Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere

This paper is primely devoted to numerical treatment and derivation of analytical expressions for the solution of steady, laminar, incompressible, viscous and electrically conducting fluid of the boundary layer flow due to a rotating sphere subjected to a uniform suction and injection through the surface in the presence of a uniform radial magnetic field. The fluid and body rotate either in the same direction or in opposite directions. Particular attention is the vicinity of equator of the sphere for which the governing mean flow and temperature equations are derived using the similarity transformations. These are first solved numerically by a spectral Chebyshev collocation integration scheme and later are treated via the recently popular homotopy analysis method to obtain the exact solutions. The homotopy series are mathematically proven to rapidly converge to the numerical solutions, provided that auxiliary convergence control parameters are selected optimally as described here. The resulting flow pattern, temperature distribution, surface shear stresses, infinite radial velocity and heat transfer characteristics are presented and discussed for the various parameter cases. Explicit formulas are also derived for some parameters of physical significance.