Natural Convection of a Heat Generating Fluid in a Closed Cavity

Abstract

Thermal convection of a heat generating fluid in a rectangular enclosure, cooled at the side walls, is investigated in the boundary-layer regime at large internal Rayleigh numbers. A boundary-layer analysis is employed to derive a system of equations valid near the vertical walls and a corresponding system valid in the core of the enclosure. The boundary-layer equations were solved using a modified Oseen linearization method. It was found that the primary convective flow consists of a bicellular circulation in which the cold, descending boundary layers at the lateral walls generate a nearly uniform, upward flow in the core. In addition, a strong, stable, vertical temperature gradient is established in the core by the process of upward transport of heat. The side-wall heat flux distribution shows that most of the heat generated within the cavity is removed along the upper one-half of each vertical wall. It is expected that the results of this work can be applied in studies of the containment of heat generating radioactive materials and in analyses of convection driven by electrical currents or exothermic chemical reactions.