Thermal Conduction in Liquid Helium II. II. Effects of Channel Geometry

The critical heat-current density $W_c$ in liquid helium II has been measured as a function of temperature in channels of various geometries. For channels of both circular and rectangular cross section, $W_c$ varies almost inversely with channel diameter, but for the same hydraulic diameter $W_c$ is about 25% smaller in rectangular channels. In channels with more irregular cross sections, $W_c$ is much smaller than in cylindrical channels of the same hydraulic diameter. The hydraulic diameter is thus not a useful parameter for comparing data obtained in channels of different shape. The temperature dependence of $W_c$ is in all cases similar to that reported in I for a cylindrical channel, and suggests that $W_c$ may be associated with ordinary turbulence below about 1.7°K but at higher temperatures is caused by some other mechanism. The effects of varying the channel length and shape of orifice were also studied. Shortening one of the channels to 60% of its original length had no observable effect on $W_c$. $W_c$ was also unaffected by moderate changes in orifice shape, but a severe constriction apparently disrupted the subcritical flow region so completely that $W_c$ could not be measured at all. Various theories of the origin of the critical velocity are discussed in the light of these measurements.