Estimation of thermal properties or diffusion properties from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Bodies of infinite extent are a particular challenge from this perspective. Even for exact analytical solutions, because the solution often has the form of an improper integral that must be evaluated numerically, lengthy computer-evaluation time is a challenge. The subject of this paper is improving the computer evaluation time for exact solutions for infinite and semi-infinite bodies in the cylindrical coordinate system. The motivating applications for the present work include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. In this paper, the computer evaluation time is improved by replacing the integral-containing solution by a suitable finite-body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized, by a suitable choice of the extent of the finite body. The key finding of this paper is that the resulting series may be accurately evaluated with a fixed number of terms at any value of time, which removes a long-standing difficulty with series solution in general. The method is demonstrated for the one-dimensional case of a large body with a cylindrical hole and is extended to two-dimensional geometries of practical interest. The computer-evaluation time for the finite-body solutions are shown to be hundreds or thousands of time faster than the infinite-body solutions, depending on the geometry.

References

References
1.
ASME
,
2009
, “
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
,” American Society of Mechanical Engineers, New York, Standard No.
ASME V V 20-2009
.
2.
McMasters
,
R. L.
,
Dowding
,
K. J.
,
Beck
,
J. V.
, and
Yen
,
D.
,
2002
, “
Methodology to Generate Accurate Solutions for Verification in Transient Three-Dimensional Heat Conduction
,”
J. Numer. Heat Transfer, Part B
,
41
(
6
), pp.
521
541
.
3.
Beck
,
J. V.
,
McMasters
,
R. L.
,
Dowding
,
K. J.
, and
Amos
,
D. E.
,
2006
, “
Intrinsic Verification Methods in Linear Heat Conduction
,”
Int. J. Heat Mass Transfer
,
49
(17–18), pp.
2984
2994
.
4.
Tian
,
T.
, and
Cole
,
K. D.
,
2012
, “
Anisotropic Thermal Conductivity Measurements of Carbon-Fiber/Epoxy Composites
,”
Int. J. Heat Mass Transfer
,
55
(23–24), pp.
6530
6537
.
5.
Guo
,
J.
,
Wang
,
X.
, and
Wang
,
T.
,
2007
, “
Thermal Characterization of Microscale Conductive and Nonconductive Wires Using Transient Electrothermal Technique
,”
J. Appl. Phys.
,
101
(
6
), p.
063537
.
6.
Woodbury
,
K. A.
,
Beck
,
J. V.
, and
Najafi
,
H.
,
2014
, “
Filter Solution of Inverse Heat Conduction Problem Using Measured Temperature History as Remote Boundary Condition
,”
Int. J. Heat Mass Transfer
,
72
, pp.
139
147
.
7.
Beck
,
J. V.
,
Blackwell
,
B.
, and
Clair
,
C. R. S.
, Jr.
,
1985
,
Inverse Heat Conduction—III: Posed Problems
,
Wiley
, New York.
8.
Busswell
,
G. S.
,
Banerjee
,
R.
,
Thambynayagam
,
R. M.
, and
Spath
,
J. B.
,
2006
, “
Generalized Analytical Solution for Reservoir Problems With Multiple Wells and Boundary Conditions
,”
Intelligent Energy Conference and Exhibition
, Amsterdam, The Netherlands, Apr. 11–13, SPE Paper No.
SPE-99288
.
9.
Cheng
,
W.-L.
,
Huang
,
Y.-H.
,
Lu
,
D.-T.
, and
Yin
,
H.-R.
,
2011
, “
A Novel Analytical Transient Heat-Conduction Time Function for Heat Transfer in Steam Injection Wells Considering the Wellbore Heat Capacity
,”
Energy
,
36
(
7
), pp.
4080
4088
.
10.
Yeh
,
H.-D.
,
Yang
,
S.-Y.
, and
Peng
,
H.-Y.
,
2003
, “
A New Closed-Form Solution for a Radial Two-Layer Drawdown Equation for Groundwater Under Constant-Flux Pumping in a Finite-Radius Well
,”
Adv. Water Resour.
,
26
(
7
), pp.
747
757
.
11.
Clow
,
G. D.
,
2015
, “
A Green’s Function Approach for Assessing the Thermal Disturbance Caused by Drilling Deep Boreholes in Rock or Ice
,”
Geophys. J. Int.
,
203
(
3
), pp.
1877
1895
.
12.
McMasters
,
R. L.
,
Dinwiddie
,
R. B.
, and
Haji-Sheikh
,
A.
,
2007
, “
Estimating the Thermal Conductivity of a Film on a Known Substrate
,”
J. Thermophys. Heat Transfer
,
21
(
4
), pp.
681
687
.
13.
Zeng
,
H. Y.
,
Diao
,
N. R.
, and
Fang
,
Z. H.
,
2002
, “
A Finite Line-Source Model for Boreholes in Geothermal Heat Exchangers
,”
Heat Transfer Asian Res.
,
31
(
7
), pp.
558
567
.
14.
Lamarche
,
L.
, and
Beauchamp
,
B.
,
2007
, “
A New Contribution to the Finite Line-Source Model for Geothermal Boreholes
,”
Energy Build.
,
39
(
2
), pp.
188
198
.
15.
Healy
,
J. J.
,
de Groot
,
J. J.
, and
Kestin
,
J.
,
1976
, “
The Theory of the Transient Hot-Wire Method for Measuring Thermal Conductivity
,”
Physica B+C
,
82
(
2
), pp.
392
408
.
16.
Beck
,
J. V.
, and
Litkouhi
,
B.
,
1988
, “
Heat Conduction Number System
,”
Int. J. Heat Mass Transfer
,
31
(
3
), pp.
505
515
.
17.
Cole
,
K. D.
,
Woodbury
,
K.
,
Amos
,
D. E.
,
Beck
,
J. V.
,
Crittenden
,
P. E.
,
De Monte
,
F.
, and
Haji-Sheikh
,
A.
,
Guimaraes
,
G.
,
McMasters
,
R.
, and
Roberty
,
N.
, 2017, “
EXACT Analytical Conduction Toolbox
,” University of Nebraska–Lincoln, Lincoln, NE, accessed Oct. 4, 2015, http://exact.unl.edu
18.
Cole
,
K. D.
,
Beck
,
J. V.
,
Haji-Sheikh
,
A.
, and
Litkouhi
,
B.
,
2011
,
Heat Conduction Using Green’s Functions
,
2nd ed.
,
CRC Press
, Boca Raton, FL.
19.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
2007
,
Numerical Recipes: The Art of Scientific Computing
,
3rd ed.
,
Cambridge University Press
, Cambridge, UK.
20.
de Monte
,
F.
,
Beck
,
J. V.
, and
Amos
,
D. E.
,
2012
, “
Solving Two-Dimensional Cartesian Unsteady Heat Conduction Problems for Small Values of the Time
,”
Int. J. Therm. Sci.
,
60
, pp.
106
113
.
21.
Cole
,
K. D.
,
2004
, “
Fast-Converging Series for Heat Conduction in the Circular Cylinder
,”
J. Eng. Math.
,
49
(
3
), pp.
217
232
.
You do not currently have access to this content.