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The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection

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Abstract

The simultaneous effect of local thermal nonequilibrium (LTNE) and magnetic field dependent (MFD) viscosity on thermal convective instability in a horizontal ferrofluid saturated Brinkman porous layer in the presence of a uniform vertical magnetic field is studied analytically. The results indicate that the onset of Brinkman ferroconvection is delayed with increasing MFD viscosity parameter but the critical wave number is found to be independent of this parameter. When compared to the simultaneous presence of buoyancy and magnetic forces, it is observed that the onset of Brinkman ferroconvection is delayed more when the magnetic forces alone are present. Asymptotic solutions for both small and large values of scaled inter-phase heat transfer coefficient H t are compared with those computed numerically and good agreement is found between them. Besides, the influence of magnetic and LTNE parameters on the stability characteristics of the system is also discussed. The available results in the literature are recovered as particular cases from the present study.

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Acknowledgements

One of the authors (ISS) wishes to thank the Brain Korea 21 (BK 21) program of the School of Mechanical Engineering, Yonsei University, Seoul, Korea for inviting him as a visiting Professor and also the Bangalore University for sanctioning sabbatical leave. The authors M.R. and R.G.R. wish to thank the Principals of their respective colleges for encouragement. We wish to thank the reviewer for useful suggestions.

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Authors and Affiliations

  1. School of Mechanical Engineering, Yonsei University, Seoul, 120-749, South Korea

    I. S. Shivakumara & Jinho Lee

  2. UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore, 560 001, India

    I. S. Shivakumara

  3. Department of Mathematics, Smt. Rukmini Shedthi Memorial National Government First Grade College, Barkur, 576210, Udupi District, India

    M. Ravisha

  4. Department of Mathematics, AMC Engineering College, Bangalore, 560 083, India

    R. Gangadhara Reddy

Authors
  1. I. S. Shivakumara
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  2. Jinho Lee
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  3. M. Ravisha
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  4. R. Gangadhara Reddy
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Correspondence to Jinho Lee.

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Shivakumara, I.S., Lee, J., Ravisha, M. et al. The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection. Meccanica 47, 1359–1378 (2012). https://doi.org/10.1007/s11012-011-9519-9

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  • DOI: https://doi.org/10.1007/s11012-011-9519-9

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