Geometry dependence of steady-state heat flow in He II

Abstract

The Gorter-Mellink equation of steady-state heat transfer in He II is used to develop a method of calculating the peak heat flux for a magnet cooled in a bath of He II. It is shown that the equivalent thermal resistance of a series or parallel arrangement of linear cooling channesl is given by R eq = f(T) 1 3 g eq where f( T) is the inverse of the heat conductivity function and g eq is the equivalent geometry factor respectively defined for series or parallel channels as g s = (Σg 3 i) 1 3 and p = [ Σ(1)/ g i )] −1. Here g i = L 1 3 i/A i where L and A are the channel length and cross-sectional area respectively. The peak heat flux is given by q ∗ = Z(T b )/(A o g en ) where Z( T b) is the integrated heat conductivity function. Specific forms of the peak heat flux are developed for three different winding geometries: a simple pancake-wound magnet, a layer-wound magnet, and a multiply connected coil pack.