Self-similar problem of the motion of a plane layer of heated material with an arbitrary equation of state

The self-similar problem of the nonstationary motion of a plane layer of material in which energy from an external source is released for values of the flux density q₀ on the boundary which are constant in time is considered. The self-similar variable is = m/t, where m is the Lagrangian mass coordinate and t is the time. The characteristic values of the velocity, density, and pressure do not vary with time. For a self-similar problem the energy flux density q must also depend only on the self-similar variable. In this case q() can be an arbitrary function of its argument and can be given by a table. Examples are presented of actual physical processes in which the mass of the energy-release zone increases linearly with time. The equation of state can have an arbitrary form, including specification by a table. The gaseous state of matter for an arbitrary variable adiabatic exponent, the condensed state, and a two-phase state can be described. A solution of the self-similar problem is presented for the heating of a half-space bounded by a vacuum for a certain specific equation of state and various flux densities q₀ and velocities M of the advance of the energy-release zone.Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 5, pp. 136–145, September–October, 1975.