The Cheng-Minkowycz problem for cellular porous materials: Effect of temperature-dependent conductivity arising from radiative transfer

The Cheng-Minkowycz problem involving natural convection boundary layer flow adjacent to a vertical wall in a saturated cellular porous medium subject to Darcy's law is investigated. The problem is formulated as a combined conductive-convective-radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics, and metals. The situation in which radiative conductivity is modeled utilizing the Stefan-Boltzmann law is investigated. If the temperature variation parameter, T(r), is equal to zero, the classical Cheng-Minkowycz solution is recovered. For a non-zero value of T(r) the results show that the reduced Rayleigh number is a decreasing function of T(r). (C) 2010 Elsevier Ltd. All rights reserved.