Higher order compact scheme for laminar natural convective heat transfer from a sphere

Steady laminar natural-convective heat transfer from a solid sphere is studied by solving the complete Navier-Stokes and energy equations using higher order compact scheme in spherical polar coordinates. Results are obtained for Grashof numbers in the range 0.05 -125 and for Prandtl numbers ranging from 0.72 to 7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity lines and isotherms are plotted. It is found that the scheme captures mushroom shaped front in temperature contours which has been observed experimentally in the literature. The same phenomenon is not captured by upwind method.