BOUNDS FOR THE GROWTH RATE OF PERTURBATION IN A COUPLE-STRESS FLUID IN THE PRESENCE OF ROTATION AND MAGNETIC FIELD IN A POROUS MEDIUM

摘要

A layer of couple-stress fluid heated from below in a porous medium is considered in the presence of uniform vertical magnetic field and rotation. 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 and rotation 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 σ of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-ring enclosed by the two semi-circles of radii, ε/2 {Q - {the square root of}(Q~2 + 4T_A)} and ε/2 {Q + {the square root of}(Q~2 + 4T_A)}, in the right half of the σ_r-σ_i plane whose centers are at the origin, where T_A is the Taylor number, Q is the Chandrasekhar number, and ε is the porosity of the porous medium. Further, it has been established that the sufficient condition for the validity of the "principle of exchange of stability" in magneto-rotatory thermal convection in a couple-stress fluid in a porous medium is that Q/{the square root of}(Q~2 + 4T_A) ≤ 1, and that the existence of oscillatory motions of growing amplitude in the present configuration depends crucially upon the magnitude of the nondimensional number Q/{the square root of}(Q~2 + 4T_A), in the sense so long as 0