The Journal of the Indian Mathematical Society

S. K. Kango ¹, G. C. Rana ²

Affiliations
1 Department of Mathematics, Government College, Haripur (Manali) – 175 136, IN
2 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, IN

Abstract

The stability of two superposed Rivlin-Ericksen viscoelastic fluids is considered in the presence of suspended particles and variable magnetic field in porous medium. The system is stable in the potentially stable case and unstable in the potentially unstable case. The effect of a variable horizontal magnetic field is also considered. The presence of magnetic field stabilizes a certain wave number band, whereas the system is unstable for all wave numbers in the absence of the magnetic field for the potentially unstable arrangement.

Keywords

Stability, Viscoelasticity, Rivlin-Ericksen Fluid, Suspended Particles, Variable Magnetic Field, Porous Medium.

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S. K. Kango ¹, Vikram Singh ², G. C. Rana ³

Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali)-175136, IN
2 Department of Mathematics, Jwalaji College, Jwalamukhi (Kangra)-176031, IN
3 Department of Mathematics, Govt. College, Hamirpur-177005, IN

Abstract

The thermosolutal instability of a layer ofWalters' B′ elasticoviscous fluid is considered in the presence of uniform horizontal magnetic field to include the Hall currents in porous medium. For the case of stationary convection, the Hall currents hasten the onset of convection, the magnetic field postpones the onset of convection, medium permeability also postpones the onset of convection in the presence of Hall currents, whereas kinematic viscoelasticity has no effect on the onset of convection. The Hall currents, kinematic viscoelasticity, magnetic field, medium permeability and solute parameter introduce oscillatory modes in the system, which were non-existent in their absence. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are obtained.

Keywords

Thermosolutal Instability, Hall Currents, Walters’ B' Fluid, Viscoelasticity.

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