Abstract
We discuss the feasibility and likely benefits of studying the superfluid transition of4He very nearT λ in the presence of gravity, and of a finite heat currentQ applied from the top of the sample and extracted from below. Part of or the entire sample can exist in a homogeneous critical state represented by a uniform reduced temperaturet=[T(z)−T λ(z)]/T λ (z is the vertical coordinate) without inducing convection in the HeI layer. Precision measurements of the thermal conductivity and boundary resistance very nearT λ, including inside the nonlinear region, should be possible; but only along a single path in theQ−t plane.
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