NATURAL CONVECTION IN A HORIZONTAL ANNULUS WITH AN INNER HEAT-GENERATING SOLID SQUARE CYLINDER AND AN OUTER ISOTHERMAL CIRCULAR BOUNDARY

摘要

A numerical study of two-dimensional conjugate natural convection flow and heat transfer in a horizontal annulus, formed between an inner heat-generating solid square cylinder placed concentrically inside an isothermal circular cylin-der is performed. Numerical solutions of the Boussinesq equations and the solid energy equation in primitive variables are obtained on a nonstaggered (collocated) grid with a pressure correction method. Results for the dimensionless max-imum solid temperature, average solid temperature, average inner boundary temperature, and average Nusselt number are obtained for the heat-generation and outer-radius-based Grashof number ranging from 10~4 to 10~9, for solid-to-fluid thermal conductivity ratio of 1, 10, 50, and 100, and aspect ratio values of 0.2 and 0.4, with air as the working medium. The streamlines and isotherms show that refraction of isotherms occurs at the solid-fluid interface. The degree of refraction is found to be higher for higher thermal conductivity ratios. Because in steady state all the heat generated is to be transferred to the outer cold boundary irrespective of the thermal conductivity ratio, the average Nusselt number is not sensitive to the thermal conductivity ratio, while the local Nusselt numbers are found to be sensitive to solid-to-fluid thermal conductivity ratio. The maximum temperature depends on the solid thermal conductivity, and hence, its determination requires the solution of the conjugate problem. The results are expected to be useful in the design of thermal systems such as spent nuclear fuel casks and underground transmission cables.