Free-convection heat transfer from a solid surface to liquid Helium II in the presence of a film of either liquid Helium I or helium gas is analyzed mathematically. The analysis includes two heater shapes, a vertical flat plate and a horizontal circular cylinder, each with an isothermal surface. The integral forms of the boundary-layer equations are used to describe the heat transfer and fluid flow processes that occur within the film. The velocity and temperature profiles within the film are approximated by fourth degree polynomials whose coefficients were evaluated by applying a system of boundary conditions which were derived in the usual fashion but are based on assumed discontinuities in both the velocity and temperature profiles at the film-Helium II interface. Calculated results, which include the film thickness, the heat transfer coefficient, and the mass flow in the film, are presented and discussed.

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