Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Ideal internal kink modes in a differentially rotating cylindrical plasma

The Velikhov effect leading to magnetorotational instability (MRI) is incorporated into the theory of ideal internal kink modes in a differentially rotating cylindrical plasma column. It is shown that this effect can play a stabilizing role for suitably organized plasma rotation profiles, leading to suppression of MHD (magnetohydrodynamic) instabilities in magnetic confinement systems. The role of this effect in the problem of the Suydam and the m = 1 internal kink modes is elucidated, where m is the poloidal mode number.