Unsteady Conjugate Natural Convective Heat Transfer in a Saturated Porous Square Domain Generalized Model

Abstract

Numerical unsteady predictions are carried out for two-dimensional natural convective heat transfer in a saturated porous square domain sandwiched between two finite wall thicknesses. The horizontal boundaries of the cavity are adiabatic and the vertical walls are maintained at fixed different temperatures T h and T c . In the core cavity (porous region), the extension of the Darcy model/Forchheimer–Brinkman-extended Darcy model with the Boussinesq approximation is used to solve the momentum equations as well as the energy and continuity equations. The conduction equation is employed to solve for the temperature distribution in the finite thickness wall layers. The nondimensional equations are solved by using the finite volume approach and the pressure velocity coupling is treated via the SIMPLE algorithm applicable in the porous media. The results are presented for different values of the nondimensional governing parameters, including the modified Rayleigh number (100 ≤ Ra* ≤ 1000), Darcy Number (10−7 ≤ Da ≤ 10−2), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), and the ratio of wall thickness to height (0.1 ≤ D ≤ 0.4). A correlation to evaluate the average Nusselt numbers on the left wall interface of the porous cavity is proposed as a function of modified Rayleigh number, Darcy number, as well as a number of physical, geometrical and material property variables.