Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

Abstract

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Péclét number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Péclét number. Fortunately, the closed-form solutions are accurate at Péclét number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.