Unsteady heat transfer in He II with cylindrical geometry

Abstract

Heat transfer in He II with cylindrical geometry, involving stepwise switching on of a heater which forms an internal cylinder, is investigated in this paper using numerical methods. The problem is solved within the framework of the hydrodynamics of superfluid turbulence (HST), in which the density of the vortex tangle L reaches its equilibrium value with respect to the value of the velocity of the normal component (the so-called adiabatic approximation). In this paper we consider two different cases: the adiabatic one, which corresponds to an isolated system; and the isothermal one, which corresponds to a system immersed in a bath filled with He II at a given temperature. The results obtained and those evolved from Dresner's approach are compared using a newly introduced parameter, the Dr number. © 1994.