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Hall effect on thermal instability of viscoelastic dusty fluid in porous medium

Singh M., Gupta R. K.

International Journal of Applied Mechanics and Engineering

2013

Vol. 18, no. 3

871--886

The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters.

Hall current effect on thermosolutal instability in a viscoelastic fluid flowing in a porous medium

Singh M.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 1

69-82

The thermosolutal instability in a layer of an electrically conducting Oldroydian viscoelastic fluid in a porous medium is studied to include the effect of Hall current. For the case of stationary convection, the Oldroydian fluid behaves like an ordinary Newtonian fluid. The magnetic field and the stable solute gradient are found to have stabilizing effects whereas Hall currents and medium permeability are found to have destabilizing effects on the system. Graphs are plotted by giving numerical values to the parameters to depict the stability characteristics. The sufficient conditions for the non-existence of overstability are also obtained.