Eur. Phys. J. AP
Volume 13, Number 3, March 2001
|Page(s)||177 - 194|
|Section||Nanomaterials and Nanotechnologies|
|Published online||15 March 2001|
Improvement of thermal nodal models with negative compensation capacitors
Laboratoire d'Études Thermiques (UMR CNRS n°6608),
ENSMA, BP 109, 86960 Futuroscope Cedex, France
Corresponding author: firstname.lastname@example.org
Revised: 12 July 2000
Accepted: 30 November 2000
Published online: 15 March 2001
The objective of the present study is to improve the modelling of heat transfer by elementary cells, aiming to increase the quality of their representation in the Laplace space. From the twoport representation and its connections with the classical nodal method, we show that the systematic increase of the order leads to improve the simulation results in transients. But, we would like to find a better reduced topology of the equivalent elementary network of heat conduction, closer to the analytical solution and verifying its terms for higher orders. The wall representation can be performed by an impedance network with “Π” or “T” shaped cells. The approximation of these impedances leads to define a new cell topology, which introduces capacitances with a negative value called "compensation capacitors". The value of these new elements only depends on the model nodal thermal capacitances in a wall. We study the transfer functions of these various equivalent networks as twoports that we will then compare to the analytical solution of the heat transfer equation. Some interesting values of the negative compensation capacitors are then obtained from transfer function; however, the optimal value would only be given from simulation results. All the established results will be confirmed by transient response simulations, which show the high performances of these new structures. These results are also validated by a modal analysis of these systems. The study of the model's accuracy show that the importance of the reduction for equivalent maximum errors corresponds to the square of the number of elementary cells.
PACS: 44.05.+e – Analytical and numerical techniques / 44.10.+i – Heat conduction / 66.70.+f – Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves
© EDP Sciences, 2001
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