Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m , the exponent of the outer flow; λ , the mixed convection parameter and B , the Biot number, as well as the Prandtl number. m = 1 5 is found to be a transitional case with different behaviour depending on whether m > 1 5 or m < 1 5 . For m > 1 5 , there is a critical value λ c with solutions only for λ ≥ λ c , a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For 0 < m < 1 5 , there is a value of B where there is a change in behaviour from that seen for m > 1 5 to solutions terminating at a finite value of λ > 0 and continuing to large values of | λ |. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m 1 5 .