Heat transfer by a free convection loop embedded in a heat-conducting solid

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An open, free convection loop embedded near the surface of a heat-conducting solid is examined numerically. The loop is in the form of a half-torous with duct diameter d and toroidal major radius D2. The solid is heated uniformly from below. Critical Rayleigh numbers (Rac) for the onset of motion are determined. Velocities, exit temperatures, and convective heat transfer rates are determined for dD values of 10−2, 10−3 and 10−4 and for Rayleigh number ratios (RaRac from 1 to 360. The Prandtl number is 2.8 and the fluid/solid thermal conductivity ratio is kfks = 0.133. Results are compared with an analytical solution {7} for a high-conductivity solid, i.e. kfks → 0.