Energies 2011, 4, 2273-2294; doi:10.3390/en4122273
energies
ISSN 1996-1073
www.mdpi.com/journal/energies
Article
Effects of Viscous Dissipation on the Slip MHD Flow and
Heat Transfer past a Permeable Surface with Convective
Boundary Conditions
Mohammad H. Yazdi 1,2,*, Shahrir Abdullah 1, Ishak Hashim 3 and Kamaruzzaman Sopian 2
1 Department of Mechanical & Materials Engineering, Faculty of Engineering & Built Environment,
Universiti Kebangsaan Malaysia, 43600, UKM, Bangi, Selangor, Malaysia;
E-Mail: shahrir.abdullah@gmail.com
2 Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600, UKM, Bangi,
Selangor, Malaysia; E-Mail: ksopian@vlsi.eng.ukm.my
3 School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia,
43600, UKM, Bangi, Selangor, Malaysia; E-Mail: ishak_h@ukm.my
* Author to whom correspondence should be addressed;
E-Mail: mohammadhossein.yazdi@gmail.com; Tel.: +603-8921-4596; Fax: +603-8921-4593.
Received: 28 October 2011; in revised form: 23 November 2011 / Accepted: 14 December 2011 /
Published: 20 December 2011
Abstract: This paper presents an analysis of the energy exchange resulting from a 2D
steady magnetohydrodynamics (MHD) flow past a permeable surface with partial slip in
the presence of the viscous dissipation effect under convective heating boundary
conditions. A magnetic field can effectively control the motion of an electrically
conducting fluid in micro scale systems, which can be applied for fluid transportation.
Local similarity solutions for the transformed governing equations are obtained, and the
reduced ordinary differential equations solved numerically via an explicit Runge-Kutta (4, 5)
formula, the Dormand-Prince pair and shooting method, which is valid for fixed positions
along the surface. The effects of various physical parameters, such as the magnetic
parameter, the slip coefficient, the suction/injection parameter, the Biot number, the
Prandtl number and the Eckert number, on the flow and heat transfer characteristics are
presented graphically and discussed. The results indicate that the heat transfer rate
increases with the increase in Biot number, slip coefficient, suction and magnetic
parameter, whereas it decreases with the increase in Eckert number and injection.
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