Inverse Heat Conduction Analysis of Cooling on Run Out Tables

In this paper, we introduced a gradient-based inverse
solver to obtain the missing boundary conditions based on the
readings of internal thermocouples. The results show that the method
is very sensitive to measurement errors, and becomes unstable when
small time steps are used. The artificial neural networks are shown to
be capable of capturing the whole thermal history on the run-out
table, but are not very effective in restoring the detailed behavior of
the boundary conditions. Also, they behave poorly in nonlinear cases
and where the boundary condition profile is different.
GA and PSO are more effective in finding a detailed
representation of the time-varying boundary conditions, as well as in
nonlinear cases. However, their convergence takes longer. A
variation of the basic PSO, called CRPSO, showed the best
performance among the three versions. Also, PSO proved to be
effective in handling noisy data, especially when its performance
parameters were tuned. An increase in the self-confidence parameter
was also found to be effective, as it increased the global search
capabilities of the algorithm. RPSO was the most effective variation
in dealing with noise, closely followed by CRPSO. The latter
variation is recommended for inverse heat conduction problems, as it
combines the efficiency and effectiveness required by these

[1] Alifanov, Oleg M., A. V. Nenarokomov, S. A. Budnik, V. V. Michailov,
and V. M. Ydin. "Identification of thermal properties of materials with
applications for spacecraft structures." Inverse Problems in Science and
Engineering 12, no. 5 (2004): 579-594.
[2] Beck, James V. Inverse heat conduction: Ill-posed problems. James
Beck, 1985.
[3] Beck, James Vere, and Kenneth J. Arnold. Parameter estimation in
engineering and science. James Beck, 1977.
[4] Beck, J. V., B. Blackwell, and A. Haji-Sheikh. "Comparison of some
inverse heat conduction methods using experimental data." International
Journal of Heat and Mass Transfer 39, no. 17 (1996): 3649-3657.
[5] Al-Khalidy, Nehad. "A general space marching algorithm for the
solution of two-dimensional boundary inverse heat conduction
problems." Numerical Heat Transfer, Part B 34, no. 3 (1998): 339-360.
[6] Jarny, Yvon. "Determination of heat sources and heat transfer coefficient
for two-dimensional heat flow–numerical and experimental study."
International Journal of Heat and Mass Transfer 44, no. 7 (2001): 1309-
[7] Huang, Cheng-Hung, I-Cha Yuan, and Herchang Ay. "A threedimensional
inverse problem in imaging the local heat transfer
coefficients for plate finned-tube heat exchangers." International Journal
of Heat and Mass Transfer 46, no. 19 (2003): 3629-3638.
[8] Girault, Manuel, Daniel Petit, and Etienne Videcoq. "The use of model
reduction and function decomposition for identifying boundary
conditions of a linear thermal system." Inverse Problems in Science and
Engineering 11, no. 5 (2003): 425-455.
[9] Kim, H. K., and S. I. Oh. "Evaluation of heat transfer coefficient during
heat treatment by inverse analysis." Journal of Materials Processing
Technology 112, no. 2 (2001): 157-165.
[10] Louahlia-Gualous, H., P. K. Panday, and E. A. Artioukhine. "Inverse
determination of the local heat transfer coefficients for nucleate boiling
on a horizontal cylinder." Journal of heat transfer 125, no. 6 (2003):
[11] Gadala, Mohamed S., and Fuchang Xu. "An FE-based sequential inverse
algorithm for heat flux calculation during impingement water cooling."
International Journal of Numerical Methods for Heat & Fluid Flow 16,
no. 3 (2006): 356-385.
[12] Roudbari, Shawhin. "Self-Adaptive Finite Element Analysis." PhD diss.,
Cornell University, 2006.
[13] Silieti, M., E. Divo, and A. J. Kassab. "An inverse boundary element
method/genetic algorithm based approach for retrieval of multidimensional
heat transfer coefficients within film cooling holes/slots."
Inverse Problems in Science and Engineering 13, no. 1 (2005): 79-98.
[14] Shiguemori, Elcio H., José Dem?Sio S. Da Silva, and Haroldo F. de
Campos Velho. "Estimation of initial condition in heat conduction by
neural network." Inverse Problems in Science and Engineering 12, no. 3
(2004): 317-328.
[15] Lecoeuche, S., G. Mercere, and S. Lalot. "Evaluating time-dependent
heat fluxes using artificial neural networks." Inverse Problems in
Science and Engineering 14, no. 2 (2006): 97-109.
[16] Ostrowski, Z., R. A. Bialstrokecki, and A. J. Kassab. "Solving inverse
heat conduction problems using trained POD-RBF network inverse
method." Inverse Problems in Science and Engineering 16, no. 1 (2008):
[17] Hassan, Rania, Babak Cohanim, Olivier De Weck, and Gerhard Venter.
"A comparison of particle swarm optimization and the genetic
algorithm." In Proceedings of the 1st AIAA multidisciplinary design
optimization specialist conference, pp. 18-21. 2005.
[18] Gosselin, Louis, Maxime Tye-Gingras, and François Mathieu-Potvin.
"Review of utilization of genetic algorithms in heat transfer problems."
International Journal of Heat and Mass Transfer 52, no. 9 (2009): 2169-
[19] Davis, Lawrence, ed. Handbook of genetic algorithms. Vol. 115. New
York: Van Nostrand Reinhold, 1991.
[20] Clerc, Maurice. Particle swarm optimization. Vol. 93. John Wiley &
Sons, 2010.
[21] Kennedy, James, James F. Kennedy, and Russell C. Eberhart. Swarm
intelligence. Morgan Kaufmann, 2001.
[22] Vakili, S., and M. S. Gadala. "Effectiveness and efficiency of particle
swarm optimization technique in inverse heat conduction analysis."
Numerical Heat Transfer, Part B: Fundamentals 56, no. 2 (2009): 119-
[23] Alrasheed, M. R., C. W. de Silva, and M. S. Gadala. "Evolutionary
optimization in the design of a heat sink." Mechatronic Systems:
Devices, Design, Control, Operation and Monitoring (2008).
[24] De Silva, Clarence W. Mechatronic Systems. Taylor and Francis, 2007.
[25] Urfalioglu, Onay. "Robust estimation of camera rotation, translation and
focal length at high outlier rates." In Computer and Robot Vision, 2004.
Proceedings. First Canadian Conference on, pp. 464-471. IEEE, 2004.