This paper concerns the transient liquid film condensation phenomenon on an isothermal vertical surface in contact with an anisotropic porous medium using the complementary error function for the temperature profile. The boundary layer equations are formulated and the time variable is involved only in the energy equation. The governing equations of the problem have been solved analytically by the similarity method using the Kärman-Pholhausen integral method. Thus, the expressions of the dimensionless thickness of the liquid film, the Nusselt number and the characteristic limit time of the transition from transient to steady state have been developed. The results found allows to extend the isotropic porous medium to take into account the anisotropic properties of the porous medium, using the flow permeability tensor and the generalised Darcy's law to describe the fluid flow in the porous medium. A good remark has been done for the temperature profile which is assumed as the complementary error function and gives the same results as the previous studies using a linear function.

Transient film condensation, complementary error function, anisotropic porous medium, Darcy flow model

This study copes with liquid film condensation along a vertical surface embedded in anisotropic porous medium whose principal axes are non-coincident with the gravity vector. With the formulation of the problem on the basis of the generalized Darcy’s law, boundary-layer equations are solved analytically by the method of characteristics, as time is taken into account in equation of energy. By the end, the results obtained for the temperature profile assuming as a complementary error function have the same trends with those for the temperature profile assuming as linear function (Sanya et al., 2021): 1. The transient convective flow along a vertical plate has a singularity characterised by the transition that the convective flow undergoes from a regime where instabilities movements in the porous medium prevail to a regime characterised by stationary movements which take place from a limit dimensionless time τ_C counted from the initial moment of heating of the surface by the initiation of the condensation phenomena. This time τ_C corresponds to the time from which the characteristic quantities of heat and mass transfer suddenly change from the transient one-dimensional conduction regime to a two-dimensional natural convection regime near to the vertical surface where a steady-state regime now prevails. The limiting dimensionless time τ_C to reach the steady state increases with increasing the anisotropy ratio K^* and the orientation angle φ of the main axes of the porous medium. 2. The dimensionless thickness of the liquid boundary layer shows the same pattern as that obtained for the case of isotropic porous medium in the transient regime by previous work. 3. The heat transfer rate depends on the time variable in the transient regime and the anisotropy permeability parameters in the steady state.

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S.A.O. Sanya, G. Chidikofan, M.F.O. Sanya, S. Osseni and C. Akowanou (2024). Transient Laminar Film Condensation on an Isothermal Vertical Surface in an Anisotropic Permeability Porous Medium using the Complementary Error Function for the Temperature Profile. International Journal on Emerging Technologies, 15(1): 09–15.