Numerical simulation of the stagnation point flow past a permeable stretching/shrinking sheet with convective boundary condition and heat generation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 4 January 2016
Abstract
Purpose
The purpose of this paper is the stagnation-point flow driven by a permeable stretching/shrinking surface with convective boundary condition and heat generation.
Design/methodology/approach
It is known that similarity solutions of the energy equation are possible for the boundary conditions of constant surface temperature and constant heat flux. However, for the present case it is demonstrated that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is constant.
Findings
The governing boundary layer equations are transformed to self-similar nonlinear ordinary differential equations using similarity transformations. Numerical results of the resulting equations are obtained using the function bvp4c from Matlab for different values of the governing parameters. In addition an analytical solution has been obtained for the energy equation when heat generation is absent. The streamlines for the upper branch solution show that the pattern is almost similar to the normal stagnation-point flow, but because of the existence of suction and shrinking effect, the flow seems like suck to the permeable wall.
Originality/value
Dual solutions are found for negative values of the moving parameter. A stability analysis has been also performed to show that the first upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible. The streamlines for the lower branch solution are also graphically shown.
Keywords
Acknowledgements
The work of Dr Alin V. Roşca and Dr Natalia C. Roşca was supported by a research project of Romanian Education Ministry, Project No. POSDRU/174/1.3/S/149155. The authors wish also to express their thanks to the very competent reviewers for the valuable comments and suggestions.
Citation
Rosca, A.V., Rosca, N.C. and Pop, I. (2016), "Numerical simulation of the stagnation point flow past a permeable stretching/shrinking sheet with convective boundary condition and heat generation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 1, pp. 348-364. https://doi.org/10.1108/HFF-12-2014-0361
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited