In this work, an analytical investigation of the heat transfer for the microchannel heat sink (MCHS) cooled by different nanofluids (Cu, Al2O3, Ag, TiO2 in water and ethylene glycol as base fluids) is studied by the porous media approach and the Galerkin method and results are compared with numerical procedure. Response surface methodology (RSM) is applied to obtain the desirability of the optimum design of the channel geometry. The effective thermal conductivity and viscosity of the nanofluid are calculated by the Patel et al. and Khanafer et al. model, respectively, and MCHS is considered as a porous medium, as proposed by Kim and Kim. In addition, to deal with nanofluid heat transfer, a model based on the Brownian motion of nanoparticles is used. The effects of the nanoparticles volume fraction, nanoparticle type and size, base fluid type, etc., on the temperature distribution, velocity and Nusselt number are considered. Results show that, by increasing the nanoparticles volume fraction, the Brownian movement of the particles, which carries the heat and distributes it to the surroundings, increases and, consequently, the difference between coolant and wall temperature becomes less.
Heat Transfer Nusselt Number Response Surface Methodology Galerkin Method Friction Factor
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Thermal conductivity ratio
Particle area ratio
Wetted area per volume
Specific heat in constant pressure
Volume flow rate of heat sink (m3/s)
Constants in trial function
Convection heat transfer coefficient
Mean fluid velocity
Horizontal axes coordinate
Vertical axes coordinate
Dimensionless vertical coordinate
Fluid particle diameter
channel aspect ratio
Brownian Reynolds number
Number of channel
Power law index
Nanoparticles volume fraction
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D.B. Tuckerman, F.R. Pease, Digest of Technical Papers, in Symposium on VLSI Tech, Maui, HI (1983) pp. 60--61.Google Scholar