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Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current

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Abstract

The aim of the present paper is to study the unsteady magneto-hydrodynamic viscous Couette flow with heat transfer in a Darcy porous medium between two infinite parallel porous plates considering Hall effect, and temperature dependent physical properties under constant pressure gradient. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is flowing through a porous medium that is assumed to obey Darcy’s law. A numerical solution for the governing nonlinear partial differential equations coupled with set of momentum equations and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions are investigated. It is found that the porosity number M has a marked effect on decreasing the velocity distribution (owing to a simultaneous increase in Darcy porous drag). Also the temperature T is decreased considerably with increasing porosity number. With increasing Hall current parameter m, the velocity component u (x-direction) is considerably increased, whereas velocity component w (z-direction) is reduced. Temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing m.

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Authors and Affiliations

  1. Department of Engineering Mathematics and Physics, Faculty of Engineering, El-Fayoum University, El-Fayoum, 63514, Egypt

    HAZEM A ATTIA

  2. Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, 2033, Egypt

    W ABBAS

  3. Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, 12211, Egypt

    MOSTAFA A M ABDEEN

  4. Department of Engineering Mathematics and Physics, Faculty of Engineering, Helwan University, Cairo, 11718, Egypt

    AHMED A M SAID

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  1. HAZEM A ATTIA
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  2. W ABBAS
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  3. MOSTAFA A M ABDEEN
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  4. AHMED A M SAID
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Correspondence to MOSTAFA A M ABDEEN.

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ATTIA, H.A., ABBAS, W., M ABDEEN, M.A. et al. Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current. Sadhana 40, 183–197 (2015). https://doi.org/10.1007/s12046-014-0307-9

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  • DOI: https://doi.org/10.1007/s12046-014-0307-9

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