CXLIII. Thermal convection in a magnetic field

Abstract

The modifications produced in the Rayleigh-Jeffreys theory of slow thermal convection by magneto-hydrodynamic effects in a conducting fluid placed in a magnetic field are examined. Even for a non-viscous fluid, a critical temperature gradient β₀ must be exceeded in order that convection occur. In this, the place of viscosity η occurring in the Rayleigh-Jeffreys formula is taken by a quantity η _H depending on the conductivity of the fluid, the magnetic field strength H and depth of fluid d, thus η _H= (4/27)(d ²/π²)(σμ ²H²/c ²). If the fluid is viscous a multiple of the normal viscosity depending on H must be added to η _H. An estimate of the critical gradient is made tor somewhat artificial boundary conditions and it is found large enough to be experimentally detectable. The applicability of Jeffreys' method of marginal stability is discussed and the nature of possible oscillations investigated.