Similarity solutions for steady laminar convection along heated plates with variable oblique suction: Newtonian and Darcian fluid flow

Abstract

The similarity solution ansatz that Burdé applied to adiabatic boundary-layer flow over flat plates and slender bodies of revolution is employed here to investigate mixed convection flow adjacent to heated inclined flat plates. Both Newtonian and Darcian fluids are considered under the assumption that they obey the Boussinesq approximation. New results fall into two distinct categories for heated plates with oblique wall suction. Class I problems correspond to radial source/sink flows interior to a wedge and class II problems pertain to uniform rectilinear flow over flat plates. Except in special cases, solutions of the class I equations must be obtained numerically while all class II equations possess explicit analytical solutions encompassing natural, mixed, or forced convection depending on the magnitude of the free-stream velocity. Numerical integration of prototype class I problems reveals single or dual solutions for radial outflow and an infinity of oscillatory solutions for radial outflow. The similarity solutions reported here describe flows with continuous distributions of temperature and suction angle along the plate, and in some cases the variation of the temperature, suction strength, or suction angle may be chosen freely.