Mixed convection boundary layer on a solid sphere with constant surface heat flux

The steady mixed convection boundary layer flow of an incompressible viscous fluid on a solid sphere with a constant surface heat flux qw is considered for both the assisting and the opposing flow cases. The transformed governing equations of the non-similar boundary layers are solved numerically using the Keller-box method. Numerical results are presented for different values of the mixed convection parameter λ and for the Prandtl number, Pr = 0.7 (air) and Pr = 7 (water). The numerical results obtained include local skin friction coefficient Cf, local wall temperature distribution θw (x) , velocity and temperature profiles. It is found that the assisting flow (λ > 0) delays the separation of the boundary layers, and if the assisting flow is strong enough, it suppresses the separation completely. On the other hand, the opposing flow (λ < 0) brings the separation point nearer to the lower stagnation point ( x ≈ 0 ) of the sphere, and for sufficiently strong opposing flows, there will not be a boundary layer on the spher