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Mixed convection non-axisymmetric Homann stagnation-point flow

Published online by Cambridge University Press:  05 January 2017

Y. Y. Lok ,
J. H. Merkin  and
I. Pop
Y. Y. Lok
Affiliation:
Mathematics Section, School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia
J. H. Merkin*
Affiliation:
Department of Applied Mathematics, University of Leeds, LeedsLS2 9JT, UK
I. Pop
Affiliation:
Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania
*
†Email address for correspondence: amtjhm@maths.leeds.ac.uk
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Abstract

The steady mixed convection non-axisymmetric (Homann, Z. Angew. Math. Mech., vol. 16, 1936, pp. 153–164) stagnation-point flow over a vertical flat wall placed in a viscous and incompressible fluid is considered. A similarity solution is derived which involves the dimensionless parameters $\unicode[STIX]{x1D6FE}$, representing the shear-to-strain-rate ratio, and $\unicode[STIX]{x1D706}$, a mixed convection parameter. Forced convection, $\unicode[STIX]{x1D706}=0$, is treated first where solutions additional to those given previously by Weidman (J. Fluid Mech., vol. 702, 2012, pp. 460–469) are found arising from singularities as $\unicode[STIX]{x1D6FE}\rightarrow \pm 1$. Numerical solutions are obtained for representative values of both $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D706}$. Critical values $\unicode[STIX]{x1D706}_{c}$ of $\unicode[STIX]{x1D706}$ are seen in opposing flow and these are treated in detail. Asymptotic results for large $\unicode[STIX]{x1D706}$ and $\unicode[STIX]{x1D6FE}$ are derived.

JFM classification

Boundary Layers: Boundary layer structure Convection: Buoyant boundary layers Convection: Convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 418 - 434
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Copyright
© 2017 Cambridge University Press 

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