg dry air) ε Effectiveness of desiccant wheel w Humidity ratio of air (kg water/kg dry air) r m & Mass flow rate of refrigerant (kg/s) w m & Moisture removal capacity (kg/s) Ratio of sensible load to total load SMER Specific moisture extraction rate (kg/kWh) Subscripts Space air inlet at desiccant wheel or refrigerant inlet at evaporator Ambient air inlet or refrigerant inlet at condenser 5 Ambient air inlet at desiccant wheel or refrigerant outlet at condenser 6 Regeneration air outlet at desiccant wheel 1. Introduction

Fig. 1 .

 1 Fig.1. Hybrid system combining heat pump and desiccant dehumidifier

Fig. 2 .

 2 Fig.2. Psychrometric diagram of an ideal heat pump desiccant dehumidifier with defined state points

Fig. 4 .

 4 Fig.4. Heat pump R134a refrigerant cycle

Fig. 5 .

 5 Fig.5. Hybrid system drying air process

Fig. 7 .

 7 Fig.7. Effect of inlet air temperature on DPT and DBT

Fig. 8 .

 8 Fig.8. Effect of air flow rate on input energy required and SMER

Fig. 9 .

 9 Fig.9. Effect of air flow rate on DPT and DBT

Acknowledgements

The authors thank Mr. David Dell from Secomak Limited, U.K. for providing support for experimental facilities.

Finally, the energy balance of the heat pump dryer system is given by [START_REF] Subramanyam | Parametric studies on a desiccant assisted air-conditioner[END_REF] The dehumidification performance of the system is evaluated by the COP of the heat pump and the SMER of the process air [START_REF] Mandegari | Introduction of a new definition for effectiveness of desiccant wheels[END_REF] (7) [START_REF] Kong | Investigation on Drying Performance and Energy Savings of the Batch-Type Heat Pump Dryer[END_REF] The moisture air dehumidification occurring in desiccant wheel and its operation can be considered by combination of its heat and mass transfer. Considering that the mass flow rates of process air and regeneration air are not equal. Hence for having a more realistic condition, that includes mass air flow rate of regeneration and process air parameters, the modified regeneration desiccant efficient is given by [START_REF] Chua | A modular approach to study the performance of a two-stage heat pump system for drying[END_REF][START_REF] Mandegari | Introduction of a new definition for effectiveness of desiccant wheels[END_REF][START_REF] Mehmet | Energy and exergy analyses of an experimental open-cycle desiccant cooling system[END_REF] (9)

Where Q laten t is the vaporization latent heat rate of the adsorbed water and Q regeneration is the input heat of regeneration rate.

Experiment setup

A heat pump desiccant dehumidifier was developed on the basis of the design parameters obtained from the energy modelling approach analysis. Temperatures and pressures of the refrigerant at several points of the system were measured during drying to determine the performance of the heat pump system. Using the temperatures, pressure, thermodynamic relations and properties, cycle of the heat pump can be drawn and the COP of the cycle can approximately be evaluated. For a given set of operating conditions, data is taken under steady-state conditions. Measurements for the process and regeneration air streams include inlet and outlet air temperature using a series of high accuracy 'T' type thermocouples sensors (±0.1 °C). The upper limit of measured temperature is 250 °C, the lower limit is -75 °C, relative humidity using RH sensor range from 0% to 100% and its linearity error is (±1.5%). Air flow rates using hotwire anemometer range from 0.2 m/s to 20 m/s accuracy (±5% +1 d). Power consumed by the compressor using 10VA maximum watt transducer accuracy is (± 0.2%).

The honeycombed silica gel composite desiccant wheels were used in this experiment. It can work well under lower regeneration temperature and achieve higher dehumidification capacity. The air channel coated with abundant desiccant materials is capable of removing the moisture from the passing process air. Hydraulic diameter of each honeycomb channel is 2.1 mm and it is coated with a 2 mm thick silica gel layer. The portion of regeneration section to adsorption section is 1/4. Diameter of the wheel is 32 cm, with a length of 20 cm. The desiccant wheel speed is 24.5 rph. The process and regeneration air flow rates were chosen 1300 and 1000 m 3 /h respectively.

Conclusions

A prototype heat pump desiccant dehumidifier assisted mechanical drying system was designed, fabricated, and tested for enhancing the drying efficiency. The system operates cost-effectively because energy required for the regeneration of the desiccant wheel is recycled from the condenser waste heat. The system is integrally designed and controlled for superior performance in even the highest humidity load conditions. The present study confirms the importance of improving heat recovery to improve the performance of heat-pump-assisted drying systems. Adopting the modular approach of increasing the complexity of the heat pump cycle, the following key conclusions may be drawn from the present investigation:

1. By utilising the waste heat from the condenser coil to drive moisture off of the desiccant wheel, up to 30% to 60% more heat energy can be saved by hybrid system depending on SHR in comparison to a system consisting of single refrigerant circuit or desiccant wheel. 2. The addition of desiccant wheel in refrigerant circuit improves the system performance in terms of SMER in the range of 12-20%. The introduction of the desiccant wheel is not only to provide efficient drying capability and low supply dew point conditions but also provides additional sensible heating to the air without the incorporation of an auxiliary heater thus achieving a very high energy efficiency, 3. Regulating the air flow of the control damper is found to be an effective method to regulate the humidity of the drying air while enhancing the amount of energy recovered from the drying air thus avoiding the need for cooling and reheating air. 4. Increasing the air flow rate over the cooling coil and desiccant wheel was found to improve the system performance in terms of moisture removal capacity, which was increased from 7.3 to 11 kg/h when air flow rate is increased from 1000 to 1500 m3/h.


Kamal Hammani

Christophe Finot

A comment on "Research on the nonlinear pulse propagation by numerical analysis" by Li Li and Aihan Yin, Optik, vol. 12 (13) (2011) pp. 1195-1200

K. Hammani and C. Finot

Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS -Université de Bourgogne, 9 av. A. Savary, 21 078 Dijon, FRANCE kamal.hammani@u-bourgogne.fr

In the article entitled "Research on the nonlinear pulse propagation by numerical analysis" [START_REF] Li | Research on the nonlinear pulse propagation by numerical analysis[END_REF], Li Li and Aihan Yin summarize the key elements affecting the nonlinear propagation of an optical pulse in an optical fiber. Based on the NonLinear Schrödinger Equation (NLSE) and on well-known scaling laws [START_REF]Nonlinear Fiber Optics[END_REF], a discussion is carried out on the influence of the dispersive regime of propagation and on the initial chirp.

In this article, a point has attracted our attention. Indeed, in Figs 3(a) and 4(a), some strong oscillations develop and the authors seem to interpret those oscillations as a splitting of the initial Gaussian pulse into numerous subpulses having a lower peak power. It is now well-understood that the interplay between normal dispersion and Kerr nonlinearity may lead to the emergence of strong oscillating substructures in the wings of any pulse [START_REF] Tomlinson | Optical wave-breaking of pulses in nonlinear optical fibers[END_REF][START_REF] Rothenberg | Observation of the formation of an optical intensity shock and wave-breaking in the nonlinear propagation of pulses in optical fibers[END_REF]: this effect, commonly known as wavebreaking , appears when the heavily chirped central part of the pulse overlaps the wings of the pulse [START_REF] Anderson | Wave-breaking in nonlinear optical fibers[END_REF] and the only pulse shape was is not affected by such an effect is the parabolic intensity profile [START_REF] Anderson | Wave-breaking-free pulses in nonlinear-optical fibers[END_REF][START_REF] Finot | Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers[END_REF]. Nevertheless, the development of the temporal oscillations in the wings of the pulse does not lead to a pulse splitting as can be observed for solitonic regime [START_REF] Mollenauer | Experimental observation of picosecond pulse narrowing and solitons in optical fibers[END_REF] and several different analytical approaches based on the analysis of single pulse have been found to accurately reproduce the dynamics recorded in the normal regime of dispersion [START_REF] Burgoyne | Nonlinear pulse propagation in optical fibers using second order moments[END_REF][START_REF] Rosenberg | Evolution of optical pulses towards wave breaking in highly nonlinear fibres[END_REF].

Therefore, regarding the present article, we do not believe that wave-breaking may explain the observed dynamics and the subpulses observed in the normal regime of dispersion. It seems for us more realistic that the so-called pulses highlighted by the numerical simulations of Li et al. are the result of a numerical artifact. More precisely, we would like to emphasize that such oscillations should not be present during the propagation of a single isolated Gaussian pulse and therefore are directly linked to the use of periodic boundary conditions in the fast Fourier transform algorithm that is intensively used in the usual split-step Fourier method [START_REF]Nonlinear Fiber Optics[END_REF]. In other words, due to these periodic boundary conditions, the authors have implicitly investigated the evolution of a periodic train of Gaussian pulses separated by the duration of the temporal window that is used numerically. Consequently, the observed oscillations should be interpreted as the temporal overlap of adjacent pulses that continuously broaden in the normal dispersion regime. The pulses being highly chirped, two local instantaneous frequencies will linearly overlap, which will induce a sinusoidal beating. Such a behavior can in some extent be related to the well-known Talbot effect [START_REF] Jannson | Temporal self-imaging effect in single-mode fibers[END_REF]. To illustrate this artifact, we have reproduced in Fig. 1 the numerical simulations of the authors by taking the same initial pulse and the same temporal window. Results clearly outline the large temporal broadening of the pulse that exceeds the width of the temporal window. Therefore, the previously mentioned oscillations appear in the edges of the pulse first and their temporal extent then increases as the broadening (i.e. the overlap by a virtual adjacent pulse) increases. If we now take into account a temporal window that is twice the size of the previous one, those oscillations disappears (Fig. 2a and2b): the pulse under consideration has not experienced a sufficient broadening so that it is still fully contained in the temporal window with no interaction with a virtual adjacent pulse. Finally, using two adjacent pulses spaced by the initial temporal window (Fig. 2c), we clearly reproduce all the aforementioned features. Let us also stress that if further propagation of high power pulses occurs, the sinusoidal beating will further evolve into a train of dark solitons, which has been experimentally demonstrated as soon as 1990 [START_REF] Rothenberg | Colliding visible picosecond pulses in optical fibers[END_REF]. Such nonlinear evolution in the overlapping regions has also been found to be a crucial limitation of optical pulse processing devices such as Mamyshev regenerators [START_REF] Finot | Numerical study of an optical regenerator exploiting self-phase modulation and spectral offset filtering at 40 Gbit/s[END_REF][START_REF] Nguyen | Self-phase-modulation-based 2R regenerator including pulse compression and offset filtering for 42.6 Gbit/s RZ-33% transmission systems[END_REF] or can also affect evolution in normally dispersive amplifiers [START_REF] Finot | Interaction between optical parabolic pulses in a Raman fiber amplifier[END_REF]. Finally, let us add that similar situations may also occur in the spatial domain [START_REF] Mamyshev | Generation of a periodic array of dark spatial solitons in the regime of effective amplification[END_REF].

Figure 1 .

 1 Figure 1. Simulation of the propagation of a Gaussian pulse in a fiber with the same parameters as in Ref [1] (a). The output temporal intensity profile (grey) is compared to the input profile (black). (b) Longitudinal evolution of the temporal intensity profile.

Figure 2 .

 2 Figure 2. (a) Same as Fig 1a with a larger temporal window. (b) Longitudinal evolution. (c) Comparison between output signal in Fig. 1a and the output signal with two adjacent pulses. (d) Magnification of Fig. 2(c).