The Effect of Variable Viscosity on Unsteady Free Convective Fluid Flow over a Stretching Surface in the Presence of Thermal Radiation and Viscous Dissipation

The unsteady free convective flow of an incompressible, viscous, electrically conducting fluid over a vertical stretching surface with variable viscosity and thermal radiation in the presence of viscous dissipation is considered. The fluid is assumed to be gray, absorbing emitting but non-scattering medium. Thus, the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The viscosity of the fluid is assumed to be an inverse linear function of temperature. Specifically, the study is aimed at determining the effects of variable viscosity parameter ( ), Eckert number ( ), and radiation parameter ( ) on temperature distribution profiles, while holding the Prandtl number constant that is corresponding to air. The specific energy equation governing the fluid flow is solved numerically by the finite difference method. The nonlinear partial differential equation is solved numerically by the finite difference method. MATLAB code is used to solve the Forward Time and Centered Space (FTCS) scheme. Further, stability and consistency analyses are performed on the FTCS scheme to determine the convergence of the scheme. Results for temperature distribution profiles are presented graphically for different values of variable viscosity ( ), Eckert number ( ), radiation parameter ( ). The findings are that an increase in variable viscosity and Eckert number causes an enhancement of temperature distribution profiles whereas an increase in radiation parameter leads to a decrease in temperature distribution profiles. The FTCS scheme was found to be unconditionally stable and consistent. The results obtained in this study follow expected trends and are in good agreement with some previous studies