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The effect of the magnetic field on the Rayleigh-Taylor instability in a couple-stress fluid

Chavaraddi K. B., Awati V. B., Nandeppanavar M. M., Gouder P. M.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 3

611--622

In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.

Onset of surface-tension-driven convection in superposed layers of fluid and saturated porous medium

Shivakumara I. S., Suma S. P., Chavaraddi K. B.

Archives of Mechanics

2006

Vol. 58, nr 2

71-92

The onset of surface-tension-driven convection is studied in a two-layer system comprising an incompressible fluid-saturated porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer is either perfectly heat conducting or insulating, while the upper heat insulating fluid boundary is free and at which the surface tension effects are allowed for. At the contact surface between the fluid-saturated porous medium and the adjacent bulk fluid, both Beavers-Joseph and the Jones conditions are employed. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is obtained for insulating boundaries by using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection is investigated in detail. It is found that the parameter ..., the ratio of the thickness of the fluid layer to that of the porous layer, has a profound effect on the stability of the system.