Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 104, 105, 106, of Darcy number effect Da = 10−5, 10−4, 10−3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k2,1 = 3.7 × 10−2, 5.7 × 10−4, 6.8 × 10−5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.