An Analysis of Exact and Approximate Equations for the Temperature Distribution in an Insulated Thick Skin Subjected to Aerodynamic Heating

The problem of calculating the temperature distribution in an insulated slab is investigated. Exact and approximate solutions are obtained, and the results are compared to determine the ranges of applicability of the approximations. The approximations are found to be within 5 percent of the exact solution when the ratio of the thermal capacitance of the metal to that of the insulation and the ratio of the conductance of the metal to that of the insulation are sufficiently large. The roots of the characteristic equation of the exact solution are generally applicable to the two-slab heat-transfer problem and are tabulated up to the first nine roots.