Heat Transfer in a Laminar Channel Flow Generated by Injection Through Porous Walls

Abstract

Steady state similarity solutions are computed to determine the temperature profiles in a laminar channel flow driven by uniform fluid injection at one or two porous walls. The temperature boundary conditions are non-symmetric. The numerical solution of the governing equations permit to analyze the influence of the governing parameters, the Reynolds and Péclet numbers. For both geometries, we deduce a scaling law for the boundary layer thickness as a function of the Péclet number. We also compare the numerical solutions with asymptotic expansions in the limit of large Péclet numbers. Finally, for non-symmetric injection, we derive from the computed temperature profile a relationship between the Nusselt and Péclet numbers.