Heat transfer at low temperatures: Application to sapphire

It is found that at low temperatures, the Callaway expression for the lattice thermal conductivity of a sample having dislocations reduces to the expression obtained by Dubey based on the nonlinear heat transfer theory. The obtained expression is used to explain the measurements of Wolfimeyer and Dillinger of phonon conductivity of sapphire in the temperature range 0.4–4 K.