One method of solving the problem of unsteady heat exchange of a body and its ablation

A simple method is suggested for solution of the unsteady heat exchange and ablation problem. A modification of the method of straight lines with approximation of the temperature field of a body in the direction of its major motion by a cubic spline is proposed. The method is tested in a one dimensional model by comparing it with a known precise solution for the problem of heating and ablation. In contrast to the method of grids at each calculation moment in time the profile of temperature in the body is described by a function which is continuous together with its first and second three dimensional derivatives. For heat exchange problems characteristic for hypersonic flow, only a few bands need be introduced in the direction of the major change in temperature. A significant savings in machine time is achieved since the problem can be solved by a limited number of differential equations for D sub i(t).