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Conjugate natural convection between two concentric spheres. Lau, Meng Hooi

Abstract

This work considers the conjugate convective heat transfer between a sphere containing heat sources and a concentric envelope maintained at a specified constant temperature. The space between the two is filled with an essentially incompressible fluid. Steady, laminar and rotationally symmetrical free convection is assumed to take place over the gap width and conduction is the sole transport mechanism considered inside the core. Two limiting cases, of an inner sphere of infinitely large relative heat conductivity, leading to an isothermal core to fluid interface; and of the converse case of small conductivity leading to a constant flux interface are considered separately. The analysis of heat transport leads to the solution of the governing equations through regular perturbation expansions with the Grashof number as main parameter. The ratio of conductivities, radius ratio and Prandtl number appear as secondary parameters. Streamlines, isovorticity curves and isotherms are obtained for various combinations of the parameters. The velocity distribution is determined and both local and overall values of the Nusselt number are obtained. A flow visualization test was undertaken and the core surface temperature distribution was determined experimentally. Reasonable qualitative agreement with the analysis is found.

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