LBM-MRT simulation of vertical flow of a non-Newtonian fluid in a channel provided with obstacles

Abstract

Forced convection heat transfer in channels with a block has been studied numerically. The vertical walls are differentially heated. The Lattice Boltzmann Method with multiple relaxation time (MRT) has been used to solve numerically the momentum and the heat transfer governing equations. This study details the effects of variations in the Reynolds number, Rayleigh number, and behavior index of fluid, to illustrate important fundamental and practical results. The results show that the recirculation caused by porous-covering block will significantly enhance the heat transfer rate on both top and right faces of second and subsequent blocks. In order to better understand the different elements of the study, we first analyzed the flow in a channel without obstacles in order to understand the behavior of non-Newtonian fluids. in such situations, we have observed that the speed profiles at establishment are essentially dependent on the behavior index, while the heat transfers are proportional to the Reynolds and Prandtl numbers but inversely to the behavior index.