Abstract
Abstract The transient temperature distribution and thermal stresses resulting from aerodynamic heating in the skin of a vehicle at hypersonic speeds are found analytically for a finite slab in which one boundary has a variable coefficient of heat transfer and a variable adiabatic wall temperature while the other boundary is insulated. The purpose of this paper is to introduce the concept of using exponential functions of time to represent the coefficient of heat transfer and the adiabatic wall temperature. In general, one can choose as many exponential functions as necessary to obtain a better solution since the solution is a straightforward mathematical problem. This paper has considered the sum of two exponential functions and a constant for the coefficient of heat transfer and the sum of two exponential functions and a constant for the adiabatic wall temperature. This represents several types of aerodynamic heating problems. Solutions for three special cases are given to show that the general solution also can be applied to simpler problems.
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