Optimization of the circular microchannel heat sink under viscous heating effect using entropy generation minimization method

The present numerical study carries out the optimization of the channel dimension (D-N corresponding to N-number of channels) under the consideration of viscous heating effects in entropy generation (EG) through a uniformly heated microchannel heat sink (MCHS). The numerical computations are performed for a constant total mass flow rate ((m) over dot(tot)) and constant total heat flow rate((q) over dot(tot)). In EG formulation, the partial differential equations (PDEs) are discretized by the first-order forward difference method and the temperature in the denominator is taken as the local one. The EG due to fluid friction (S-gen,S-FR) and heat conduction (S-gen,S-HT) individually as well as simultaneously is also reported. The EG due to fluid heat conduction in the radial (S-gen,S- HT-rad) and axial (S-gen,S-HT-ax) directions are also examined. The results indicate that the frictional entropy generation (S-gen,S-FR) is significant towards the micro dimensions of the channel. Additionally, the optimum diameter (D*) corresponding to the optimum number (N*) of the channels is designed at minimum total EG (S-gen,S-tot).