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 [STIX]x1D6FE , representing the shear-to-strain-rate ratio, and [STIX]x1D706 , a mixed convection parameter. Forced convection, [STIX]x1D706=0 , 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 [STIX]x1D6FE→ ± 1 . Numerical solutions are obtained for representative values of both [STIX]x1D6FE and [STIX]x1D706 . Critical values [STIX]x1D706c of [STIX]x1D706 are seen in opposing flow and these are treated in detail. Asymptotic results for large [STIX]x1D706 and [STIX]x1D6FE are derived.