Mixed convection along a vertical surface: Similarity solutions for uniform flow

Abstract

The similarity equations for mixed convection boundary-layer flow over a vertical semi-infinite flat plate in which the free stream velocity is uniform and the wall temperature is inversely proportional to the distance along the plate are considered. The solutions are analysed for both small and large values of the Prandtl number, σ, and for different values of the mixed convection parameter, λ, including forced (λ = 0), free (λ → ∞) and mixed (λ ≠ 0) convection flow regimes. It is found that, for mixed convection, there are qualitative differences in the solution structure for σ < σc, and σ > σc, (σc ≃ 0.761). In the former case, solutions exist for all positive λ (aiding flows) but there is only a finite range of negative λ for which solutions exist with two solution branches for λ in this range. For σ > σc solutions exist for all negative λ (opposing flows) with solutions possible for only a finite range of positive λ. The critical role that the Prandtl number plays in the present results is different to previously published results. © 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.