J. Taler et S. Gradziel, THE INVERSE PROBLEMS OF NONLINEAR HEAT-CO NDUCTION IN THERMAL-STRESS MONITORING, Forschung im Ingenieurwesen, 63(4), 1997, pp. 102-111
A new method to solve the problem of transient a heat conduction in cy
lindrical bodies is presented. This method allows transient temperatur
e and thermal stress distribution to be determined from interior tempe
rature histories. The thermal stresses at the inner surface can be est
imated by a temperature sensor placed only at the outer surface. The p
roblem of inverse heat conduction was solved using the least squares m
ethod with the following stabilizing techniques: smoothing of the temp
erature-time curves, regularization of the inverse algorithm, future t
ime 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 temperatu
re coefficient and thermal stresses at the inner surface of a thick-wa
lled cylinder using temperature histories from three locations on the
outer surface.