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An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation1
Authors:D W Tang  N Araki
Affiliation:(1) Department of Mechanical Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu, 432-8561, Japan
Abstract:This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.
Keywords:inverse analysis  Levenberg–  Marquardt algorithm  pulse heating  relaxation parameters  thermal diffusivity  universal heat conduction model
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