On a heat exchange problem under sharply changing external conditions

The heat exchange problem between carbon particles and an external environment (water) is stated and investigated based on the equations of heat conducting compressible fluid. The environment parameters are supposed to undergo large and fast variations. In the time of about 100 $\mu$s, the temperature of the environment first increases from the normal one to 2400 K, is preserved at this level for about 60 $\mu$s, and then decreases to 300 K during approximately 50 $\mu$s. At the same periods of time, the pressure of the external environment increases from the normal one to 67 GPa, is preserved at this level, and then decreases to zero. Under such external conditions, the heating of graphite particles of various sizes, their phase transition to the diamond phase, and the subsequent unloading and cooling almost to the initial values of the pressure and temperature without the reverse transition from the diamond to the graphite phase are investigated. Conclusions about the maximal size of diamond particles that can be obtained in experiments on the shock compression of the mixture of graphite with water are drawn.