NATURAL CONVECTIVE HEAT TRANSFER FLOW OF A NON-NEWTONIAN SECOND-GRADE FLUID PAST AN ISOTHERMAL SPHERE

An analysis is performed to study free convective boundary layer flow of second-grade fluid along an isothermal, impermeable sphere. The Clausius-Duhem inequality is used to describe the second-grade fluid, the presence at stress terms in momentum boundary layer equations. The governing boundary layer equations are transformed into nondimensional form by using specified nonsimilarity variables. A numerical solution is obtained by employing the validated, efficient, implicite finite difference method with Keller box scheme. A parametric study of physical parameters, Deborah number, and Prandtl number involved in the problem is conducted and a representative set of numerical results for velocity and temperature profiles as well as skin friction coefficient and Nusselt number are illustrated graphically and in tabular form. Comparisons with previously published work for different values of the physical parameter of the problem are reported and the existing results are found to be in excellent agreement. An increasing Deborah number retards the velocity and Nusselt number inside the boundary layer region while accelerating the temperature profile and skin friction coefficient. Increasing Prandtl number results in depreciation in the velocity, temperature profiles, and skin friction coefficient while the Nusselt number increased. Applications of the model arise in polymer processing in chemical engineering as well as metallurgical materials processing.