Horizontal temperature gradient driven flow and its stability in a horizontal channel of rectangular cross-section with the effects of transversal magnetic field

摘要

An MHD flow is considered which is relevant to horizontal Bridgman crystal growth technique. In the unidirectional parallel flow approximation an analytical solution is found accounting for the finite rectangular cross-section of the channel. Numerical pseudospectral solutions are used to account for the secondary temperature and transversal flow distributions in the approximation of small Peclet number. In the case of vertical magnetic field (parallet to the gravity) complicated flow profiles with "overvelocities "in the corners are typical in the case of finite cross-section channel. The linear stability of the superposed longitudinal and transversal basic flow is investigated by use of Chebyshev pseudospectral method for the longitudinal rolls instability in the finite cross-section channel. The critical Gr number values are computed in the dependence of the Ha number and the aspect ratio, the oscillating unstable flow is represented graphically.