Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder

The mixed convection flow near an axisymmetric stagnation point on a vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R and a mixed convection parameter lambda, as well as the Prandtl number sigma. Numerical solutions are obtained for representative values of these parameters, which show the existence of a critical value lambda (c) = lambda (c) (R, sigma) for the existence of solutions in the opposing (lambda < 0) case. The variation of lambda (c) with R is considered. In the aiding (lambda > 0) case solutions are possible for all lambda and the asymptotic limit lambda -> az is obtained. The limits of large and small R are also treated and the nature of the solution in the asymptotic limit of large Prandtl number is briefly discussed.