A NUMERICAL ANALYSIS OF LAMINAR FREE CONVECTION AROUND AN ISOTHERMAL SPHERE: FINITE-DIFFERENCE SOLUTION OF THE FULL NAVIER-STOKES AND ENERGY EQUATIONS BETWEEN CONCENTRIC SPHERES

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Abstract
A numerical solution of transient laminar free convection between two concentric spheres is presented for Pr= 0.7 and Ra =100. The steady average heat transfer coefficient for the inner sphere becomes independent of the radius of the outer sphere when it is more than 40 times that of the inner sphere, and independent of the number of grid points when they are at least 61 and 46 for the radial and azi-muthal directions, respectively. Steady state is reached at a dimensionless time τ = 6 for the average heat transfer coefficient and at τ = 12 for the convection flow. The steady local Nusselt number near the top and bottom stagnation points is different from that of the previous solution of the boundary-layer equations containing curvature terms, while the average Nusselt numbers of both solutions agree within 2%.