Mixed convection in a Falkner–Skan system

Abstract

The effects of mixed convection on the classical Falkner–Skan similarity solutions are considered, now involving a mixed convection parameter $$\lambda $$ as well as the exponent m associated with the outer flow. The forced convection solutions indicate a singularity in the temperature field as $$m \rightarrow 0.070722$$ . Numerical solutions for $$m>0$$ show the existence of a critical value $$\lambda _\mathrm{c}$$ with $$\lambda _\mathrm{c}<0$$ and solutions only for $$\lambda \ge \lambda _\mathrm{c}$$ . The nature of the solution for $$\lambda \gg 1$$ is investigated. For $$m=0$$ , there are solutions for all $$\lambda <0$$ , opposing flow, and only for a finite range of $$\lambda $$ in aiding flow with the asymptotic solution as $$\lambda \rightarrow -\infty $$ also being considered. Solutions for $$m<0$$ are obtained in the cases when there is a solution to the Falkner–Skan system and for a value of m when no solution to this system exists. In the former case, two completely separate parts to the solution are seen, whereas in the latter case, a solution exists only in aiding flow for a limited range of $$\lambda $$ . The variation of solution with the exponent m is also treated for both aiding and opposing flows. In both cases, a solution is seen to exist for all $$m>0$$ , which, however, is limited to a relatively small range of m when $$m<0$$ .