EFFECT OF CORIOLIS FORCE AND NON UNIFORM BASIC TEMPERATURE GRADIENT ON THE ONSET OF
RAYLIEGH B??NARD - MARANGONI CONVECTION WITH MAXWELL - CATTANEO LAW
The effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law in Rayleigh-B??nard-Marangoni convection in a rotating Newtonian fluid are studied using the Galerkin technique. The effects of one linear and five nonlinear basic temperature gradients are studied on the onset of convection. In the case of Rayleigh ?? B??nard convection, the eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic boundaries. In the case of Marangoni and Rayleigh-B??nard-Marangoni convection the eigenvalues are obtained for an upper free / adiabatic and a lower rigid / isothermal boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.
GURAY RITU
Mathematics