Phase transitions in materials with thermal memory

A model for thermally induced phase transitions in materials with thermal memory is explored. From a general starting point of the thermodynamics of materials with memory, field equations with an order parameter, temperature and temperature gradient are derived. The heat flux is given by an integral over the history of the temperature gradient. Asymptotic analysis yields that to leading order, there is a relation connecting the discontinuity in the temperature field with the normal velocity of the transition zone. The temperature discontinuity is negligible for low transition zone velocity. The latent heat must depend on velocity and becomes negligible compared with the specific heat as the normal velocity approaches the speed of propagation of thermal disturbances. There is also a condition which is different from the Stefan condition connecting discontinuities in the temperature gradient with velocity, but reduces to this form, under certain approximations, in the low transition zone velocity limit. The circumstances where the transition zone velocity may exceed the speed of thermal disturbances are discussed.