A critical heat flux in superfluid helium is defined applying Landau's criterion for critical velocities to second sound. The velocity of second sound is calculated in the presence of a heat flux and vanishes in the direction of the heat flux at its critical value. As the second-sound modes are the critical modes connected with the $\lambda$ transition this mechanism is expected to be important close to $T_{\lambda }$. Numerical results are obtained from an assumption about the dependence of the entropy on the relative velocity of the normal and superfluid components. They are in reasonable agreement with experimental results.

• Received 1 July 1968

DOI:https://doi.org/10.1103/PhysRev.179.166