Conjugate Natural Convection in Non-Circular Horizontal Annulus

ABSTRACT

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 cylinder is performed. Numerical solutions of the Boussinesq equations and the solid energy equation in primitive variables are obtained on a non-staggered (collocated) grid with a pressure correction method. Results for the dimensionless maximum 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 10⁴ to 10⁸, for solid-to-fluid thermal conductivity ratio of 1, 10, 50 and 100, and aspect ratio (ratio of the side of the inner square to the diameter of the outer cylinder) values of 0.2 and 0.4, with air as the working medium. The streamlines and isotherms have shown that refraction of isotherms occurs at the solid-fluid interface. The degree of refraction is found to be higher for higher thermal conductivity ratios. Since in the 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 upon 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 the spent nuclear fuel casks and underground transmission cables.

Keywords: Conjugate, Natural convection, Horizontal annulus.

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