Magneto Thermosolutal Convection in a Compressible Viscoelastic Fluid

  • Pardeep Kumar Department of Mathematics, ICDEOL, Himachal Pradesh University, Summer-Hill, Shimla-171005 (HP) INDIA
Keywords: Thermosolutal Convection, Compressible Viscoelastic Fluid, Porous Medium, Uniform Magnetic Field

Abstract

In the presence of a magnetic field, a thermosolutal convection is postulated to occur in a compressible Rivlin-Ericksen viscoelastic fluid in a porous media. The dispersion relation is found by using the linear stability theory and the normal mode analysis approach, respectively. In the scenario of stationary convection, it was discovered that compressibility, magnetic fields, and steady solute gradients all serve to delay the beginning of the convection process, but medium permeability serves to speed up the beginning of the convection process. In addition to this, it has been discovered that the system is reliable for [equation not detected by OJS] and under the condition  [equation not detected by OJS]. The system goes into an unstable state. Overstability has also been looked at from the perspective of a scenario in which sufficient circumstances are met to rule out the possibility of the phenomenon occurring. It has been discovered that the steady gradient of the solute and the magnetic field both induce oscillatory modes into the system.

References

Aggarwal, A. K., & Dixit, D. (2017). Thermosolutal instability of Rivlin-Ericksen fluid under the effect of suspended particles and compressibility in porous medium. AIP Conference Proceedings 1897, 020010. https://doi.org/10.1063/1.5008689.

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

Kumar, P. (2000). Rayleigh-Taylor instability of Rivlin-Ericksen elastico-viscous fluids in presence of suspended particles through porous medium. Indian J. Pure Appl. Math. 31, 533-539.

Kumar, P., Lal, L., Sharma, P. (2004). Instability of two rotating viscoelastic (Rivlin-Ericksen) superposed fluids with suspended particles in porous medium. Rom. J. Phys. 49, 209-218.

Kumar, P., Lal, R., Singh, M. (2007). Hydrodynamic and hydromagnetic stability of two stratified Rivlin-Ericksen elastico-viscous superposed fluids. Int. J. Appl. Mech. Engng. 12, 645-653.

Kumar, P., Singh G.J. (2006). Stability of two superposed Rivlin-Ericksen viscoelastic fluids in the presence of suspended particles. Rom. J. Phys. 51, 927-935.

Kumar, P., Singh, G.J., Lal. R. (2005). MHD instability of rotating superposed Rivlin-Ericksen viscoelastic fluids through porous medium. Ganita Sandesh, Rajasthan Ganita Parishad, India. 19, 89-96.

McDonnel, J.A.M. (1978). Cosmic Dust, p. 330, Wiley, New York.

Oldroyd, J.G. (1958). Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc. Roy. Soc. London. A245, 278-297.

Philips, O.M. (1991). Flow and Reaction in Permeable Rocks. Cambridge University Press, Cambridge.

Rivlin, R.S., Ericksen, J.L. (1995). Stress-deformation relaxations for isotropic materials. J. Rat. Mech. Anal. 4, 323-425.

Sharma, R.C. (1977). Thermal instability in compressible fluids in the presence of rotation and magnetic field. J. Mathematical Analysis and Application. 60, 227-235.

Sharma, R.C., Kumar, P. (1997). Hydromagnetic stability of Rivlin-Ericksen elastico-viscous superposed conducting fluids. Z. Naturforsch. 52a, 369-371.

Sharma, R.C., Sharma, K.C. (1978). Rayleigh-Taylor instability of two viscoelastic superposed fluids. Acta Phys. Hung. 45, 213-220.

Spiegel, E.A., Veronis, G. (1960). On the Boussinesq approximation for compressible fluid. Astrophysical J. 131, 442-447.

Toms, B.A., Strawbridge, D.J. (1953). Elastic and viscous properties of dilute solutions of polymethyl methacrylate in organic liquids. Trans. Faraday. 49, 1225-1232.

Veronis, G. (1965). On the finite amplitude instability in thermohaline convection. J. Marine Res. 23, 1-17.

Published
2022-06-20
How to Cite
Kumar, P. (2022). Magneto Thermosolutal Convection in a Compressible Viscoelastic Fluid. Journal La Multiapp, 3(3), 93-103. https://doi.org/10.37899/journallamultiapp.v3i3.650