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应用传热学原理建立了轮轨接触传热的二维模型，应用Laplace变换法求出了轮轨接触区的接触温升的解析解。由于解析法难以求出接触区以外的温升，数值方法得以应用，因而应用有限差分法求得了轮轨接触温升的完全数值解。通过比较分析得出，数值解和解析解间的差别随列车速度和蠕滑率的增大而增大;如果只要求轮轨接触区的温升，鉴于解析解计算速度比数值解快得多，从工程应用上来说，解析解可以满足要求。
The two-dimensional model of wheel-rail contact heat transfer was established by applying the principle of heat transfer. The analytical solution of contact temperature rise of wheel-rail contact zone was obtained by Laplace transform method. Because analytic method is difficult to find the temperature rise outside the contact zone, the numerical method is applied. Therefore, the complete numerical solution of the temperature rise of the wheel-rail contact is obtained by finite difference method. Through comparative analysis, the difference between numerical solution and analytical solution increases with the increase of train speed and creep rate. If only the temperature rise of the wheel-rail contact zone is required, the analytical solution is faster than the numerical solution From the engineering point of view, the analytical solution can meet the requirements.