Double- Diffusive Convection of a Kuvshiniski Viscoelastic Fluid through a Porous Medium

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Published: 2021-01-30

Page: 216-232


Mahinder Singh *

Department of Mathematics, Govt Post Graduate College Seema (Rohru), Distt Shimla, Himachal Pradesh, 171207, India.

*Author to whom correspondence should be addressed.


Abstract

The effect of magnetic field on an incompressible Kuvshiniski viscoelastic rotating fluid heated and soluted from below is considered. For the case of stationary convection medium permeability and stable solute gradient have destabilizing and stabilizing effect on the double- diffusive convection. Magnetic field and stable solute gradient have stabilizing effect, where as medium permeability has destabilizing effect in absence of rotation and in presence of rotation having both stabilizing as well as destabilizing  effect in the double- diffusive convection of  kuvshiniski viscoelastic fluid. It is also found that rotation, magnetic field and stable solute gradient introduce oscillatory modes in the system, where as in their absence principal of exchange of stabilities is satisfied. Graphs also have been plotted by giving some numerical values to the parameters.

Keywords: Thermosolutal instability, kuvshiniski viscoelastic incompressible fluid, effect of rotation, magnetic field and porous medium.


How to Cite

Singh, M. (2021). Double- Diffusive Convection of a Kuvshiniski Viscoelastic Fluid through a Porous Medium. Asian Journal of Pure and Applied Mathematics, 2(1), 216–232. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/938

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References

Benard H. Les tourbillions cellulaires dans une nappe liquid. Revue General des Science Pures et appliqués. 1900;11:1261-1271.

Rayleigh L. On convection currents in a horizontal layer of fluid, when the higher temperature is on the underside. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science. 1916;32(192):529-546.

Jeffreys H. The stability of a layer of fluid heated below. The London Edinburgh and Dublin Philosophical Magazine and Journal of Science. 1926;2(10):833–844.

Chandrasekhar S. Hyderodynamic and hyderomagnetic stability. Oxford Claredon Press; 1961.

Lapwood ER. Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 1948;44:508- 521.

Wooding RA. Rayleigh instability of a thermal boundary layer in flow through a porous medium. J. Fluid Mechanics. 1960;9:183–192.

Chaudhary RKS, Singh KK. Flow of a dusty visco – elstic (Kuvshiniski – Type) liquid down an inclined plane, Proc. Nat. Acad., India. 1999;61A(II):223.

Johari R, Gupta GD. MHD flow of a dusty visco – elastic (Kuvshiniski– type) liquid past an inclined plane, Acta Cin. India. 1999;XXVM(3):275.

Varshney NK, Dwivedi RK. Unsteady effect on MHD free convection and mass transfer flow of Kuvshiniski fluid through porous medium with constant suction, heat and mass flux. Acta Ciencia Indica. 2004;2:271–280.

Kumar P, Singh M. On a viscoelastic fluid heated from below in a porous medium. J. Non – Equilibrium Thermodynamics. 2006;31:189–203.

Kumar P, Singh M. Thermal instability of Kuvshiniski viscoelastic fluid with fine dust in a porous medium. IJAME( Poland). 2008;13(1):193–201.

Prakash O, Kumar D, Dwivedi RK. MHD free convective flow of a visco – elastic (Kuvshiniski – type) dusty gas through a semi infinite plate moving with velocity decreasing exponentially with time and radiative heat transfer. AIP Advances. 2011;221-229.

Kumar P. Magneto – rotatory stability of two stratified Kuvshiniski viscoelastic superposed fluids in porous medium. GJP & A. Sc. and Tech. 2011;1:28–35.

Kumar V, Kumar P. Thermal convection in a (Kuvshiniski – type) viscoelastic rotating fluid in the presence of magnetic field through porous medium. IJE Transaction A: Basic. 2013;26(7):753–760.

Kuvshiniski EV. Flow of dusty visco – elastic fluid ( Kuvshiniski type) between two oscillating plates. J. Experimental Theoretical Physics( USSR). 1951;21:88.

Mandal GC, Mukherjee SK, Kukherjee S. Unsteady flow of dusty visco – elastic liquid between two oscillating plates. J. Indian Institute of Science. 1986;66:77–83.

Singh M. On thermal instability of Kuvshiniski fluid with suspended particles saturated in a porous medium in the presence of magnetic field. IJAME. 2017;22(4):981–994.

Spiegel EA. Stellar Evolution. Astrophys. J. 1965;141:1068.