The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet: A revised model
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 4 September 2017
Abstract
Purpose
The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface.
Design/methodology/approach
Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters.
Findings
It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically.
Originality/value
Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.
Keywords
Acknowledgements
The first author would like to acknowledge the financial support received from the Ministry of Higher Education, Malaysia, in the form of PhD sponsorship (MyBrain15 @ MyPhD), and the second author would like to acknowledge the research university grant from the Universiti Kebangsaan Malaysia (project code: DIP-2015-010) and the FRGS TOPDOWN (project code: FRGSTOPDOWN/2014/SG04/UKM/01/1) research grant from the Ministry of Higher Education, Malaysia. In addition, the authors wish to express their thanks to the very competent reviewers for the valuable comments and suggestions.
Citation
Pop, I., Naganthran, K., Nazar, R. and Ishak, A. (2017), "The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet: A revised model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 9, pp. 1910-1927. https://doi.org/10.1108/HFF-05-2016-0207
Publisher
:Emerald Publishing Limited
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