Single domain integral transform analysis of natural convection in cavities partially filled with heat generating porous medium

Abstract

An analysis of natural convection within a rectangular cavity partially filled with a heat-generating porous medium is carried out through the Generalized Integral Transform Technique (GITT), in which the laminar flow and energy equations are solved with automatic error control. A single domain reformulation strategy is adopted to rewrite the governing equations within the fluid and the porous medium as a single heterogeneous medium formulation, with spatially variable physical properties and source terms that account for the abrupt transition of the two regions. This fundamental study is motivated by the analysis of wet storage of spent nuclear fuel elements with passive cooling of the pool and physical conclusions are drawn from the hybrid numerical-analytical solution. Increases in the Rayleigh number with constant internal heat generation are found to lower the maximum temperature within the cavity. Moreover, decreasing the aspect ratio also has positive effects on the cooling of the cavity.