Some comments on Beck's solution of the inverse problem of heat conduction through the use of Duhamel's theorem

An alternative physical interpretation of Beck's integral solution (1968) of the inverse problem of heat conduction by using Duhamel's theorem, is presented. The use of future temperature data and the minimizing of the least-square error between computed and experimental thermocouple data can be interpreted as matching the thermocouple data accurately over r future times (where r is the number of future temperatures used in inverse solution) and averaging the resulting heat flux values. Limiting values of temperature and heat-flux weighting coefficients for large values of (alpha)(Delta t)/L-squared are presented, where alpha is the thermal diffusivity, Delta t is the time increment, and L is the slab thickness.