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UNSTEADY BOUNDARY LAYERS: CONVECTIVE HEAT TRANSFER OVER A VERTICAL FLAT PLATE

Part of: Diffusion and convection

Published online by Cambridge University Press:  04 December 2009

ROBERT A. VAN GORDER  and
K. VAJRAVELU
ROBERT A. VAN GORDER
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA (email: vajravel@pegasus.cc.ucf.edu)
K. VAJRAVELU*
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA (email: vajravel@pegasus.cc.ucf.edu)
*
✉For correspondence; e-mail: vajravel@pegasus.cc.ucf.edu
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Abstract

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In this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Keywords

unsteady boundary layerscoupled nonlinear ordinary differential equationssimilarity solutionanalytical solutionnumerical solution

MSC classification

Secondary: 76R10: Free convection
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 541 - 549
Copyright
Copyright © Australian Mathematical Society 2009

References

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