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In the present paper, the thermal convection in couple stress fluid under rotation saturating a porous medium is considered. By applying linear stability theory and normal mode analysis method, a semi-circle theorem is derived. The mathematical analysis on the onset of thermal convection in a couple-stress fluid under rotation in a porous medium for the case of rigid boundaries shows that the complex growth rate σ of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside a semi-circle in the right half of a complex σ-plane, which prescribes the upper limits to the complex growth of arbitrary oscillatory motions of growing amplitude

A semi-circle theorem on the onset of couple stress fluid under rotation saturated by a porous medium