Mixed convection flow, heat transfer, species concentration near the stagnation point on a vertical flat plate with Stefan coupled blowing

Abstract

Purpose

The purpose of this study is to consider the effects that buoyancy arising from the combination of both thermal and concentration gradients can have on the mixed convection boundary-layer flow near a forward stagnation point with the effect of Stefan blowing being included. Ad suitable choice for the functional forms of the outer flow and the wall temperature and concentration enables the problem to be reduced to a similarity form involving the dimensionless parameters, λ (mixed convection), κ (Stefan blowing) and N (relative strength of concentration driven buoyancy to that of thermal driven), as well as the Prandtl and Schmidt numbers. Numerical solutions to this similarity system for a range of representative parameter values indicate a finite, non-zero range of κ where there can be four solutions in opposing flow with only one solution in aiding flow. Asymptotic solutions for large values of N and κ are derived, the latter having two different structures in the opposing flow.

Design/methodology/approach

This paper sets up a similarity problem to examine the effects of Stefan blowing on a mixed convection flow with the aims of solving the equations numerically and complementing the results with appropriate asymptotic analysis.

Findings

The findings of the study include multiple solution branches, saddle-node bifurcations and singularities appearing in the solution.

Originality/value

The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

Citation

Rosca, N.C., Rosca, A.V., Merkin, J.H. and Pop, I. (2017), "Mixed convection flow, heat transfer, species concentration near the stagnation point on a vertical flat plate with Stefan coupled blowing", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 1, pp. 77-103. https://doi.org/10.1108/HFF-11-2015-0463