A transient study of coupled natural convection and radiation in a porous vertical channel using the finite-volume method

The present article deals with a numerical study (if coupled fluid flow and heat transfer by transient natural convection and thermal radiation in a vertical channel opened at both ends and filled with a fluid-saturated porous medium. The bounding walls of the channel are isothermal and gray. In the present study we suppose the validity of the Darcy law and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The net radiative heat flux as well as its divergence is also calculated using the same method. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely the conduction-radiation parameter or Planck number or Stark number, N, the optical thickness, tau(D), and the wall emissivity, epsilon, are addressed. The results indicate that the controlling parameters of the problems, namely, N, tau(D), and epsilon, have significant effects on the flow and thermal fields and on the transient process of heating or cooling of the medium. It has also been shown that the volumetric flow rate, q(v), and the convected heat flux at the channel's exit increase when N is decreased and/or tau(D) and epsilon are increased.