Mixed convection non-axisymmetric Homann stagnation-point flow

The steady mixed convection non-axisymmetric (Homann, Z. Angew. Math. Mech., vol. 16, 1936, pp. 153–164) stagnation-point flow over a vertical flat wall placed in a viscous and incompressible fluid is considered. A similarity solution is derived which involves the dimensionless parameters , representing the shear-to-strain-rate ratio, and , a mixed convection parameter. Forced convection, , is treated first where solutions additional to those given previously by Weidman (J. Fluid Mech., vol. 702, 2012, pp. 460–469) are found arising from singularities as . Numerical solutions are obtained for representative values of both and . Critical values of are seen in opposing flow and these are treated in detail. Asymptotic results for large and are derived.