Heat Transfer in Liquid Helium II by Internal Convection

The heat transfer in liquid helium II by internal convection is calculated on the basis of Tisza's two-fluid model. One arrives at the following differential equation for the heat current density, q: curlcurlq=-Λ gradTHere T=temperature, Λ=(ρs)²Tηₙ is a numerical constant depending on temperature and pressure only (ρs=entropydensity and ${{η}}ₙ=the{{0ex}{0ex}}viscosity{{0ex}{0ex}}of{{0ex}{0ex}}the{{0ex}{0ex}}normal''{{0ex}{0ex}}fluid$). Comparison with the measurements of the heat transfer in very fine slits by Keesom and co-workers shows only partial agreement. It appears that the heat conductivity of helium II in narrow slits, even in the limit of very small flow, cannot be described by the usual laminary flow solutions of hydrodynamics within the two fluid model, even if one introduces further assumptions such as viscous slip and an Ohm's law type resistance.