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Research Papers: Natural and Mixed Convection

On Laminar Magnetoconvection Flow in a Vertical Channel in the Presence of Heat Generation and Heat Absorption

[+] Author and Article Information
J. C. Umavathi

Department of Mathematics,
Gulbarga University,
Gulbarga 585106, India

B. Patil Mallikarjun

Department of Studies and Research
in Mathematics,
Tumkur University, Tumkur,
Karnataka 572102, India

S. Narasimha Murthy

Department of Mathematics,
College of Science,
Bahir Dar University,
P.O. Box 3080,
Bahir Dar, Ethiopia
e-mail: simhamurthy44@gmail.com

1Present address: Department of Mathematics, Tumkur University, Tumkur, Karnataka, India.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 19, 2011; final manuscript received November 19, 2012; published online March 20, 2013. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 135(4), 042503 (Mar 20, 2013) (8 pages) Paper No: HT-11-1359; doi: 10.1115/1.4023222 History: Received July 19, 2011; Revised November 19, 2012

The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel and asymmetric wall heating conditions in the presence of electrical conductivity effect is considered through proper choice of dimensionless variables. The governing with symmetric equations are developed and three types of thermal boundary conditions are presented. These boundary conditions are isothermal–isothermal, isoflux–isothermal, and isothermal–isoflux for the left–right walls of the channel respectively. The velocity field and the temperature field are obtained by perturbation series method which employs a perturbation parameter proportional to the Brinkman number. In addition, closed form expressions for reversal flow conditions at both the left–right channel walls are derived. Selected set of graphical results illustrating the effects of the various parameters involved in the problem including magnetic dissipation, heat generation or absorption, and the electrical conductivity on the velocity and temperature profiles as well as flow reversal situation are presented. The solutions obtained are also compared with that of results obtained by finite difference method.

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Figures

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Fig. 1

Physical configuration

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Fig. 2

Plots of u versus y in the case of asymmetric heating for different values of λ and E

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Fig. 3

Plots of θ versus y in the case of asymmetric heating for different values of Br

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Fig. 4

Plots of u versus y in the case of asymmetric heating for different values of λ,ɛ, and E

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Fig. 5

Plots of u versus y in the case of asymmetric heating for different values of heat generation coefficient φ

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Fig. 6

Plots of θ versus y in the case of asymmetric heating for different values of heat generation coefficient φ

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Fig. 7

Plots of u versus y for different values of φ and λ for isoflux –isothermal case

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Fig. 8

Plots of θ versus y for different values of φ and λ for isoflux–isothermal case

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Fig. 9

Plots of u versus y for different values of φ and λ for isothermal–isoflux case

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Fig. 10

Plots of θ versus y for different values of φ and λ for isothermal–isoflux case

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