In this present study, we analyzed the effects of Prandtl and Jacob numbers and dimensionless thermal conductivity on the velocity profiles in 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 advection and diffusion terms are discretized with a back-centered and centered scheme respectively. The coupled systems of algebraic equations thus obtained are solved numerically using an iterative line-by-line relaxation method of the Gauss-Seidel type. The results show that the parameters relating to the thermal problem (the dimensionless thermal conductivity, the Prandtl (Pr) and Jacob (Ja) numbers) have no influence on the dimensionless speed, although the thermal and hydrodynamic problems are coupled. Via the heat balance equation. The results obtained show that the parameters relating to the thermal problem have no influence on the dimensionless speed, although the thermal and hydrodynamic problems are coupled via the heat balance equation. So, at first approximation with the chosen constants, we can solve the hydrodynamic problem independently of the thermal problem.
