J. Taler, ANALYTICAL SOLUTION OF THE OVERDETERMINED INVERSE HEAT-CONDUCTION PROBLEM WITH AN APPLICATION TO MONITORING THERMAL-STRESSES, Heat and mass transfer, 33(3), 1997, pp. 209-218
The paper presents a technique for determining the transient temperatu
re distribution, when input data as thermocouple responses are known a
t 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 be
tween the computed and measured thermocouple temperatures. The present
method incorporates the advantages of simplicity and accuracy of anal
ytical solutions. Several numerical examples and measurements are pres
ented as an indication of the accuracy of the presented method.