The study incorporates the time-dependent condensation model embedded in a porous medium with variations in liquid-vapor densities along with variable heat generation. A semi-implicit discretization is employed to convert the enthalpy based partial differential equations into a system of nonlinear algebraic equations. The dimensionless form of a two-phase model, along with the heat jump condition, is solved via an Adaptive Moving Mesh Method (AMMM), which uses a smooth enthalpy-temperature relationship. The unsteady liquid-vapor phase change front with internal heat variations are achieved with the manifestation of various appropriate parameters. The obtained results are elucidated graphically. Results indicate that the upsurge in internal heat generation is assisting to reduce the condensation liquid-vapor phase front. With the enormous time variations, the condensation front position is found to be maximum as compared to a short time variation. The study further indicates that liquid density, liquid thermal conductivity, and temperature have enhanced the position of the liquid-vapor front with the variations in dimensionless time.

This article presents a comprehensive analysis of time dependent condensation model embedded in a porous medium with variations in liquid-vapour densities. Both similarity and asymptotic solutions for the unsteady liquid-vapour phase change front are obtained with the manifestation of various pertinent parameters. The obtained results are compared which congregate well as depicted clearly in graphs. Results indicate that with different diffusivity and contrast ratios, the similarity front parameter is found to be gradually declining with variation in a density ratio. We have shown for the condensation process, the ratio of sensible to latent heat is independent of time and is equal to the half of the Stefan number of the liquid phase.