Ablation by frictional heating

The ablation problem of a semi-infinite solid, moving at a constant speed parallel to its surface, is investigated. The study includes all induced motions caused by the density differences of various phases of the materials. Some appropriate transformations are introduced to reduce the problem to one where all phases behave as if they had the same density. The reduced problem is then solved by similarity transformations. It is found that the exact solution exists if and only if an inequality is satisfied. The physical interpretation of the inequality is examined. A numerical example is given to illustrate the result.