A mathematical theorem on the onset of Couple-Stress fluid permeated with suspended dust particles saturating a porous medium

Authors

  • G Rana
  • R Thakur

DOI:

https://doi.org/10.1260/1750-9548.6.1.61

Abstract

In this paper, the effect of suspended particles on thermal convection in Couple-Stress fluid saturating a porous medium is considered. By applying linear stability theory and normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pl, the couple-stress parameter F and suspended particles parameter B, satisfy the inequality.

References

Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981.

Lapwood, E. R., Convection of a fluid in porous medium, Proc. Camb. Phil. Soc., 1948, 44, 508-519. https://doi.org/10.1017/s030500410002452x

Wooding, R. A., Rayleigh instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 1960, 9, 183-192. https://doi.org/10.1017/s0022112060001031

Scanlon, J. W. and Segel, L. A., Effect of suspended particles on the onset of Benard convection, Physics Fluids, 1973, 16, 1573-78.

Stokes, V. K., Couple-stress in fluids, Phys. Fluids, 1966, 9, 1709-1715.

Walicki, E. and Walicka, A., Inertial effect in the squeeze film of couple-stress fluids in biological bearings, Int. J. Appl. Mech. Engg., 1999, 4, 363-373.

Sharma, R. C. and Sharma, M., Effect of suspended particles on couple-stress fluid in the presence of rotation and magnetic field, J. pure Appl. Math., 2004, 35, 973-989.

Ingham, D. and Pop, L. Transport Phenomena in Porous Media, Elsevier, New York 1981.

Nield, D. A. and Bejan, A., Convection in Porous Medium, Springer, New York, 2006.

Vafai, K. and Hadim, H. A., Hand Book of Porous Media, M. Decker, New York, 2000.

Sharma, V. and Rana, G. C., Thermal instability of a Walters' (model B') elastico-viscous fluid in the presence of variable gravity field and rotation in porous medium, J. Non-Equilib. Thermodyn., 2001, 26, 31-40. https://doi.org/10.1515/jnetdy.2001.003

Rana, G. C. and Kumar, S., Thermal instability of Rivlin-Ericksen Elastico-Viscous rotating fluid permitted with suspended particles and variable gravity field in porous medium, Studia Geotechnica et Mechanica, 2010, XXXII, 39-54. https://doi.org/10.2478/ausm-2014-0016

Kumar, V., Stability of stratified couple-stress dusty fluid in the presence of magnetic field through porous medium, Appl. and Appl. Math., 2011, 6, 510-521.

Rana, G. C. and Sharma, V., Hydromagnetic thermosolutal instability of compressible Walters' (model B') rotating fluid permeated with suspended particles in porous medium, Int. J. of Multiphysics, 2011, 5, 325-338. https://doi.org/10.1260/1750-9548.5.4.325

Published

2012-03-31

How to Cite

Rana, G. and Thakur, R. (2012) “A mathematical theorem on the onset of Couple-Stress fluid permeated with suspended dust particles saturating a porous medium”, The International Journal of Multiphysics, 6(1), pp. 61-72. doi: 10.1260/1750-9548.6.1.61.

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Section

Articles