Effects of Prandtl and Jacob numbers and dimensionless thermal conductivity on the hydrodynamic field

Abstract

In this present study we have analyzed the effects of the Prandtl and Jacob numbers and the dimensionless thermal conductivity on the velocity profiles in the media (porous and liquid). The transfers in the porous medium and the liquid film are described respectively by the improved Wooding model and the classical boundary layer equations. The mesh of the digital domain is considered uniform in the transverse and longitudinal directions. The terms of advection and diffusion are discretized respectively with a back-offset and a center scheme. The systems of coupled algebraic equations thus obtained are solved numerically thanks to an iterative method of relaxation line by line of the Gauss-Seidel type. The results obtained show that the parameters relating to the thermal problem (the dimensionless thermal conductivity, the numbers of Prandtl (Pr) and Jacob (Ja)) have no influence on the dimensionless speed although the thermal and hydrodynamic problems are coupled via the heat balance equation.