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Stable solution to nonstationary inverse heat conduction equation

Joachimiak M., Ciałkowski M.

Archives of Thermodynamics

2018

Vol. 39, no 1

25--37

The paper presents investigations related to solving of a direct and inverse problem of a non-stationary heat conduction equation for a cylinder. The solution of the inverse problem in the form of temperature distributions has been obtained through minimization of a functional being the measure of the difference between the values of measured and calculated temperatures in M points of the heated cylinder. The solution of the conduction equation was presented in the convolutional form and then numerically integrated approximating one of the integrand with a step function described with parameter Θ ∈ (0, 1]. The influence of the integration parameter Θ on the obtained solution of the inverse problem (including a number of temperature measurement points inside the heated body) has been analyzed. The influence of the parameter Θ on the sensitivity of the obtained temperature distributions has been investigated.