Solution of an inverse heat conduction problem with third-type boundary conditions

2022 ◽  
Vol 175 ◽  
pp. 107466
Author(s):  
Michele Ciofalo
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Type Boundary

scholarly journals A spacetime collocation Trefftz method for solving the inverse heat conduction problem

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986127 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang ◽  
Yan Su
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Heat Conduction Problem ◽  
Domain Boundary ◽  
Inverse Heat Conduction Problem ◽  
Test Problems ◽  
Inverse Heat Conduction ◽  
Trefftz Method ◽  
Base Functions

In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted to solve the inverse heat conduction problem by approximating numerical solutions using Trefftz base functions satisfying the governing equation. The validity of the proposed method is established for a number of test problems. We compared the accuracy of the proposed method with that of the Trefftz method based on exponential basis functions. Results demonstrate that the proposed method obtains highly accurate numerical solutions and that the boundary data on the inaccessible boundary can be recovered even if the accessible data are specified at only one-fourth of the overall spacetime boundary.

scholarly journals Influence of Errors in Known Constants and Boundary Conditions on Solutions of Inverse Heat Conduction Problem

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3313
Author(s):  
Sun Kyoung Kim
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Material Properties ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
One Dimensional ◽  
Boundary Location ◽  
Inverse Heat Conduction Problems

This work examines the effects of the known boundary conditions on the accuracy of the solution in one-dimensional inverse heat conduction problems. The failures in many applications of these problems are attributed to inaccuracy of the specified constants and boundary conditions. Since the boundary conditions and material properties in most thermal problems are imposed with uncertainty, the effects of their inaccuracy should be understood prior to the inverse analyses. The deviation from the exact solution has been examined for each case according to the errors in material properties, boundary location, and known boundary conditions. The results show that the effects of such errors are dramatic. Based on these results, the applicability and limitations of the inverse heat conduction analyses have been evaluated and discussed.

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