Numerical Modeling of the Effect of the Ratio of Thermal Conductivity on the Thin Film Condensation in Forced Convection in a Canal Whose Walls are Covered with a Porous Material

A numerical modeling of the effect of the ratio of thermal conductivity on the thin film condensation in forced convection in a canal whose walls are covered with a porous material is presented. In this work, the generalized Darcy-Brinkman-Forchheimer (DBF) equations in the porous medium and the hydrodynamic and thermal boundary layer equations in the pure liquid, were used.

Rendered dimensionless and homotopically transformed into a new rectangular basis, we used a finite difference method to discretize them. The advection and the diffusion terms are discretized with respectively a backward-centered scheme and a centered scheme.

After validation, we find that a variation of the longitudinal velocity as a function of the ratio of thermal conductivity only for low values of the Peclet number. When the ratio of thermal conductivity increases, corresponding to an increasingly conductive medium, the longitudinal velocity, the temperature and the Nusselt number increase (even when the Peclet number is high for the thermal field). While the thickness of the liquid film decreases (disadvantaged condensation) and leads to an increase in the length of entry, increase almost linear. The sensitivity of condensation to variations in the ratio of thermal conductivity is constant, whatever its value.

The ratio of thermal conductivity is a very decisive and predictable physical quantity to properly examine the performance of condensation.