An efficient higher order compact scheme to capture heat transfer solutions in spherical geometry

A higher order compact scheme (HOCS) is developed for solving energy equation in spherical polar coordinates for the flow past a sphere. The velocity components are obtained by solving the Navier-Stokes equations using HOCS in spherical geometry. The convection terms in the momentum and energy equations are handled in an effective manner so as to get fourth order accurate solutions. The higher order compact scheme is made efficient by combining with the coarse grid correction based multigrid method. In the absence of an exact solution, the order of accuracy of the results is illustrated. The results are compared with first order accurate upwind scheme, second order accurate defect correction technique(DC) and other recent numerical results of the literature. It is found that HOCS captures heat transfer solutions accurately when compared to other conventional schemes at higher values of Re and Pr. The angular variation of thermal boundary layer thickness is also presented.