Laminar conjugate natural convection in horizontal annuli

A numerical study of two-dimensional conjugate natural convection in a horizontal cylindrical annulus formed between an inner heat generating solid square cylinder and an outer isothermal circular boundary is performed. The two orientations considered for the inner solid square cylinder are the square-on-side (SOS) and the square-on-edge (SOE). A cylindrical annulus with an inner solid circular cylinder (CC) of equivalent heat generation is also studied for the purpose of comparison. The flow equations cast in vorticity-stream function form and the energy equations are solved using numerical methods. The steady state results show that the flow in the annulus is characterized by double or quadruple vortex patterns. Of the dimensionless maximum solid temperature, average solid temperature and average inner boundary temperature, the first two are much sensitive to solid-to-fluid thermal conductivity ratio. The dependence of the average Nusselt number on the average inner boundary temperature based Grashof number is found to be in good agreement with the heat transfer data computed for differentially heated annuli with isothermal boundaries, within the parametric space covered. Correlations as functions of Grashof number are developed for the estimation of various quantities of interest for different configurations, aspect ratios and thermal conductivity ratios. The results are expected to be useful in the design of thermal systems such as the spent nuclear fuel casks and underground transmission cables.