Analysis of the Accuracy of the Inverse Marching Method Used to Determine Thermal Stresses in Cylindrical Pressure Components with Holes

In the paper, the inverse solution of the heat conduction problem is analysed, which is applied to calculate transient thermal stresses on the internal surface of a thick-walled pipe weakened by a hole. The analysis considered a one-dimensional heat transfer problem when heat is transferred in a radial direction. In the inverse marching method, the measurement of the wall temperature at one point of a thermally insulated pipeline is used. The technique was verified regarding the distance between the point where the wall temperature is measured and the internal surface, the number of finite volumes in the inverse region, and the time step size are selected. The influence of these parameters on the accuracy of the calculated temperature, thermal stresses, heat transfer coefficient on the internal surface of the pipeline and thermal stresses at the hole edge was assessed. The reference values used to verify the technique were those calculated using the analytical method and the direct solution of the heat conduction problem, and the generated ‘measurement data’ were disturbed by random errors.