Natural convection in porous media heated from above

Transient natural convection in horizontal porous media is analyzed for geometries with permeable boundaries, and with upper boundary heating. A mathematical model is postulated for porous layers in which continuously stable density gradients exclude the problem of marginal stability. In natural convection, temperature coupling through buoyancy is exhibited in the governing partial differential equations of the mathematical model for mixed mode heat transfer. Corresponding asymptotic solutions for small and large Rayleigh number exhibit negligible momentum energy coupling. The system model is descriptive of conduction opposed natural convection heat transfer, with a continuous applicable range of driving force. Effectiveness of the one dimensional system model is demonstrated in numerical simulation of heat transfer in a packed bed of uniform spheres. Time dependent heating and interface radiation to the environment are considered in the mathematical model of a physical system with large solid to fluid phase conductivity ratio. It is indicated that effective conductivity should be determined by nothing the initial stages of transient response, whereas effective interface emissivity should be inferred from the large time response. This method internal convection and radiant exchange with the environment.