Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T17:01:45.881Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Amati, G., Koal, K., Massaioli, F., Sreenivasan, K. R. and Verzicco, R., “Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number”, Phys. Fluids 17 (2005) 121701.CrossRefGoogle Scholar
[2]Fang, T., “A note on the unsteady boundary layers over a flat plate”, Internat. J. Non-Linear Mech. 43 (2008) 1007–1011.CrossRefGoogle Scholar
[3]Liao, S., “An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate”, Commun. Nonlinear Sci. Numer. Simul. 11 (2006) 326–339.Google Scholar
[4]Liao, S., “Series solutions of unsteady boundary-layer flows over a stretching flat plate”, Stud. Appl. Math. 117 (2006) 239–263.CrossRefGoogle Scholar
[5]Mehmood, A., Ali, A. and Shah, T., “Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method”, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 902–912.CrossRefGoogle Scholar
[6]Nazar, R., Amin, N. and Pop, I., “Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium”, Int. J. Heat Mass Transfer 47 (2004) 2681–2688.CrossRefGoogle Scholar
[7]Nazar, R., Amin, N. and Pop, I., “Unsteady boundary layer flow due to a stretching surface in a rotating fluid”, Mech. Res. Comm. 31 (2004) 121–128.CrossRefGoogle Scholar
[8]Pop, I. and Na, T. Y., “Unsteady flow past a stretching sheet”, Mech. Res. Comm. 23 (1996) 413–422.CrossRefGoogle Scholar
[9]Todd, L., “A family of laminar boundary layers along a semi-infinite flat plate”, Fluid Dynam. Res. 19 (1997) 235–249.Google Scholar
[10]Vajravelu, K., “Convective heat transfer at a stretching sheet with suction or blowing”, J. Math. Anal. Appl. 188 (1994) 1002–1011.CrossRefGoogle Scholar
[11]Williams, J. C., Mulligan, J. C. and Rhyne, T. B., “Semisimilar solutions for unsteady free-convective boundary-layer flow on a vertical flat plate”, J. Fluid Mech. 175 (1987) 309–332.CrossRefGoogle Scholar
[12]Xu, H., Liao, S. J. and Pop, I., “Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate”, Eur. J. Mech. B Fluids 26 (2007) 15–27.Google Scholar