Thermal networks from heat wave equation

In this paper passive and reciprocal thermal networks are introduced which model the finite velocity of heat propagation. In particular it is shown that the theory of distributed and discretized thermal networks deduced from the heat diffusion equation and the multi-point moment matching technique for deriving approximated lumped thermal networks of small state-space dimensions can be extended to thermal networks ruled by the hyperbolic heat equation.

[1]  D.L. Blackburn,et al.  Simulating the dynamic electro-thermal behavior of power electronic circuits and systems , 1992, [Proceedings] 1992 IEEE Workshop on Computers in Power Electronics.

[2]  P. Maffezzoni,et al.  Analytical multipoint moment matching reduction of distributed thermal networks , 2004, IEEE Transactions on Components and Packaging Technologies.

[3]  V. Székely,et al.  Accurate algorithm for temperature calculation of devices in nonlinear-circuit-analysis programs , 1972 .

[4]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[5]  Paolo Maffezzoni,et al.  Compact modeling of electrical devices for electrothermal analysis , 2003 .

[6]  P. Duhamel A new finite integral transform pair for hyperbolic conduction problems in heterogeneous media , 2001 .

[7]  D. L. Blackburn,et al.  Simulating the dynamic electrothermal behavior of power electronic circuits and systems , 1993 .

[8]  Michael B. Steer,et al.  Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems , 2001 .

[9]  D. Tzou,et al.  On the Wave Theory in Heat Conduction , 1994 .

[10]  Paolo Maffezzoni,et al.  An Arnoldi based thermal network reduction method for electro-thermal analysis , 2003 .

[11]  P. Maffezzoni,et al.  Compact thermal networks for modeling packages , 2004, IEEE Transactions on Components and Packaging Technologies.

[12]  E. Zanchini,et al.  Hyperbolic heat conduction and local equilibrium: a second law analysis , 1997 .

[13]  Paolo Maffezzoni,et al.  Thermal networks for electro-thermal analysis of power devices , 2001 .