On the upper limits for complex growth rate in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium

It is proved analytically that the complex growth rate n = n_r + in_i (n_r and n_i are the real and imaginary parts of n , respectively) of an arbitrary neutral or unstable oscillatory disturbance of growing amplitude in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium heated from below, for the case of free boundaries, is located inside a semicircle in the right half of the n_rn_i − plane, whose centre is at the origin and radius = maxTaPr2,ReaPrA \sqrt {\max \left( {{T_a}P_r^2,{{{R_{ea}}{P_r}} \over A}} \right)} , where T_a is the modified Taylor’s number, P_r is the modified Prandtl number, R_ea is electric Rayleigh number and A is the ratio of heat capacities. The upper limits for the case of rigid boundaries are derived separately. Furthermore, similar results are also derived for the same configuration when heated from above.