A common occurrence in many practical systems is that the desired result is known or given, but the conditions needed for achieving this result are not known. This situation leads to inverse problems, which are of particular interest in thermal processes. For instance, the temperature cycle to which a component must be subjected in order to obtain desired characteristics in a manufacturing system, such as heat treatment or plastic thermoforming, is prescribed. However, the necessary boundary and initial conditions are not known and must be determined by solving the inverse problem. Similarly, an inverse solution may be needed to complete a given physical problem by determining the unknown boundary conditions. Solutions thus obtained are not unique and optimization is generally needed to obtain results within a small region of uncertainty. This review paper discusses several inverse problems that arise in a variety of practical processes and presents some of the approaches that may be used to solve them and obtain acceptable and realistic results. Optimization methods that may be used for reducing the error are presented. A few examples are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. These examples include the heat treatment process, unknown wall temperature distribution in a furnace, and transport in a plume or jet involving the determination of the strength and location of the heat source by employing a few selected data points downstream. Optimization of the positioning of the data points is used to minimize the number of samples needed for accurate predictions.

References

References
1.
Li
,
T.
, ed.,
1985
,
Optical Fiber Communications, Vol. 1: Fiber Fabrication
,
Academic Press
,
New York
.
2.
Jaluria
,
Y.
,
2017
, “
Thermal Transport in the Manufacture of Optical Fibers
,”
Ann. Rev. Heat Transfer
,
20
, pp.
193
239
.
3.
Ozisik
,
M. N.
,
2000
,
Inverse Heat Transfer: Fundamentals and Applications
,
Taylor & Francis
,
Philadelphia, PA
.
4.
Orlande
,
H. R. B.
,
Fudym
,
O.
,
Maillet
,
D.
, and
Cotta
,
R. M.
,
2011
,
Thermal Measurements and Inverse Techniques
,
Taylor and Francis Group, CRC Press
,
Boca Raton, FL
.
5.
Orlande
,
H. R. B.
,
2012
, “
Inverse Problems in Heat Transfer: New Trends on Solution Methodologies and Applications
,”
ASME J. Heat Transfer
,
134
(
3
), p.
031011
.
6.
Ghosh
,
A.
, and
Mallik
,
A. K.
,
1986
,
Manufacturing Science
,
Ellis Horwood
,
Chichester, UK
.
7.
Jaluria
,
Y.
,
1984
, “
Numerical Study of the Thermal Processes in a Furnace
,”
Numer. Heat Transfer
,
7
(
2
), pp.
211
224
.
8.
Jarny
,
Y.
,
Ozisik
,
M. N.
, and
Bardon
,
J. P.
,
1991
, “
A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction
,”
Int. J. Heat Mass Transfer
,
34
(
11
), pp.
2911
2919
.
9.
Prud'homme
,
M.
, and
Nguyen
,
T. H.
,
2001
, “
Solution of Inverse Free Convection Problems by Conjugate Gradient Method: Effects of Rayleigh Number
,”
Int. J. Heat Mass Transfer
,
44
, pp.
2011
2027
.
10.
Burmeister
,
L. C.
,
1993
,
Convective Heat Transfer
,
2nd ed.
,
Wiley Interscience
,
New York
.
11.
Stikker
,
U. O.
,
1970
, “
Numerical Simulation of the Coil Annealing Process
,”
Math. Models Metall. Proc. Dev., Iron Steel Inst., Spec. Rep.
,
123
, pp.
104
113
.
12.
Harvey
,
G. F.
,
1977
, “
Mathematical Simulation of Tight Coil Annealing
,”
J. Australas. Inst. Met.
,
22
, pp.
28
37
.
13.
Jaluria
,
Y.
,
2008
,
Design and Optimization of Thermal Systems
,
2nd ed.
,
CRC Press
,
Boca Raton, FL
.
14.
Cheng
,
X.
, and
Jaluria
,
Y.
,
2005
, “
Effect of Furnace Thermal Configuration on Optical Fiber Heating and Drawing
,”
Numer. Heat Transfer
,
48
(
6
), pp.
507
528
.
15.
Paek
,
U. C.
,
1999
, “
Free Drawing and Polymer Coating of Silica Glass Optical Fibers
,”
ASME J. Heat Transfer
,
121
(4), pp.
775
788
.
16.
Izawa
,
T.
, and
Sudo
,
S.
,
1987
,
Optical Fibers: Materials and Fabrication
,
KTK Scientific Publishers
,
Tokyo, Japan
.
17.
Issa
,
J.
,
Yin
,
Z.
,
Polymeropoulos
,
C. E.
, and
Jaluria
,
Y.
,
1996
, “
Temperature Distribution in an Optical Fiber Draw Tower Furnace
,” ,
4
(3), pp.
221
232
.
18.
Ma
,
Q.
,
Luo
,
Y.
,
Rossmann
,
T.
,
Knight
,
D.
, and
Jaluria
,
Y.
,
2006
, “
Diode Laser Measurements for DDDAS: Flow Field Reconstruction Using Dynamic Experimental and Numerical Data
,”
AIAA
Paper No. 2006-2974.
19.
Knight
,
D.
,
Ma
,
Q.
,
Rossman
,
T.
, and
Jaluria
,
Y.
,
2007
, “
Evaluation of Fluid-Thermal Systems by Dynamic Data Driven Application Systems—Part II
,” ,
Reading, UK
,
May 28–31
, pp.
1189
1196
.
20.
Vanderveer
,
J. R.
, and
Jaluria
,
Y.
,
2013
, “
Solution of an Inverse Convection Problem by a Predictor–Corrector Approach
,”
Int. J. Heat Mass Transfer
,
65
, pp.
123
130
.
21.
Vanderveer
,
J. R.
, and
Jaluria
,
Y.
,
2015
, “
Optimization of an Inverse Convection Solution Strategy
,”
Int. J. Heat Mass Transfer
,
73
, pp.
664
670
.
22.
Mossi
,
A.
,
Vielmo
,
H.
,
Franca
,
F.
, and
Howell
,
J.
,
2008
, “
Inverse Design Involving Combined Radiative and Turbulent Convective Heat Transfer
,”
Int. J. Heat Mass Transfer
,
51
(
11–12
), pp.
3217
3226
.
23.
Hong
,
Y. K.
,
Baek
,
S. W.
, and
Kim
,
M. Y.
,
2010
, “
Inverse Natural Convection Problem With Radiation in Rectangular Enclosure
,”
Numer. Heat Transfer
,
57
(
5
), pp.
315
330
.
24.
Park
,
H.
, and
Chung
,
O.
,
1999
, “
An Inverse Natural Convection Problem of Estimating the Strength of a Heat Source
,”
Int. J. Heat Mass Transfer
,
42
(
23
), pp.
4259
4273
.
25.
Ghosh
,
S.
,
Pratihar
,
D.
,
Maiti
,
B.
, and
Das
,
P.
,
2011
, “
Inverse Estimation of Location of Internal Heat Source in Conduction
,”
Inverse Probl. Sci. Eng.
,
19
(
3
), pp.
337
361
.
26.
Ostrach
,
S.
,
1953
, “
An Analysis of Laminar Free-Convection Flow and Heat Transfer About a Flat Plate Parallel to the Direction of the Generating Body Force
,”
NASA
,
Washington, DC
, Report No. .
27.
Tabrizi
,
A. B.
, and
Jaluria
,
Y.
,
2018
, “
An Optimization Strategy for the Inverse Solution of a Convection Heat Transfer Problem
,”
Int. J. Heat Mass Transfer
,
124
, pp.
1147
1155
.
28.
Poli
,
R.
,
2008
, “
Analysis of the Publications on the Applications of Particle Swarm Optimization
,”
J. Artif. Evol. Appl.
,
2008
, pp.
1
10
.
29.
Kennedy
,
J.
,
1997
, “
The Particle Swarm: Social Adaptation of Knowledge
,”
IEEE International Conference on Evolutionary Computation
,
Indianapolis, IN
,
Apr. 13–16
, pp.
303
308
.
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