NUMERICAL SOLUTION FOR FREE CONVECTION BETWEEN CONCENTRIC SPHERES AT MODERATE GRASHOF NUMBERS

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Abstract
Steady axisymmetric natural convection between two isothermal concentric spheres is Investigated by the method of series truncation. The flow variables and temperature distribution are expressed as series of orthogonal Gegenbauer functions and Legendre polynomials, respectively, with variable coefficients. Thus, the governing equations are reduced to three coupled sets of nonlinear ordinary differential equations of the second order with two-point boundary conditions. Numerical solutions are obtained by truncating the series at a certain stage and by using step-by-step methods. Detailed calculations are carried out for Grashof numbers in the range 1000-20,000 and for Prandtl numbers equal to 0.02, 0.7, and 6. Flow patterns, velocity components, and heat transfer results obtained are compared with published results.