Heat and Mass Transfer at a General Three-Dimensional Stagnation Point

Abstract

Theme 1 presented detailed results for compressible laminar three-dimensional stagnation-point flow of a gas with constant properties (i.e., density-viscosity product p\i is constant and Prandtl number a is unity). This work was extended to include mass transfer (injection only) and nonunity Prandtl number by Libby. While Foots solved the governing equations numerically, using the forward integration scheme, Libby used the quasilinearization technique. In recent years, Libby and his coworkers' have extended the quasilinearization technique to study the laminar boundary-layer problem with variable gas properties at an axisymmetric stagnation point with hydrogen injection. This three-dimensional problem with variable gas properties, employing model gas equations (^ oc /f, p oc h~, a = 0.7, where h is the enthalpy and co is the viscosity exponent) without mass transfer, was considered by Wortman' and Wortman et al. With mass transfer (i.e., only injection with or without a foreign gas), it was considered by Wortman and Mills and Wortman. The governing equations in Refs. 5-9 were solved by a method based on functional analysis. The main objective here is to obtain values of critical wall parameters which were not obtained by the previous studies of this problem. With this in mind, the solution of the preceding problem with variable gas properties for both suction and injection has been obtained by the use of the method of parametric differentiation. The values of the shear stress and heat transfer parameters for various values of physical parameters of the flow are presented in tabular form. These results show that, irrespective of the nature of the stagnation point, the critical wall values are affected appreciably with the variations of co, the exponent in power law, only at low wall temperatures, their variations with co being considerably small at high values of the wall temperature. Another important feature that is observed is that the variation of the density-viscosity product (i.e., co ^ 1) across the boundary layer gives rise to a point of inflexion in the velocity and enthalpy profiles.