Combined effects of thermal radiation and heat generation on natural convection in a square cavity filled with Darcy-Forchheimer porous medium

Combined effects of thermal radiation and internal heat source/sink, formulation for natural-convection flow in a square cavity filled with porous medium using isothermal vertical walls and adiabatic horizontal ones, has been studied numerically by using finite-difference technique in staggered grid distribution. The simulations have been carried out by considering for both Darcian and non-Darcian models. The hydrodynamic field in the porous medium is modelled according to the general model involving Brinkman and Forchheimer terms. The present numerical approach yields consistent performance over the range of parameters for Rayleigh number, Thermal radiation parameter, Heat generating parameter in order to obtain the solutions in terms of streamlines, isotherms, velocity profiles, temperature profiles, local Nusselt numbers and the average Nusselt number. For the purpose of numerical simulation we have considered P r = 1.0 and Ɛ= 0.4. The results are also computed for vertical velocity and temperature profiles for non-porous case by taking Ɛ =1.0 and Da=10 4 . Heat transfer rates at the heated walls are presented in terms of local Nusselt number.