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Thermal Modulation of Raleigh-Benard Convection in a Sparsely Packed Porous Medium

Volume 10, Issue 2, 2007, pp. 175-188
DOI: 10.1615/JPorMedia.v10.i2.50
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ABSTRACT

The linear stability of thermal convection in a horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation using the Brinkman model with effective viscosity larger than the fluid viscosity. The temperature field between the walls of the porous layer consists of two parts; a steady part and a time-dependent part that varies periodically. The combined effect of permeability and modulation of the walls' temperature on the stability of flow through a porous medium has been investigated using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of amplitude and frequency of modulation, porous parameter, viscosity ratio, and Prandtl number. It is found that the permeability has a stabilizing influence on the onset of thermal instability. Furthermore, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls' temperature. The effects of other parameters are also discussed.

CITED BY
  1. Om , Bhadauria B. S., Khan A., Modulated Centrifugal Convection in a Vertical Rotating Porous Layer Distant from the Axis of Rotation, Transport in Porous Media, 79, 2, 2009. Crossref

  2. Bhadauria B. S., Sherani Aalam, Onset of Darcy-Convection in a Magnetic-Fluid-Saturated Porous Medium Subject to Temperature Modulation of the Boundaries, Transport in Porous Media, 73, 3, 2008. Crossref

  3. Bhadauria B. S., Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium, Journal of Heat Transfer, 130, 5, 2008. Crossref

  4. Om , Bhadauria B. S., Khan A., Rotating Brinkman–Lapwood Convection with Modulation, Transport in Porous Media, 88, 3, 2011. Crossref

  5. Shivakumara I. S., Lee Jinho, Malashetty M. S., Sureshkumar S., Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium, Transport in Porous Media, 87, 1, 2011. Crossref

  6. Bhadauria B.S., Srivastava Atul K., Magneto-double diffusive convection in an electrically conducting-fluid-saturated porous medium with temperature modulation of the boundaries, International Journal of Heat and Mass Transfer, 53, 11-12, 2010. Crossref

  7. Siddheshwar P. G., Bhadauria B. S., Srivastava Alok, An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation, Transport in Porous Media, 91, 2, 2012. Crossref

  8. Malashetty M. S., Begum Irfana, Effect of Thermal/Gravity Modulation on the Onset of Convection in a Maxwell Fluid Saturated Porous Layer, Transport in Porous Media, 90, 3, 2011. Crossref

  9. Bhadauria B. S., Siddheshwar P. G., Kumar Jogendra, Suthar Om P., Weakly Nonlinear Stability Analysis of Temperature/Gravity-Modulated Stationary Rayleigh–Bénard Convection in a Rotating Porous Medium, Transport in Porous Media, 92, 3, 2012. Crossref

  10. Siddheshwar P.G., Bhadauria B.S., Suthar Om P., Synchronous and asynchronous boundary temperature modulations of Bénard–Darcy convection, International Journal of Non-Linear Mechanics, 49, 2013. Crossref

  11. Bhadauria B. S., Kiran Palle, Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid Under Temperature Modulation, Transport in Porous Media, 100, 2, 2013. Crossref

  12. Bhadauria B. S., Hashim I., Siddheshwar P. G., Effects of Time-Periodic Thermal Boundary Conditions and Internal Heating on Heat Transport in a Porous Medium, Transport in Porous Media, 97, 2, 2013. Crossref

  13. Kolchanova E.A., Kolchanov N.V., Periodic modulation of an equilibrium temperature gradient in a fluid layer and a saturated porous medium layer, Computational Continuum Mechanics, 8, 2, 2015. Crossref

  14. Kiran Palle, Bhadauria B. S., Chaotic Convection in a Porous Medium Under Temperature Modulation, Transport in Porous Media, 107, 3, 2015. Crossref

  15. Kiran Palle, Bhadauria B.S., Nonlinear throughflow effects on thermally modulated porous medium, Ain Shams Engineering Journal, 7, 1, 2016. Crossref

  16. Suthar Om P., Siddheshwar P. G., Bhadauria B. S., A study on the onset of thermally modulated Darcy–Bénard convection, Journal of Engineering Mathematics, 101, 1, 2016. Crossref

  17. Saravanan S., Meenasaranya M., Nonlinear stability of modulated Horton–Rogers–Lapwood problem, International Journal of Engineering Science, 120, 2017. Crossref

  18. Bhadauria B. S., Double diffusive convection in a porous medium with modulated temperature on the boundaries, Transport in Porous Media, 70, 2, 2007. Crossref

  19. Bhadauria B. S., Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries, Journal of Heat Transfer, 129, 7, 2007. Crossref

  20. Bhadauria B. S., Fluid convection in a rotating porous layer under modulated temperature on the boundaries, Transport in Porous Media, 67, 2, 2007. Crossref

  21. Kiran P., Narasimhulu Y., Manjula S.H., Weakly Nonlinear Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium with Throughflow and Temperature Modulation, International Journal of Applied Mechanics and Engineering, 23, 3, 2018. Crossref

  22. Manjula S.H., Kiran Palle, Narsimlu G., Roslan R., The Effect of Modulation on Heat Transport by a Weakly Nonlinear Thermal Instability in the Presence of Applied Magnetic Field and Internal Heating, International Journal of Applied Mechanics and Engineering, 25, 4, 2020. Crossref

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