Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

Abstract

The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in $\mathrm{R}{\mathrm{e}}_x^{\mathrm{1}/\mathrm{2}}{C}_{fx}$ is guaranteed with $S_t$ when magnitude of $\beta$ is large. $\mathrm{R}{\mathrm{e}}_x^{\mathrm{1}/\mathrm{2}}{C}_{fx}$ decreases with $E_c$ and $m$.