Keller-Box Scheme to Mixed Convection Flow Over a Solid Sphere with the Effect of MHD

Abstract

Mixed convection is the combination of a free convection caused by the buoyancy forces due to the different density and a forced convection due to external forces that increase the heat exchange rate. This means that, in free convection, the effect of external forces is significant besides buoyancy forces. In this study the fluid type with viscoelastic effect is non-Newtonian. The viscoelastic fluids that pass over a surface of a sphere form a thin layer, which due to their dominant viscosity is called by the border layer. The obtained limiting layer is analyzed with the thickness of the boundary layer- near the lower stagnating point, then obtained dimensional boundary layer equations, continuity, momentum, and energy equations. These dimensional boundary layer equations are then transformed into non-dimensional boundary layer equations by using non-dimensional variables. Further, the non-dimensional boundary layer equations are transformed into ordinary differential equations by using stream function, so that obtained the non-similar boundary layer equations. These non-similar boundary layer equations are solved numerically by using finite difference method of Keller-Box. The discretization results are non-linear and it should be linearized using newton linearization technique. The numerical solutions are analyzed the effect of Prandtl number, viscoelastic, mixed convection, and MHD parameters towards velocity profile, temperature profile, and wall temperature.

Numerical results of Crank-Nicolson scheme on unsteady nano fluid under the effect of Prandtl, Mixed Convection, and Magnetohydrodynamics

“…where the dimensional variables of x, ȳ are the cartesian coordinate system. Moreover, the dimensional variables of ū, v are related to the velocity of fluid moving in the x, ȳ, and r is the radial distance of sphere which has been derived more detail from the previous study (see [16], Appendix).…”