Determination of temperature due to slip between the wheel and the rail taking into account convective cooling of free surfaces

A computational algorithm for determining temperature due to slip between the train wheel and the rail is proposed. The algorithm uses Ling's solution of the mixed two-dimensional quasisteady state thermal-conductivity problem for a half space heated locally by a fast moving distributed heat flow. This solution is calculated using the method of piecewise linear approximation by finite functions. An analytical solution of the problem is obtained for the particular case of uniform distribution of the frictional heat flow rate. The effect of different forms of heat flow rate distribution and the Biot number on the rail temperature field is studied.