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Numerical simulation is performed to investigate the laminar force convection of Al_{2}O_{3}/water nanofluid in a flow channel with discrete heat sources. The heat sources are placed on the bottom wall of channel which produce much thermal energy that must be evacuated from the system. The remaining surfaces of channel are kept adiabatic to exchange energy between nanofluid and heat sources. In the present study the effects of Reynolds number (

Localized areas of high temperature on microprocessors and various electronic components produce hot spots that have an unfavorable effect on their performance and operating conditions. With increasing of power density of these electronic components, good attempts have been carried out to enhance the heat exchanger rate of them by active as well as passive methods. While the former usually offers higher augmentation, it requires additional external forces that can increase the capital and operating cost of the system. In contrast, passive heat transfer enhancement can be obtained by changing the geometry or modifying thermal properties of working fluid [

Many researchers experimentally showed nanofluids have higher thermal conductivity than those of the base fluids and a lot of correlations were reported. For example Lee et al. [_{2}O_{3}-water/ethylene glycol with particle diameters 24.4 and 38.4 nm as well as CuO-water/ethylene glycol with particle diameters 18.6 and 23.6 nm and showed that thermal conductivity increases to 20% as particle volume fraction increases from 0 to 4%. Chopkar el al. [_{2}Al-water nanofluids and Al_{2}Cu-water nanofluids and found that it increases about 130% with a volume fraction less than 1%. Some researchers [

Santra et al. [_{2}O_{3} and Ethylene Glycol-Al_{2}O_{3} mixtures for a system of parallel, coaxial, and heated disks. A remarkable augmentation of heat transfer coefficient has been observed with increasing of the volume fraction of nanoparticles for both nanofluids. They have reported that the rate of increase of heat transfer is more for Ethylene Glycol-Al_{2}O_{3} nanofluid in comparison with the water-Al_{2}O_{3} nanofluid. However, the wall shear stress also increases considerably with increasing of volume fraction of nanoparticles. Feng and Kleinstreuer [

With respect the problem under study, that is, heat transfer of discrete heat sources in channel flows, there are numerous works [

Bhowmik et al. [

In the present paper, the flow and heat transfer characteristics of channel flow with discrete heat sources for base fluid (distilled water) and a nanofluid that is composed of distilled water and Al_{2}O_{3} nanoparticles are numerically investigated. The main aim of this study is how the nanofluid affects on the heat transfer rate and pressure drop of flow in a channel with hot spots.

In this study the velocity and temperature fields are determined in a parallel plates channel with height

Parallel plates channel with discrete heat sources.

Since nanofluids are composed of extremely small particles, it is assumed that the nanoparticles and basefluid are in thermal equilibrium and they flow at same velocity. In the present work, the nanofluid is considered incompressible with temperature-dependent properties. The compression work and viscous dissipation terms were considered negligible in the energy equation. Under such assumptions, the general governing equations written are as the followings.

Conservation of mass:

Conservation of momentum:

Conservation of energy:

The thermophysical properties of nanofluid are chiefly functions of particle volumetric concentration and temperature. In the absence of experimental data, nanofluid density and specific heat are defined only as a function of volume fraction as follow.

Density:

Specific heat:

Viscosity:

Thermal conductivity:_{2}O_{3} nanofluid based on available experimental results published by Putra et al. [

The governing differential equations are solved using the control volume method. A second order upwind method is used for energy and momentum equations. The SIMPLE procedure is chosen to couple pressure and velocity. The solution converge was met when the normalized residuals for all equations reached to the 10^{−7}. The algebraic discretized equations throughout the physical domain are solved by means of well-known TDMA techniques.

In order to assess the grid independent of numerical solution, three grid densities are checked. Figure

Effect of grid density on the temperature of channel outlet (

The thermal performance of the channel is characterized in terms of average heat transfer coefficient along the heat sources,

Thermalhydraulic performance factor is defined as:

The heat transfer performance of cooling channel is discussed in term of the figure of merit, FoM, which is given by [

In order to show the validity and also accuracy of the model and numerical method, two comparisons with the available data are carried out. The first comparison is related to a parallel plates channel that all its walls are heated with a constant heat flux and the water is used as fluid working. In this case, the Nusselt number is compared which is given by the following definitions:

Comparison of present numerical results with those obtained by Shah and London [

The second comparison is concerned with experimental data of nanofluid heat transfer in a circular tube with diameter (_{2}O_{3} with

Comparison of heat transfer coefficient between present simulation and experimental data [_{2}O_{3} nanofluid with

The values of velocity at channel outlet for

Effect of particle loading parameter

Figures

Effect of particle loading parameter

Since the variations of temperature on the top wall is negligible (less than 2 K), the local viscosity is illustrated in Figures

Effect of particle loading parameter

Results reveal that the presence of nanoparticles has a remarkable effect on heat transfer enhancement. The average heat transfer coefficient profiles on the heat sources as a function of Reynolds number are depicted in Figure ^{2} k for

Effect of parameters

Figure

As we are also interested to analysis the cooling benefits of nanofluid on bottom wall, Figures

Effect of particle loading parameter

The effect of particle volume fraction on temperature along the channel height can be seen on Figures

Effect of volume fraction

It will be predictable that the use of nanoparticles in basefluid can have an adverse influence on pressure drop because of increased viscosity. The pressure drop profiles as a function of Reynolds number are depicted in Figure

Effect of parameters

The pressure drop ratio (

Since we use temperature-dependent properties, it is interesting to determine the effect of heat sources heat flux (

Effect of parameters

As discussed in previous sections, the use of nanofluids increases the heat transfer rate as well as pressure drop. In order to investigate the order of magnitude of augmentation of heat transfer and pressure drop for various Reynolds number and volume fraction, the thermal hydraulic performance factor as a function of Reynolds number is depicted in Figure

Effect of parameters

It is observed that the thermal hydraulic performance has different behaviors for

In order to have a comparison between ratio of output (heat transfer rate) to the input (pumping power), the overal heat transfer performance of channel in term of figure of merit (FoM) as a function of Reynolds number is illustrated in Figure

Effect of parameters

A numerical analysis of flow and heat transfer characteristics of nanofluid in a parallel plates channel with discrete heat sources has been presented. The heat sources are placed on bottom wall at a constant heat flux and remaining channel surfaces are considered adiabatic. The basefluid is water and three volume fractions of Al_{2}O_{3} nanoparticles (

nabla operatoe (1/m)

specific heat of the fluid (J/kg K)

figure of merit

channel height (m)

average heat transfer coefficient along heat sources (W/m^{2} K)

thermal conductivity (W/m K)

mass flow rate (Kg/s)

local Nusselt number (

pressure (Pa)

heat flux of heat sources (W/m^{2})

reynolds number (

coordinate along heat sources (m)

temperature (K)

velocity vector (m/s)

total heat transfer rate (J/s)

inlet velocity (m/s).

thermal hydraulic performance factor

pump efficiency

dynamic viscosity (Pa·s)

density (kg/m^{3})

particle volume fraction (%).

refers to the wall conditions

refers to the base fluid

refers to the nanofluid

refers to particles

refers to a ratio

refers to the inlet conditions.

First, the authors would like to thank Editor Dr. M. F. El-Amin and two anonymous referees for their useful suggestions, which greatly improve the paper. We also would like to express our appreciation to the Iran nanotechnology initiative council for their financial support for this project.