Laminar two-dimensional forced convective heat transfer of CuO-water and Al_{2}O_{3}-water nanofluids in a horizontal microchannel has been studied numerically, considering axial conduction effects in both solid and liquid regions and variable thermal conductivity and dynamic viscosity. The results show that using nanoparticles with higher thermal conductivities will intensify enhancement of heat transfer characteristics and slightly increases shear stress on the wall. The obtained results show more steep changes in Nusselt number for lower diameters and also higher values of Nusselt number by decreasing the diameter of nanoparticles. Also, by utilizing conduction number as the criterion, it was concluded from the results that adding nanoparticles will intensify the axial conduction effect in the geometry considered.

In the last two decades, many cooling technologies have been pursued to meet the high heat dissipation rate requirements and maintain a low junction temperature for electronic components. Among these efforts, the microchannel heat sink (MCHS) has received much attention because of its ability to produce high heat transfer coefficient, small size and volume per heat load, and small coolant requirements [

Tuckerman and Pease [

Nanofluids have been proposed as a means to enhance the performance of heat transfer liquids currently available. Recent experiments on nanofluids have indicated significant increase in thermal conductivity compared with liquids without nanoparticles or larger particles, strong temperature dependence of thermal conductivity, and significant increases in critical heat flux in boiling heat transfer. Fluid flow and heat transfer of nanofluid in different geometries have been studied by several authors such as Santra et al. [

Koo and Kleinstreuer [

Jang and Choi [_{2}O_{3}-water nanofluid flowing in a silicon microchannel heat sink. They found that the improvement of microchannel heat sink performance due to use of nanofluid becomes more pronounced with increase in nanoparticle concentration. They also showed that fully developed heat transfer coefficient for nanofluid flow in microchannel heat sink increases with Reynolds number even in laminar flow regime rather than a constant.

Ho et al. [_{2}O_{3}-water nanofluid of 1 and 2 vol.% as the coolant and the Reynolds number ranging from 226 to 1676. It was demonstrated that adding nanofluids significantly increases the average heat transfer coefficient.

In this paper, the effect of concentration of 18 [nm] CuO nanoparticles in water will be studied from hydrodynamic and heat transfer point of view. Then, the effect of nanoparticles type and diameter in the performance of the microchannel will be considered. And finally, the effect of nanofluid on conjugate heat transfer will be discussed by means of Conduction number.

The problem under consideration consists of steady, forced laminar convection flow and heat transfer of a nanofluid flowing inside a straight 2D microchannel. The geometry and boundary conditions of the 2D microchannel are shown in Figure

Schematic illustration of the 2D microchannel.

The flow condition is laminar, and a wide range of Reynolds number from 10 to 1200 has been considered. The solid region is made of silicon (_{s} = 120 [Wm^{−1 }K^{−1}]) with different heights from _{s}/

No slip condition for all solid surfaces, or

Finally the conjugate heat transfer boundary condition for the interface between the two regions is

The finite volume method is used to solve governing equations in a collocated grid arrangement and the well-known Rhie and Chow interpolation scheme [

Supposing thermal equilibrium between nanoparticles and the base fluid and neglecting the velocity slip, the nanofluid can be considered as a single fluid with modified properties [

momentum:

For solid region the energy equation is

In this paper the Reynolds number of the base fluid is considered as the comparing parameter and will be shown by

The fluid flow with Pr = 0.7 in a channel without solid region is considered for validation of the results by comparing with the formula presented by Bejan and Sciubba [

Grid independent study of the code.

Considering the nanofluid as a single phase fluid, properties of the mixture (nanofluid) as a function of concentration of nanoparticles can be determined as follows.

Density and heat capacitance of the nanofluid are simply determined from

Here we use Chon et al. [_{2}O_{3}-water nanofluids [

There are a vast range of different relations for calculating the dynamic viscosity of nanofluid. Value of this property has a substantial effect on hydrodynamic and heat transfer characteristics of nanofluid. Many of the literatures suggest using the well-known relation of Brinkman [

It is claimed by several authors that this relation is proper for concentration less than 5%.

Maïga et al. [_{2}O_{3}-water nanofluid they proposed

Masoumi et al. [

Here we use the Chon et al. [

Figures

Variation of Nusselt number in axial direction of lower wall of fluid region, CuO-water nanofluid in comparison to pure water (

Temperature distribution in the lower wall of fluid region (CuO-water nanofluid,

The temperature distribution of the down wall of the channel is illustrated in Figure _{w} = 150000 W/m^{2}. Adding nanoparticles will decrease outlet temperature and consequently enhance heat transfer characteristics of the channel. As a result, we can conclude that higher heat rates can be removed by nanofluids rather than pure fluids in the single phase regime.

Figure _{w} = 50000 [W/m^{2}]. In the fully developed region all the curves will converge to the same value and the only difference is in the developing length. In higher Reynolds numbers, the entrance length increases and this will cause a slight enhancement in heat transfer.

Effect of Reynolds number on Nusselt number distribution of 2% volume fraction CuO-water nanofluid along horizontal axis.

In Re = 50, the Nusselt number in fully developed region increases which is a result of rapid changes in temperature along

Temperature distribution of 2% volume fraction CuO-water nanofluid along horizontal axis for different Reynolds numbers.

Applied models for thermal conductivity and dynamic viscosity in this paper can predict the effect of the type and diameter of nanoparticles. Figure _{2}O_{3} nanoparticles in Figure _{2}O_{3} has a higher thermal conductivity (_{p} = 36 [Wm^{−1 }K^{−1}] comparing _{p} = 20 [Wm^{−1 }K^{−1}] for CuO), the Nusselt number in this case is larger. Nanofluids containing 6 [nm] nanoparticles of Al_{2}O_{3} will yield a fully developed Nusselt value of 6.57 which is higher than the corresponding value of CuO nanoparticles (6.091). However, the overall trend of both nanofluids is similar.

The effect of nanoparticles diameter on Nusselt number distribution for _{2}O_{3}-water nanofluid.

Chiou [

Using the corresponding values of the problem, we can find a critical Reynolds number value for each _{s}/

Effect of CuO-water nanofluid volume fraction on axial conduction. (a) Variation of critical Reynolds number with volume fraction for different

It means that, for pure water, the axial conduction effect should be considered in Reynolds numbers less than 138.5 but, for a CuO-water nanofluid with

Effect of axial conduction on Nusselt number distribution can be demonstrated by reducing the Reynolds number to values less than critical one. Figure

Effect of axial conduction on distribution of Nusselt number in the channel, for

Another way to consider the effect of axial conduction is to compare the interface wall temperature distribution along the channel for different height ratios. Figure

Effect of axial conduction on wall temperature distribution along the channel for different

Effect of different parameters on the shear stress in the lower wall of the fluid region is shown in Figure

The influence of different parameters on shear stress of the lower wall in fluid region,

The two-dimensional laminar flow and heat transfer of CuO- and Al_{2}O_{3}-water nanofluids in a microchannel are solved considering axial conduction in both fluid and solid regions. The overall results can be categorized as follows.

It was shown that adding nanoparticles will increase Nusselt number and decrease temperature difference between inlet and outlet. Nanofluid will intensify heat transfer characteristics of the microchannel but on the other hand will slightly increase shear stress on the walls.

Although the Reynolds number affects the Nusselt number by increasing the entrance length, in the fully developed region, its effect is weakened.

Axial conduction will cause nonlinear temperature distribution along the wall and lower average Nusselt number using constant properties assumption.

Nanoparticles will boost axial conduction effect in microchannels but the geometry and other parameters of the flow are also important from this point of view.

Using nanoparticles with higher thermal conductivities and decreasing the diameter of nanoparticles will increase the Nusselt number of the flow. For smaller diameters, the rate of the changes in Nusselt number is higher.

Using variable properties causes higher Nusselt numbers and lower shear stress at the end of the channel and should be considered specially in lower Reynolds numbers.

Height ratio

Conduction number [–]

Constant pressure specific heat [Jkg^{−1} K^{−1}]

Hydraulic diameter

Graetz number (= Re Pr

Height of the channel [–]

Nusselt number (=

Pressure [Nm^{−2}]

Peclet number (=Re·Pr) [–]

Prandtl number (=

Heat transfer rate at the wall [Wm^{−2}]

Reynolds number (

Temperature [K]

Bulk temperature [K]

Horizontal velocity component [ms^{−1}]

Vertical velocity component [m/s^{−1}].

Volume fraction of nanoparticles [–]

Dynamic viscosity [Pa·s]

Density [kgm^{−3}].

Average at the inlet [–]

Fluid [–]

Nanofluid [–]

Solid [–]

Nanoparticles [–].

_{2}O

_{3}/H

_{2}O nanofluid

_{2}O

_{3}/water nanofluid

_{2}O

_{3}) thermal conductivity enhancement