Effect of spacing on laminar natural convection flow and heat transfer from two spheres in vertical arrangement

Abstract

Laminar natural convection heat transfer from two vertically arranged spheres has been investigated numerically in air (Pr=0.72) for large Rayleigh number (Ra=105). The effect of sphere spacing (S) on fluid flow and heat transfer is comprehensively analyzed within the ratio of spacing to radius (S/R) ranging from 4 to 48, i.e., 2⩽S/D⩽24. Extensive results are obtained for complete descriptions on natural convection of two-sphere system, such as the streamline patterns and isotherm contours, dimensionless velocities and temperature profiles, drag coefficient, local and average Nusselt numbers. Comparisons with the isothermal bisphere have also been reported with the previous studies. Due to the interaction of preheating effect and flow mixing, the lower sphere has a great influence on the fluid flow and heat transfer around the upper sphere with the change of spacing between the two spheres. The variation of dimensionless temperature with the dimensionless distance between the two spheres has been also concluded to explain the impact of preheating effect. Finally, correlations have been developed for accurate prediction of natural convection heat transfer for each single sphere and the whole two-sphere system, which can be applied to relevant engineering calculations, and provide values for academic research.