Numerical Simulation of Heat Distribution with Temperature-Dependent Thermal Conductivity in a Two-Dimensional Liquid Flow

Abstract

Abstract This paper is a contribution to a better understanding of heat transfer through porous channels used for mechanical sieving and filtration of liquids. The problem modeled by means of the Navier–Stokes equations and the energy equation is similar to a viscous flow between two uniformly permeable walls fixed at different temperatures. Thermal behaviors are determined through three branches denoted solutions of types I, II and III of a diagram of bifurcations presenting the values of the wall shear stress as the Reynolds number varies. We found that the distribution of temperature is similar through branches I and II where a large horizontal inflection area is observed as the Péclet number increases. This large horizontal inflection area inside the channel denotes the presence of thermal boundary layers which more precisely occur across branches I and II when the Péclet number approaches the value of 10. On the other hand, along branch III, thermal boundary layers do not exist and temperature presents a different behavior compared to those of branches I and II.