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

Abstract

Abstract It is proved analytically that the complex growth rate n = nr + ini (nr and ni 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 nrni − plane, whose centre is at the origin and radius = max T a P r 2 , R ea P r A \sqrt {\max \left( {{T_a}P_r^2,{{{R_{ea}}{P_r}} \over A}} \right)} , where Ta is the modified Taylor’s number, Pr is the modified Prandtl number, Rea 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.