Transient Heat Transfer in Superfluid Helium — Part II

Abstract

Three classical problems associated with the ordinary diffusion equation concern the temperature in (1) a half-space with clamped heat flux at the free face, (2) a half-space with clamped temperature at the free face, and (3) an infinite medium with a pulsed plane heat source. These problems are also important for the nonlinear diffusion equation based on the Gorter-Mellink relation, which describes heat transport in superfluid helium. A similarity solution to problem (1) , the champed-flux problem, has already been found¹ and compared, with goou agreement, with experimental data of van Sciver.² [A similarity solution is one in which the profiles of temperature rise AT versus distance Z at different times t can be obtained from one another by suitable (different) stretching of the temperature and distance axes.] In this paper, I give similarity solutions in analytic form to problems (2) and (3) , the clamped-temperature and pulsed-source problems.

Research sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corporation.