Analytical solution of the one-dimensional nonlinear inverse heat conduction problem and its applications

1993 ◽  
Vol 65 (6) ◽  
pp. 1240-1245 ◽  
Author(s):  
N. M. Tsirel'man ◽  
Yu. Yu. Rykachev
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
One Dimensional ◽  
The One

An Initial Value Approach to the Inverse Heat Conduction Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 248-256 ◽  
Author(s):  
E. Hensel ◽  
R. G. Hills
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Initial Value ◽  
Surface Conditions ◽  
One Dimensional ◽  
The One

The one-dimensional linear inverse problem of heat conduction is considered. An initial value technique is developed which solves the inverse problem without need for iteration. Simultaneous estimates of the surface temperature and heat flux histories are obtained from measurements taken at a subsurface location. Past and future measurement times are inherently used in the analysis. The tradeoff that exists between resolution and variance of the estimates of the surface conditions is discussed quantitatively. A stabilizing matrix is introduced to the analysis, and its effect on the resolution and variance of the estimates is quantified. The technique is applied to “exact” and “noisy” numerically simulated experimental data. Results are presented which indicate the technique is capable of handling both exact and noisy data.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

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