Stability of stratified incompressible viscoelastic plasma arranged in horizontal strata with quantum pressure and dust particles saturated by a porous medium is investigated. The rheology of the plasma is described by the Walters (model B). The set of non-linear partial differential equations defining the physical system are reduced to linear ordinary differential equations by using the perturbation method, linear theory and normal mode technique. The density, viscosity, viscoelasticity and quantum pressure are assumed to stratify exponentially along the vertical, to obtain exact solutions satisfying the physical boundary conditions and the dispersion relation. The values of growth rate of the unstable perturbed modes are computed numerically to investigate roles that the various variables play on the stability on the considered physical system and are shown graphically. It is observed that the suspended dust particles density and relaxation time factor have a destabilizing effect on the system; whereas viscoelasticity in the presence of suspended dust particles lead to more damping in the frequency of perturbed waves. This work finds applications in diverse fields viz. modern technology, industries, astrophysics, petroleum oil additives, equipment of aero planes etc.
Alfven H, Carlqvist P. Interstellar cloud and the formation of stars. Astrophysics and Space Science. 1978;487–509.
2.
Bird R, Armstrong R, Hassager O. Dynamics of Polymeric Liquids. Fluid Dynamics. 1987;
3.
Chandrashekhar S. Hydrodynamic and hydromagnetic stability. . Oxford University Press. 1961;
4.
Darcy H. Les fontaines publiques de la ville de Dijon. 1856;
5.
Dolai B, Prajapati R. The rotating Rayleigh–Taylor instability in strongly coupled dusty plasma. . Physics of Plasmas. 2018;83708.
6.
Gardner C. The Quantum hydrodynamic model for semiconductor devices. SIAM Journal on Applied Mathematics. 1994;409–27.
7.
Hoshoudy G. Quantum effects on the Rayleigh-Taylor instability of stratified fluid/plasma through porous media. Physics Letters A. 2009;2560–7.
8.
Hoshoudy G. External magnetic field effects on the RTI in an inhomogeneous rotating Quantum plasma. Journal of modern Physics. 2012;1792–801.
9.
Hoshoudy G. Quantum effects on the Rayleigh-Taylor instability of stratified fluid/plasma through porous media. Journal of Modern Physics. 2011;1146–55.
10.
Houshoudy G, Prajapati R. Quantum effects on the Rayleigh Taylor instability of stratified plasma in the presence of suspended particles. Pramana-Journal of Physics. 2016;99.
11.
Houshoudy G, Awasthi M. Compressibility effect on the Kelvin–Helmholtz and Rayleigh–Taylor instabilities. Physics of Plasmas. 2020;
12.
Kumar P, Lal R. On the stability of two superposed viscous viscoelastic Walter B’ fluids. J fluids Eng. 2007;116–9.
13.
Larson G. Instabilities in viscoelastic flows. RheolActa. 1992;213–21.
14.
Lewis D. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc Roy Soc. 1950;81–96.
15.
Prajapati R, Soni D, Chhajlani K. Kelvin-Helomholtz and Rayleigh Taylor instability of two superposed magnetized fluids with suspended dust particles. Z Naturforsch. 2009;455–66.
16.
Prajapati R, Chhajlani R. Kelvin-Helomholtz and Rayleigh Taylor instability of streaming fluids with suspended dust particles flow through porous media. Journal of porous media. 2010;765–77.
17.
Prajapati R. Rayleigh Taylor instability in a non-uniform magnetized strongly coupled viscoelastic fluid. Physics of Plasma. 2016;22106.
18.
Rayleigh L. Investigations of the character of the equilibrium of a incompressible heavy fluid of variable density, Scientific Papers Camb. 1900;
19.
Sharma R. Magneto-Gravitational instability and suspended particles. Astrophysics and Space Science. 1975;255–9.
20.
Sharma C, Sharma K. Rayleigh Taylor instability of two superposed conducting fluids in the presence of suspended particles. Acta Physica Academiae Scientiarum Hungaricae. 1977;251–8.
21.
Sharma V, Rana GC, Kumar S. Stability of stratified Walters’(model B’) fluid in porous medium in the presence of suspended particles and variable magnetic field. Jnanbha. 1999;97–110.
22.
Sharma V, Gupta U. Stability of stratified visco-elastic Walters’(model B’) fluid in presence of uniform horizontal magnetic field and rotation in porous medium. Archives of Mechanics. 2006;187–97.
23.
Sharma V, Shyam R, Sharma S. Numerical investigations of a stability of stratified viscoelastic Walters’ (model B’) fluid/plasma in the presence of quantum physics saturating a porous medium. Journal of Porous Media. 2014;169–76.
24.
Singh M, Kumar P. Hydrodynamic and hydromagnetic stability of stratified Walters B’ elastico-viscous superposed fluids. Int J of Applied Mechanics and Engineering. 2011;233–41.
25.
Singh K. MHD of a viscoelastic fluid through a porous medium in a hot vertical channel. Int journal of applied mechanics. 2016;342–6.
26.
Strömgren B. The Physical State of Interstellar Hydrogen. Astrophysical Journal. 1939;526.
27.
Sunil, Sharma R, Sharma V. Stability of stratified Walters’ (model B’) viscoelastic fluid in stratified porous medium. Studia Geotechnica et Mechenica. 2004;261–235.
28.
Taylor G. The instability of liquid surfaces when accelerated in direction perpendicular to their planes. Proc Roy Soc (Lon) A. 1950;192–6.
29.
Taylor instabilities between two immiscible fluids flowing through a porous medium. The European Physical Journal Plus. :169.
30.
Walters K. The motion of an elastico-viscous liquid contained between concentric spheres. The Quarterly Journal of Mechanics and Applied Mathematics. 1960;325–33.
31.
Yadav B, Ray T. Unsteady flow of n-immiscible viscoelastic fluids through a porous medium between two parallel plates in presence of a transverse magnetic field. Proc Nat Acad. 1991;389.
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