EFFECT OF SECOND SOUND ON THE ONSET OF RAYLEIGH-B??NARD-MARANGONI MAGNETO CONVECTION

EFFECT OF SECOND SOUND ON THE ONSET OF RAYLEIGH-B??NARD-MARANGONI MAGNETO CONVECTION

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 an electrically conducting Newtonian fluid are studied using the Galerkin technique. 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.

K.K MALA.

Mathematics