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Research Papers: Porous Media

Differential Transformation Method for the Flow and Heat Transfer Due to a Permeable Stretching Surface Embedded in a Porous Medium With a Second Order Slip and Viscous Dissipation

[+] Author and Article Information
M. M. Khader

Department of Mathematics and Statistics,
College of Science,
Al-Imam Mohammad Ibn Saud Islamic
University (IMSIU),
Riyadh 11566, Saudi Arabia
Department of Mathematics,
Faculty of Science,
Benha University,
Benha, Egypt
e-mail: mohamedmbd@yahoo.com

Ahmed M. Megahed

Department of Mathematics,
Faculty of Science,
Benha University,
Benha, Egypt
e-mail: ah_mg_sh@yahoo.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 30, 2013; final manuscript received March 5, 2014; published online April 1, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(7), 072602 (Apr 01, 2014) (7 pages) Paper No: HT-13-1336; doi: 10.1115/1.4027146 History: Received June 30, 2013; Revised March 05, 2014

This paper is devoted to introduce a numerical simulation using the differential transformation method (DTM) with a theoretical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second order slip. The governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations (ODEs) by using similarity variables. The resulting ODEs are successfully solved numerically with the help of DTM. Graphic results are shown for nondimensional velocities and temperatures. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first and second order velocity slip parameters and the Prandtl number on the flow and temperature profiles are given. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

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Figures

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Fig. 1

Flow geometry and coordinate system

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Fig. 2

The behavior of the velocity distribution for various values of β

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Fig. 3

The behavior of the temperature distribution for various values of β

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Fig. 11

The behavior of the temperature distribution for various values of Pr

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Fig. 10

The behavior of the temperature distribution for various values of fw

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Fig. 9

The behavior of the velocity distribution for various values of fw

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Fig. 4

The behavior of the temperature distribution for various values of Ec

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Fig. 5

The behavior of the velocity distribution for various values of λ

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Fig. 6

The behavior of the temperature distribution for various values of λ

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Fig. 7

The behavior of the velocity distribution for various values of γ

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Fig. 8

The behavior of the temperature distribution for various values of γ

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