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A study on the onset of thermally modulated Darcy–Bénard convection

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Abstract

A stability analysis of linearized Rayleigh–Bénard convection in a densely packed porous layer was performed using a matrix differential operator theory. The boundary temperatures were assumed to vary periodically with time in a sinusoidal manner. The correction in the critical Darcy–Rayleigh number was computed and depicted graphically. It was shown that the phase difference between the boundary temperatures rather than the frequency of modulated temperatures decides the nature of influence of modulation on the onset of convection. Conclusions were drawn regarding the possible transitions from harmonic to subharmonic solutions. The results on the onset of thermally modulated convection in a rectangular porous enclosure were obtained using those on the modulated Darcy–Bénard convection.

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Acknowledgments

The authors are grateful to the three referees and the editor whose instructive comments helped us to refine our paper.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, 632014, India

    Om P. Suthar

  2. Department of Mathematics, Bangalore University, Jnanabharathi Campus, Bangalore, 560 056, India

    P. G. Siddheshwar

  3. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    B. S. Bhadauria

Authors
  1. Om P. Suthar
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  2. P. G. Siddheshwar
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  3. B. S. Bhadauria
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Correspondence to Om P. Suthar.

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Suthar, O.P., Siddheshwar, P.G. & Bhadauria, B.S. A study on the onset of thermally modulated Darcy–Bénard convection. J Eng Math 101, 175–188 (2016). https://doi.org/10.1007/s10665-016-9853-y

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  • DOI: https://doi.org/10.1007/s10665-016-9853-y

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