The inverse problems of nonlinear heat conduction in thermal stress monitoring

A new method to solve the problem of transient a heat conduction in cylindrical bodies is presented. This method allows transient temperature and thermal stress distribution to be determined from interior temperature histories. The thermal stresses at the inner surface can be estimated by a temperature sensor placed only at the outer surface. The problem of inverse heat conduction was solved using the least squares method with the following stabilizing techniques: smoothing of the temperature-time curves, regularization of the inverse algorithm, future time steps. Two examples are shown to demonstrate the influence of the number of temperature sensors on the accuracy of the calculation In a third example, the developed method is used to calculate the temperature coefficient and thermal stresses at the inner surface of a thick-walled cylinder using temperature histories from three locations on the outer surface.