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Mixed Convection Heat Transfer in MHD Non-Darcian Flow Due to an Exponential Stretching Sheet Embedded in a Porous Medium in Presence of Non-uniform Heat Source/Sink

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Engineering Mathematics I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 178))

Abstract

A mathematical analysis has been carried out to describe mixed convection heat transfer in MHD non-Darcian flow due to an exponential stretching sheet embedded in a porous medium in presence of non-uniform heat source/sink. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations and are solved very efficiently by using fifth order Runge–Kutta–Fehlberg method with shooting technique for various values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The computed results are compared with the previously published work on various special cases of the problem and are in good agreement with the earlier studies. The effect of various physical parameters, such as the Prandtl number, the Grashoff number, the Hartmann number, porous parameter, inertia coefficient and internal heat generation on flow and heat transfer characteristics are presented graphically to show some interesting aspects of the physical parameter.

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Acknowledgements

The first author is grateful to Erasmus Mundus project FUSION (Featured Europe and south-east Asia mobility Network) for support and to the Division of Applied Mathematics, School of Education, Culture and Communication at Mälardalen University for creating excellent research environment during his visit and work on this paper. The author is also thankful to Prof. M. Subhas Abel and Prof. Sergei Silvestrov for making useful suggestions as contributing editors. Further the authors wish to express their thanks to Gulbarga University Gulbarga, Karnataka, India and Mälardalen University, Västerås, Sweden.

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Authors and Affiliations

  1. Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, Box 883, 721 23, Västerås, Sweden

    Prashant G. Metri & Sergei Silvestrov

  2. Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India

    M. Subhas Abel

  3. Department of Mathematics, PDA College of Engineering, Gulbarga, Karnataka, India

    Veena M. Bablad

  4. Department of Physics, Sangameshwar College, Solapur, Maharashtra, India

    Pushpanjali G. Metri

Authors
  1. Prashant G. Metri
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  2. Veena M. Bablad
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  3. Pushpanjali G. Metri
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  4. M. Subhas Abel
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  5. Sergei Silvestrov
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Correspondence to Prashant G. Metri .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Metri, P.G., Bablad, V.M., Metri, P.G., Abel, M.S., Silvestrov, S. (2016). Mixed Convection Heat Transfer in MHD Non-Darcian Flow Due to an Exponential Stretching Sheet Embedded in a Porous Medium in Presence of Non-uniform Heat Source/Sink. In: Silvestrov, S., Rančić, M. (eds) Engineering Mathematics I. Springer Proceedings in Mathematics & Statistics, vol 178. Springer, Cham. https://doi.org/10.1007/978-3-319-42082-0_12

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