Mixed convection flow near the axisymmetric stagnation point on a stretching or shrinking cylinder

The steady mixed convection flow near an axisymmetric stagnation point on a stretching or shrinking vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R, a mixed convection parameter lambda, a parameter gamma representing the motion of the cylinder and the Prandtl number sigma. Numerical solutions of the similarity equations are obtained for representative values of these parameters, which show the existence of critical values lambda(c) = lambda(c) (R,gamma,alpha) with the existence of dual solutions in the opposing (lambda < 0) case. The variation of the skin friction coefficient f ''(1) and heat flux theta'(1) with lambda and R when sigma = 1.0 are shown graphically. Also variations of lambda(c) with R, and gamma are determined again in the case when sigma = 1.0. It is found that in the aiding flow (lambda > 0) case solutions are possible for all lambda and the asymptotic solution in the limit lambda -> infinity is obtained. The nature of the solution in the asymptotic limit of large values of R is also treated in the cases when lambda is of O (1) and when lambda is of O (R). (C) 2012 Elsevier Masson SAS. All rights reserved.