Self-similar expansion of dense matter due to heat transfer by nonlinear conduction

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Abstract
The hydrodynamic flow, called the ablative heat wave, from a dense body which is suddenly brought into contact with a thermal bath with a temperature of the order of 105–108°K is investigated theoretically. It is shown that the hydrodynamic equations with nonlinear conduction admit a self‐similar solution of the asymptotic type, i.e., approached by the flow for t→∞. Self‐similarity is a consequence of the fact that the solid may be considered as infinitely dense in this limit, even for a bath temperature varying in time according to T∼tτ (within certain limits for τ). The self‐similar solution is calculated in detail, and scaling relations for the hydrodynamic variables are given. Numerical values are obtained for the radiative heating of gold. The range of validity of the solution is discussed.