This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

Issue Section:
Technical Brief
Keywords:
Conduction
Topics:
Algorithms, Boundary-value problems, Errors, Heat conduction, Noise (Sound), Robustness

References

1.
Hensel
,
A.
, and
Hills
,
R.
,
1987
, “
Steady-State Two-Dimensional Inverse Heat Conduction
,”
Inverse Probl. Sci. Eng.
,
15
(
2
), pp.
227
–
240
.
2.
Taler
,
J.
, and
Duda
,
P.
,
2006
,
Solving Direct and Inverse Heat Conduction Problems
,
Springer-Verlag
,
Berlin
.
3.
Hao
,
D. H.
, and
Dinh
,
N. H.
,
1998
,
Methods for Inverse Heat Conduction
,
Peter Lang GmbH
,
Frankfurt, Germany
.
4.
Lattes
,
R.
, and
Lions
,
J.
,
1960
,
Method of Quazi-Reversibility: Application to Partial Differential Equations
,
Elsevier
,
Amsterdam, The Netherlands
.
5.
Wu
,
X.-H.
, and
Tao
,
W.-Q.
,
2008
, “
Meshless Method Based on the Local Weak-Forms for Steady-State Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
,
51
(
11–12
), pp.
3103
–
3112
.
Google Scholar
Crossref
Search ADS
 
6.
Gu
,
Y.
,
Chen
,
W.
, and
He
,
X.-Q.
,
2012
, “
Singular Boundary Method for Steady-State Heat Conduction in Three Dimensional General Anisotropic Media
,”
Int. J. Heat Mass Transfer
,
55
(
17–18
), pp.
4837
–
4848
.
Google Scholar
Crossref
Search ADS
 
7.
Kanjanakijkasem
,
W.
,
2015
, “
A Finite Element Method for Prediction of Unknown Boundary Conditions in Two-Dimensional Steady-State Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
,
88
, pp.
891
–
901
.
Google Scholar
Crossref
Search ADS
 
8.
Wroblewska
,
A.
,
Frackowiak
,
A.
, and
Cialkowski
,
M.
,
2016
, “
Regularization of the Inverse Heat Conduction Problem by the Discrete Fourier Transform
,”
Inverse Probl. Sci. Eng.
,
24
(
2
), pp.
195
–
212
.
Google Scholar
Crossref
Search ADS
 
9.
Mohebbi
,
F.
, and
Sellier
,
M.
,
2016
, “
Parameter Estimation in Heat Conduction Using a Two-Dimensional Inverse Analysis
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
17
(
4
), pp.
274
–
287
.
Google Scholar
Crossref
Search ADS
 
10.
Olson
,
L.
, and
Throne
,
R.
,
2000
, “
A Comparison of Generalized Eigensystem, Truncated Singular Value Decomposition, and Tikhonov Regularization for the Steady Inverse Heat Conduction Problem
,”
Inverse Probl. Eng.
,
8
(
3
), pp.
193
–
227
.
Google Scholar
Crossref
Search ADS
 
11.
Hao
,
D. N.
,
Thanh
,
P. H.
,
Lesnic
,
D.
, and
Johansson
,
B. T.
,
2012
, “
A Boundary Element Method for a Multi-Dimensional Inverse Heat Conduction Problem
,”
Int. J. Comput. Math.
,
89
(
11
), pp.
1540
–
1554
.
Google Scholar
Crossref
Search ADS
 
12.
Tadi
,
M.
, and
Sritharan
,
S. S.
,
2012
, “
Identification of Far-Field Electric Field Based on Near Field Distributed Measurements
,”
Int. J. Comput. Appl. Math.
,
7
(
3
), pp.
235
–
249
.
13.
Hamad
,
A.
, and
Tadi
,
M.
,
2016
, “
A Numerical Method for Inverse Source Problems for Possion and Helmholtz Equations
,”
Phys. Lett. A
,
380
(
44
), pp.
3707
–
3716
.
Google Scholar
Crossref
Search ADS
 
14.
Tadi
,
M.
,
Nandakumaran
,
A. K.
, and
Sritharan
,
S. S.
,
2011
, “
An Inverse Problem for Helmholtz Equation
,”
Inverse Probl. Sci. Eng.
,
19
(
6
), pp.
839
–
854
.
Google Scholar
Crossref
Search ADS
 
15.
Wang
,
Y.
,
Tadi
,
M.
, and
Radenkovic
,
M.
, “
A Numerical Method for an Inverse Problem for Helmholtz Equation With Separable Wave Number
,”
Int. J. Comput. Sci. Math.
(in press).
Copyright © 2017 by ASME
You do not currently have access to this content.