A transient inverse heat conduction problem focused on gas quenching of steel plates and rings is posed and solved, both analytically and numerically. The quenching objective is to calculate the transient convective heat transfer coefficient which would produce an optimized phase transformation cooling curve. The governing nonlinear heat equation is nondimensionalised, and a small parameter, the reciprocal of the Fourier number, is identified. This allows the construction of an analytic solution in the form of an asymptotic series. For higher values of the reciprocal Fourier number, a numerical scheme incorporating the function specification and Keller Box methods is used to generate solutions. Comparison of the results proves favorable, and suggests that for this inverse problem asymptotic methods provide an attractive alternative to solely numerical ones.

Issue Section:
Conduction
Keywords:
inverse problems, heat conduction, quenching (thermal), cooling, Inverse Heat Transfer Solutions, Gas Quenching, Heat Treatment, Metal Phase Transformation, Transient Heat Conduction
Topics:
Cooling, Inverse problems, Phase transitions, Quenching (Metalworking), Temperature, Heat transfer coefficients, Heat conduction, Plates (structures), Convection
1.
Thuvander, A., Melander, A., Lind, M., Lior, N., and Bark, F., 1999, “Prediction of Convective Heat Transfer Coefficients and Their Effects on Distortion and Mechanical Properties of Cylindrical Steel Bodies Quenched by Gas Cooling,” Paper AJTE99-6289, presented at ASME/JSME Joint Thermal Engng. Conf., San Diego, CA, March 15–19, 1999.
2.
Burggraf
,
O. R.
,
1964
, “
An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications
,”
ASME J. Heat Transfer
,
86C
, pp.
373
–
382
.
3.
O¨zis¸ik, M. N., and Orlande, H. R. B., 2000, Inverse Heat Transfer, Taylor & Francis, New York.
4.
http://www.maplesoft.com
5.
Beck
,
J. V.
,
Litkouhi
,
B.
, and
St. Clair
,
C. R.
, Jr.,
1982
, “
Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem
,”
Numer. Heat Transfer
,
5
, pp.
275
–
286
.
6.
Raynaud
,
M.
, and
Bransier
,
J.
,
1986
, “
A New Finite-Difference Method for the Nonlinear Inverse Heat Conduction Problem
,”
Numer. Heat Transfer
,
9
, pp.
27
–
42
.
7.
Jarny
,
Y.
,
O¨zis¸ik
,
M. N.
, and
Bardon
,
J. P.
,
1991
, “
A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction
,”
Int. J. Heat Mass Transf.
,
34
, pp.
2911
–
2919
.
8.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag.
9.
Beck, J. V., Blackwell, B., and St. Clair, C. R., Jr., 1985, Inverse Heat Conduction-III Posed Problems, Wiley, New York.
10.
Cebeci, T., and Bradshaw, P., 1984, Physical and Computational Aspects of Convective Heat Transfer, Springer, Berlin.
11.
Archambault
,
P.
, and
Azim
,
A.
,
1995
, “
Inverse Resolution of the Heat-Transfer Equation: Application to Steel and Aluminum Alloy Quenching
,”
J. Mater. Eng. Perform.
,
4
, pp.
730
–
736
.
12.
Archambault
,
P.
,
Denis
,
S.
, and
Azim
,
A.
,
1997
, “
Inverse Resolution of the Heat-Transfer Equation With Internal Heat Source: Application to the Quenching of Steels With Phase Transformations
,”
J. Mater. Eng. Perform.
,
6
, pp.
240
–
246
.
13.
Matsevityi
,
Y. M.
,
Multanovskii
,
A. V.
, and
Nemirovskii
,
I. A.
,
1991
, “
Optimization of the Heat-Engineering Processes Involving Utilization of Control and Identification Methods
,”
J. Eng. Phys.
,
59
, pp.
1055
–
1063
.
Copyright © 2003
 by ASME
You do not currently have access to this content.