Estimation of Thermal Boundary Conditions by Using Hybrid Inverse Approach

Article Preview

Abstract:

The estimation of thermal boundary conditions occurring during heat treatment processes is an essential requirement for characterization of heat transfer phenomena. In this work, the performance of five optimization techniques is studied. These models are the Conjugate Gradient Method, the Levenberg-Marquardt Method, the Simplex method, the NSGA II algorithm and a hybrid approach based on the NSGA II and Levenberg-Marquardt Method sequence. The models are used to estimate the heat transfer coefficient in 2D axis symmetrical case during transient heat transfer. The performance of the optimization methods is demonstrated using numerical experiments.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

419-424

Citation:

Online since:

February 2015

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2015 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] J.V. Beck, B. Blackwell, C.R. St Clair Jr., Inverse Heat Conduction, Wiley, New York, (1985).

Google Scholar

[2] A.N. Tikhonov, V.Y. Arsenin, Solution of Ill-posed Problems, Winston, Washington, DC, (1977).

Google Scholar

[3] O.M. Alifanov, Inverse Heat Transfer Problems, Springer, Berlin/Heidelberg, (1994).

Google Scholar

[4] M.N. Özisik, H.R.B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor & Francis, New York, (2000).

Google Scholar

[5] J.A. Nelder, R. Mead, A simplex method for function minimization, Comput. J. 7 (1965) 308–313.

Google Scholar

[6] J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the Nelder–Mead simplex method in low dimensions, SIAM J. Optimiz. 9 (1996) 112–147.

DOI: 10.1137/s1052623496303470

Google Scholar

[7] R. Das: A simplex search method for a conductive–convective fin with variable conductivity, International Journal of Heat and Mass Transfer 54 (2011) 5001–5009.

DOI: 10.1016/j.ijheatmasstransfer.2011.07.014

Google Scholar

[8] O. Nelles, Nonlinear system identification, Springer-Verlag, Berlin, (2001).

Google Scholar

[9] Fletcher, R. and Reeves C. M., Function Minimization by Conjugate Gradients, Computer J. 7 (1964) 149-154.

Google Scholar

[10] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6 (2002) 182–197.

DOI: 10.1109/4235.996017

Google Scholar

[11] K. Deb, Multi-objective Optimization Using Evolutionary Algorithms, Wiley Chichester UK (2001).

Google Scholar

[12] D.A.V. Veldhuizen, G.B. Lamont, Multi-objective evolutionary algorithms: analyzing the state-of-the-art, Evolutionary Computation 8 (2000) 125–147.

DOI: 10.1162/106365600568158

Google Scholar

[13] J. Clark and R. Tye: Thermophysical properties reference data for some key engineering alloys,. High temperatures – high pressures 35/362003/2004 1-14.

DOI: 10.1068/htjr087

Google Scholar

[14] A. Majorek, B. Scholtes, H. Müller, E. Macherauch: Influence of heat transfer on development of residual stresses in quenched steel cylinders Steel research 41994 146-151.

DOI: 10.1002/srin.199400944

Google Scholar

[15] H. M. Tensi, A. Stick : Martens hardening of steel - Prediction of temperature distribution and surface hardness, Materials Science Forum 102-104 (1992) 741-75.

DOI: 10.4028/www.scientific.net/msf.102-104.741

Google Scholar