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Appl. Sci. 2018, 8(7), 1128; https://doi.org/10.3390/app8071128

Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip

1
Department of Mathematics, Universiti Pertahanan Nasional Malaysia, Kuala Lumpur 57000, Malaysia
2
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor 43600, Malaysia
3
Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Received: 17 April 2018 / Revised: 23 May 2018 / Accepted: 6 June 2018 / Published: 12 July 2018
(This article belongs to the Special Issue Nanofluids and Their Applications)
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Abstract

In this paper, the steady three-dimensional magnetohydrodynamic (MHD) mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions is investigated in a numerical manner. As such, two types of nanofluids, Cu-water and Ag-water, had been considered. A similarity transformation was employed to reduce the governing equations to ordinary differential equations, which were then solved numerically using the MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA, 1984) programme bvp4c. The numerical solutions derived from the ordinary differential equations subjected to the associated boundary conditions, were obtained to represent the values of the mixed convection parameter. Dual (upper and lower branch) solutions were discovered in the opposing flow region of the mixed convection parameter. A stability analysis was carried out to prove that the upper branch solution was indeed stable, while the lower branch solution was unstable. The significant effects of the governing parameters on the reduced skin friction coefficients, the reduced local Nusselt number, as well as the velocity and temperature profiles, were presented graphically and discussed in detail. View Full-Text
Keywords: magnetohydrodynamic; mixed convection; nanofluids; slip conditions; dual solutions; stability analysis magnetohydrodynamic; mixed convection; nanofluids; slip conditions; dual solutions; stability analysis
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Jamaludin, A.; Nazar, R.; Pop, I. Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip. Appl. Sci. 2018, 8, 1128.

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