Effect of Suspended Particles on Thermal Convection in Rivlin-Ericksen Fluid in a Darcy-Brinkman Porous Medium

G.C.  Rana; R.C.  Thakur

doi:10.15282/jmes.2.2012.3.0014

Authors

G.C. Rana Department of Mathematics NSCBM Govt. P. G. College, Hamirpur-177 005, Himachal Pradesh INDIA
R.C. Thakur Department of Mathematics Government P. G. College Dhaliara- 177103 Himachal Pradesh INDIA

DOI:

https://doi.org/10.15282/jmes.2.2012.3.0014%20

Keywords:

Brinkman porous medium, Rivlin-Ericksen fluid, suspended particles, thermal convection, viscosity, viscoelasticity.

Abstract

In this paper, the effect of suspended particles on thermal convection in an incompressible Rivlin-Ericksen elastico-viscous fluid in a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying a normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the Darcy number has a stabilising effect, whereas the suspended particles and medium permeability have destabilising effects on the system. The effects of suspended particles, the Darcy number and the medium permeability have been presented graphically to depict the stability characteristics, which are in good agreement with the results derived analytically.

References

Chandrasekhar, S. (1981). Hydrodynamic and hydromagnetic stability. New York: Dover Publication.

Ingham, D. D., & Pop, L. (1981). Transport phenomena in porous media. New York: Elsevier.

Kuznetsov, A. V., & Nield, D. A. (2010). Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transport in Porous Media, 81(3), 409-422.

Lapwood, E. R. (1948). Convection of a fluid in porous medium. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 508-519.

Nield, D. A., & Bejan, A. (2006). Convection in Porous Medium. New York: Springer.

Rana, G.C. 2011. The onset of convection in Rivlin-Ericksen fluid in a Darcy-Brinkman porous medium. International Journal of Pure and Applied Mathematical Sciences, 5, 73-80.

Rana, G. C. (2012). Thermal instability of compressible Rivlin-Ericksen elastico-viscous rotating fluid permitted with suspended dust particles in porous medium. Journal of Applied Mathematics and Mechanics, 8(4), 97-110.

Rana, G. C., & Kumar, S. (2010). Thermal instability of Rivlin-Ericksen Elastico-Viscous rotating fluid permitted with suspended particles and variable gravity field in porous medium. Studia Geotechnica et Mechanica, 32, 39-54.

Rana, G.C., & Thakur, R. C. (2012). A mathematical theorem on the onset of couple-stress fluid permeated with suspended particles saturating a porous medium. International Journal of Multiphysics, 6, 61-72.

Rivlin, R. S., & Ericksen, J. L. (1955). Stress-deformation relations for isotropic materials. Chemistry Biodiversity, 4(2), 323-425.

Satya Narayana, P. V., Ramireddy, G., & Venkataramana, S. (2011). Hall current effects on free-convection MHD flow past a porous plate. International Journal of Automotive and Mechanical Engineering, 3, 350-363.

Scanlon, J. W., & Segel, L. A. (1973). Effect of suspended particles on the onset of Be′nard convection. Physics Fluids, 16, 1573-1578.

Sharma, R. C., & Sharma, V. (1991). Stability of stratified fluid in porous medium in the presence of suspended particles and variable magnetic field. Czech. Journal of Physics, 41, 450-462.

Sharma, R. C., & Sunil. (1994). Thermal instability of an Oldroydian fluid with suspended particles in hydromagnetics in porous medium. Polymer-Plastics Technology and Engineering, 33(3), 323-339.

Sharma, V., Kishore, K., & Rana, G. C. (2001). The instability of streaming Rivlin-Ericksen fluids in porous medium. Studia Geotechnica et Mechanica, 13, 83-93.

Vafai, K., & Hadim, H. A. (2000). Handbook of porous media. New York: M. Decker.

Wooding, R. A. (1960). Rayleigh instability of a thermal boundary layer in flow through a porous medium. Journal of Fluid Mechanics, 9, 183-192.