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Ferroconvection in a porous medium with vertical throughflow

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Abstract

The problem of thermal convection in a horizontal layer of ferrofluid-saturated porous medium is investigated theoretically in the presence of a uniform vertical magnetic field and throughflow. The flow in the porous medium is described by the modified Brinkman equation with fluid viscosity different from effective viscosity. The rigid, however permeable ferromagnetic boundaries are considered to be insulated to temperature perturbations. The resulting eigenvalue problem is solved both numerically using the Galerkin technique and analytically using regular perturbation technique with wave number a as a perturbation parameter and observed that the results complement with each other. The direction of throughflow has no influence on the stability characteristics of the system, and the effect of throughflow-dependent Peclet number Q is to delay the onset of ferroconvection. The Prandtl number Pr(>1) has insignificant while the nonlinearity of fluid magnetization parameter M 3 has no influence on the onset of ferroconvection. Besides, an increase in the value of the Darcy number Da and the magnetic number M 1 is to hasten, while an increase in the ratio of viscosity parameter λ is to delay the onset of ferroconvection.

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Authors and Affiliations

  1. Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore, 560 056, India

    C. E. Nanjundappa

  2. Department of Mathematics, Bangalore University, Bangalore, 560 001, India

    I. S. Shivakumara

  3. Department of Mathematics,, Sai Vidya Institute of Technology, Bangalore, 560 064, India

    R. Arunkumar

  4. Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX, 77710, USA

    Rafael Tadmor

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  1. C. E. Nanjundappa
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  2. I. S. Shivakumara
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  3. R. Arunkumar
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  4. Rafael Tadmor
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Correspondence to C. E. Nanjundappa.

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Nanjundappa, C.E., Shivakumara, I.S., Arunkumar, R. et al. Ferroconvection in a porous medium with vertical throughflow. Acta Mech 226, 1515–1528 (2015). https://doi.org/10.1007/s00707-014-1267-1

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  • DOI: https://doi.org/10.1007/s00707-014-1267-1

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