Upper Limits to the Complex Growth Rate in Rotatory-Thermal Instability in a Couple-Stress Fluid in a Porous Medium

The thermal instability of a couple-stress fluid acted upon by uniform vertical rotation and heated from below in a porous medium is investigated. 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 rotation in porous medium, for the case of rigid boundaries shows that the complex growth rate of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle, in the right half of a complex -plane, where is the Taylor number, is the dimensionless medium permeability of the porous medium and F is the couple-stress parameter, which prescribes the upper limits to the complex growth rate of arbitrary oscillatory motions of growing amplitude in a rotatory couple-stress fluid in porous medium heated from below. Further, It is established that the existence of oscillatory motions of growing amplitude in the present configuration, depends crucially upon the magnitude of the non-dimensional number, in the sense so long as, no such motions are possible, and in particular PES is valid.