Analytical solution of the overdetermined inverse heat conduction problem with an application to monitoring thermal stresses
The paper presents a technique for determining the transient temperature distribution, when input data as thermocouple responses are known at several interior locations. If the temperature field is known, then the thermal stresses can be calculated. The problem is overdetermined and is solved using a least squares method that minimizes the error between the computed and measured thermocouple temperatures. The present method incorporates the advantages of simplicity and accuracy of analytical solutions. Several numerical examples and measurements are presented as an indication of the accuracy of the presented method.