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, Tr, is equal to zero, the classical Cheng–Minkowycz solution is recovered. For a non-zero value of Tr the results show that the reduced Rayleigh number is a decreasing function of Tr.