Determination of the temperature dependent thermophysical properties from temperature responses measured at medium’s boundaries

Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data

“…4(b) is very small with a normalized maximum error of NME(y) = 2.027 × 10 In Table I we further compare our results of this σ = s = 0 case with others. When the average relative errors of thermal conductivity and heat capacity are, respectively, ARE(k)=0.00154% and ARE(c)=0.00023% in the present approach, the results of Yang [8] are ARE(k)=0.012% and ARE(c)=0.012% and the results of Huang and Yan [3] are ARE(k)=0.510% and ARE(c)=0.69%. The accuracy in these estimations are, respectively, in the fifth order of our method, the fourth order of Yang [8], and the third order of Huang and Yan [3].…”

“…The accuracy of our estimations are lost about two orders, which shows that the present approach can be improved. The robustness of the results obtained by Yang [8] can be seen. However, the method by Yang [8] required to suppose some suitable thermophysical functions a priori and the numbers of measured data up to 120 was used to estimate the unknown coefficients.…”

“…The robustness of the results obtained by Yang [8] can be seen. However, the method by Yang [8] required to suppose some suitable thermophysical functions a priori and the numbers of measured data up to 120 was used to estimate the unknown coefficients. The numbers of iteration (NI) used in the solutions were also compared in Table I.…”

“…In this table we have written T and n used in our method at the second column and u 0 at the third column. [8] 5 × 10 For the noised estimations we are also compared our results with that calculated by Huang and Yan [3] and Yang [8] in Table I. The accuracy of our estimations are lost about two orders, which shows that the present approach can be improved.…”

“…It is more difficult than that of the determination of the thermophysical properties of the temporal-dependent type and the spatial-dependent type. In order to calculate this inverse problem, there have appeared certain progress of the methodologies in this issue, including the Laplace transformation method [1], the conjugate gradient method [2][3][4], the least-square method [5], the linear inverse method [6][7][8], the Davidon-Fletcher-Powell method [9], the Kirchhoff and other transformation methods [10][11][12], and the boundary element method [13], as well as the finite difference method [14,15].…”