Thermal optimization of square pin-fins in crossflow using the Lattice Boltzmann Method with quadratic thermal equilibrium

Abstract

The geometric spacing and operating Reynolds number (Re) for the best thermal performance of square pin-fin heat sinks is found numerically at a Prandtl number of 0.7. The numerical model used is the double population thermal Multiple-Relaxation-Time Lattice Boltzmann Method (MRT LBM). The Nusselt number (Nu), friction factor (f) and the Thermal Performance Factor (TPF) are calculated for a range of streamwise (0.5 to 3) and cross-streamwise (1 to 2) spacing ratios at Re numbers from 20 to 140. A quadratic thermal equilibrium distribution function is used instead of the commonly used linear function to enhance the simulation accuracy. It is found that the Nu number of each row of the pin-fins array increases with the increase in the spacing in the streamwise direction and the reduction of the spacing in the cross-streamwise direction specially at higher Re numbers. The effect of the reduction in the cross-streamwise direction spacing is more significant than the increase in the streamwise direction one.