Heat Transfer in Liquid Helium II through an Extremely Fine Slit

Abstract

Assuming a film of pure superfluid on the wall and introducing a mutual friction somewhat different from that suggested by Gorter, the heat conductivity is calculated on the basis of the two fluid model and internal convection. Our formula of the heat conductivity shows a fairly good agreement with the experiments including the case of very narrow slits. The London-Zilsel’s formula is also included as a special case.
In very narrow slits, the heat conductivity approximates to ⟨K⟩=s_λ²T^r+1d⁄2BT_λ. Here T: absolute temperature, d: slit width, T_λ: transition temperature, s_λ: entropy per gram at T_λ, r: numerical constant 5.5∼5.6, B is the quantity concerning with the film and the mutual friction. At the temperature near T_λ, ⟨K⟩ is approximately s_λ²⁄A₁T_λ^2r·(T_λ^r−T^r)T^r+1. A₁ is the quantity concerning with the mutual friction. At the intermediate slit width and temperature, ⟨K⟩ approximates to the London-Zilsel’s formula. B, A₁, and critical velocity are discussed and the numerical values are calculated.