Eur. Phys. J. Plus (2015) 130: 22
https://doi.org/10.1140/epjp/i2015-15022-8

Regular Article

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

¹ Mechanical Engineering Department, Babol University of Technology, Babol, Mazandaran, Iran
² Mechanical Engineering Department, Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

^* e-mail: m69.rahimi@yahoo.com

Received: 26 November 2014
Revised: 18 December 2014
Accepted: 27 December 2014
Published online: 6 February 2015

Abstract

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.