Bounds for Complex Growth Rate of Perturbations in Magneto-Thermal Instability in Couple-Stress Fluid in a Porous Medium Re-visited

Monika Khanna1 and Ajaib S. Banyal2

1Research Scholar, Department of Mathematics, Singhania University, Jhunjhunu, Raj., INDIA. 2Department of Mathematics, Govt. College Nadaun, Dist. Hamirpur, H. P., INDIA


A layer of couple-stress fluid heated from below in a porous medium is considered in the presence of uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of couple-stress fluid convection with a uniform vertical magnetic field in porous medium, for any combination of perfectly conducting free and rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, established that the complex growth rate ? of oscillatory perturbations, neutral or unstable, must lie inside a semi-circle , in the right half of a complex ? -plane, Where R is the thermal Rayleigh number, F is the couple-stress parameter of the fluid, l P is the medium permeability, ? is the porosity of the porous medium, 1 p is the thermal Prantl number and 2 p is the magnetic Prandtl number, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in the couple-stress fluid heated from below in the presence of uniform vertical magnetic field in a porous medium. The result is important since the exact solutions of the problem investigated in closed form, are not obtainable for any arbitrary combinations of perfectly conducting dynamically free and rigid boundaries

Keywords :Thermal convection; Couple-Stress Fluid; Magnetic field; PES; Chandrasekhar number.

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