CLOSED-FORM EXPRESSION FOR TEMPERATURE IN A SEMI-INFINITE SOLID DUE TO A FAST MOVING SURFACE HEAT-SOURCE

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 Peclet 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 Peclet number. Fortunately, the closed-form solutions are accurate at Peclet number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.