## Reduced-Order Models for the Calculation of Thermal Transients of Heat Conduction/Convection FE Models

The text is written in November 2008 for the http://groups.google.com/group/mor4ansys group.

D. Botto, S. Zucca, and M. M. Gola, (2007) ‘Reduced-Order Models for the Calculation of Thermal Transients of Heat Conduction/Convection FE Models’, Journal of Thermal Stresses, 30:8, 819-839
http://dx.doi.org/10.1080/01495730701415806

The link to Prof Gola is

http://didattica.polito.it/pls/portal30/sviluppo.scheda_pers_swas.show?m=525

The paper presents an interesting engineering application that requires reduced thermal models. The authors have used the Guyan reduction and the component mode synthesis to reduce the models. Moreover the fluid part first has been statically reduced to leave the transient behavior in the solid part only.

The engineering problem concerns nuclear and aeronautical applications where the change in temperature causes thermal stresses and hence fatigue. Online calculation of temperatures is needed to assess fatigue damage accumulation and residual life.

My first observation was that the background mathematical problem in the paper is very similar to that in electronics for cooling of chips. There they need to estimate the temperature distribution in a chip because when the chip temperature is too high, the chip fails. Clearly the damage mechanisms in a chip are more complicated as pure fatigue in a mechanical structure. Yet, the part related to thermal engineering is pretty similar. See for example papers for the ROFIT project

http://www.hitech-projects.com/euprojects/profit/

The second thought was that this would be an interesting application for MOR for ANSYS. We have compared Arnoldi with Guyan in [1]. I have not seen the comparison Arnoldi with CMS yet. It would be interesting to make it. Well, I should confess that I have not yet understood how many inputs will be necessary to introduce to treat the model in question. Guyan and CMS are input independent and in this case this does not matter. For Arnoldi the right answer is crucial for success. Anyway for Arnoldi the unsymmetric heat conductivity matrix is not a problem. It is working in this case the same way [2].

[1] T. Bechtold, E. B. Rudnyi and J. G. Korvink, Automatic Generation of Compact Electro-Thermal Models for Semiconductor Devices. IEICE Transactions on Electronics, 2003, v. E86C, N 3, pp. 459 – 465.
http://search.ieice.org/2003/files/e000c03.htm#e86-c,3,459
Preprint at http://modelreduction.com/doc/papers/bechtold03IEICE.pdf

[2] C. Moosmann, E. B. Rudnyi, A. Greiner, J. G. Korvink, Model Order Reduction for Linear Convective Thermal Flow. THERMINIC 2004, 10th International Workshop on Thermal Investigations of ICs and Systems, 29 September – 1 October 2004, Sophia Antipolis, France, p. 317-321.
http://modelreduction.com/doc/papers/moosmann04THERMINIC.pdf

See discussion at