A class of magnetic fileds which keep the self-similarity for the problems of free magnetohydrodynamic thermal convection

M. Ya. Antimirov , I. M. Volodko , O. V. Zhirnov , A. Yu. Podvysotskii

Riga Technical University, Riga LV-1000, Latvia

Abstract
In this paper the exact asymptotic solutions for the self-similar problems of the free thermal convection near a semi-infinite vertica l plate and above a wall plume in the transverse magnetic fields for Prandtl number Pr << 1 and Lykoudis number Ly -> ininity are obtained. The matched asymptotic expansions method was used. Moreover, the exact numerical solutions of these problems also were obtained for Pr = 0.01, 0.0625, 0.1, 1.0 and for such large Ly, at which the free thermal convection is fully sup-pressed (up to Ly = 20 for the vertical plate and up to Ly = 50 for the wall plume). Simultaneously the exact numerical solutions for a free thermal convection above line horizontal heat source in the similar transverse magnetic field were obtained and the region of Gray s asymptotic and approximate solutions applicability was es-timated. The new asymptotic formula was also obtained for the velocity of fluid on a vertical axis above line horizontal heat source at Pr << 1 and Ly -> infinity; this formula gives very small error for Ly >= 2 and Pr << 1. In all cases the asymptotic solutions practically coincide with the exact numerical solutions for Ly = 10 and are very close to them for Ly = 4.