Conducting infrared thermographic nondestructive testing (NDT) by the internal heat generated by Joule effect of components is a new heating approach for flaw detection. Due to the combination of electric field and thermal field, the irregular geometric boundary and the complicated internal heat source distribution, the theoretical solution of transient temperature field is very difficult. Nowadays numerical solution by FEM and FDM is mainly applied. By adopting certain assumptions, this paper presents a method to obtain the approximate temperature field by using Green’s function, and gives the solution of a two-dimensional rectangular field including a circular flaw. By contrast, the result tallies with the FEM results well.

1.
Huang
,
Li
,
Zhuoqiu
,
Li
,
Xianhui
,
Song
, and
Hongbing
,
Qian
, 2003, “
Infrared Thermographic Inspection for the Crack in Carbon Fiber Reinforced Concrete
,”
Exp. Mech.
0014-4851,
18
, pp.
403
408
.
2.
Sakagami
,
Takahide
, and
Ogura
,
Keiji
, 1994, “
Thermographic NDT Based on Transient Temperature Field Under Joule Effect Heating
,”
Proc. SPIE
0277-786X,
2245
, pp.
120
130
.
3.
Sakagami
,
Takahide
, and
Kubo
,
Shiro
, 2002, “
Applications of Pulse Heating Thermography and Lock-In Thermography to Quantitative Nondestructive Evaluations
,”
Infrared Phys. Technol.
1350-4495,
43
, pp.
211
218
.
4.
Cole
,
Kevin D.
, and
Yen
,
David H. Y.
, 2001, “
Green’s Functions, Temperature and Heat Flux in the Rectangle
,”
Int. J. Heat Mass Transfer
0017-9310,
44
, pp.
3883
3894
.
5.
Efstathios
,
Zhi-Gangfeng
, and
Mirchaelides
,
E.
, 1997, “
The Use of Modified Green’s Functions in Unsteady Heat Transfer
,”
Int. J. Heat Mass Transfer
0017-9310,
40
, pp.
2997
3002
.
6.
Melnikov
,
Y. A.
, 2000, “
An Alternative Construction of Green’s Functions for the Two-Dimensional Heat Equation
,”
Eng. Anal. Boundary Elem.
0955-7997,
24
, pp.
467
475
.
7.
Ozisik
,
M. N.
, and
Changming
,
Yu
, 1984,
Heat Conduction
,
Advanced Education Press
.
8.
Carslaw
,
H. S.
, and
Jaeger
,
J. S.
, 1947,
Conduction of Heat in Solids
,
Clarendon Press
, Oxford.
9.
Beck
,
J. V.
,
Cole
,
K. D.
,
Haji-Sheikh
,
A.
, and
Litkouhi
,
B.
, 1992,
Heat Conduction Using Green’s Functions
,
Hemisphere
, Washington, D.C.
10.
Stakgold
,
I.
, 1979,
Green’s Functions and Boundary Value Problems
,
Wiley–Interscience
, New York.
11.
Beck
,
J. V.
, 1984, “
Green’s Function Solution for Transient Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
0017-9310,
27
, pp.
1235
1244
.
12.
Qiangsheng
,
Yang
, and
Baorong
,
Pu
, 2001,
Advanced Heat Conduction
,
Shanghai Communication University Press
.
13.
Kunmiao
,
Xu
, 1979,
Method of Mathematical Physics
,
The People’s Education Press
.
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