A note on the effects of healing and relaxation in helium II due to heat transfer at a wall

The problem of heat transfer at a wall bounding a half-space (z > 0) containing liquid helium II is considered. The helium is modelled as a two-fluid continuum (after Landau and Lifshitz, Course of Theoretical Physics. Vol. 6. Reading. Mass. Addison-Wesley (1959)) with both relaxation and healing terms incorporated into the governing equations. The heat transfer is taken to be small so that the problem can be treated as the perturbation of the equilibrium state (i.e. at zero heat transfer). It is shown that if the relaxation coefficient varies as (superfluid density)sup(-m) (1 > m => 1/2) then the superfluid velocity behaves like czsup(2m-1) as z → 0. The constant c can be obtained by invoking a scaling property of the full equations. It is found that the healing parameter can be scaled out of the full equations although c can be found explicitly for small healing: c, and the related temperature at the wall, are therefore known for all values of the healing coefficient. These results reduce to those obtained by Clark (Ph.D. Thesis. (1963)) when healing and relaxation are ignored. (author)