Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis

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.