Natural Convection in a Rectangular Cavity with Internal Heat Generation

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Abstract
Applications to nuclear reactors have revived interest in natural convection. A rectangular closed cavity with internal heat generation and wall-cooling roughly simulating a channel of an internally-cooled homogeneous reactor core has been studied theoretically and experimentally.The basic equations of continuity, Navier-Stokes, and a modified energy relation including a volumetric heat source are normalized to show the dependence on the following nondimensional parameters: i) Nusselt number based on width; ii) Prandtl number, and iii) product of Rayleigh number based on width and aspect ratio, a/b, of the cavity. The complexity of these equations allows only numerical solutions, which are obtained following a modified Squire’s method consisting in assuming temperature and velocity profiles. These are substituted into the nondimensional equations, and integrated across the cavity, resulting in a still complex system of differential equations in which the dependent variables and unknown functions are the t...

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