Some comments on Beck's solution of the inverse problem of heat conduction through the use of Duhamel's theorem
Abstract
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 leastsquare 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 heatflux weighting coefficients for large values of (alpha)(Delta t)/Lsquared are presented, where alpha is the thermal diffusivity, Delta t is the time increment, and L is the slab thickness.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 February 1983
 DOI:
 10.1016/S00179310(83)800350
 Bibcode:
 1983IJHMT..26..302B
 Keywords:

 Conductive Heat Transfer;
 Heat Flux;
 Heat Transfer Coefficients;
 Least Squares Method;
 Surface Temperature;
 Temperature Measurement;
 Integral Equations;
 Temperature Profiles;
 Thermocouples;
 Truncation Errors;
 Weighting Functions;
 Fluid Mechanics and Heat Transfer