Thermal quadrupole method with internal heat sources

Jérôme Pailhès (1) , Christophe Pradere (1) , Jean-Luc Battaglia (1) , Jean Toutain (1) , Andrzej Kusiak (1, 2) , Waste Aregba (1) , Jean-Christophe Batsale (1)

1 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux
2 TREFLE - Transferts, écoulements, fluides, énergétique

A new method based on the thermal quadrupoles technique for heat transfer modelling in multilayered slabs with heat sources is proposed. Classical thermal quadrupoles use hyperbolic functions and numerical problems occur according to the argument value that depends on thermophysical and geometrical properties as well as characteristics times. We propose a new formulation based on exponential function with negative argument. Using this formulation in the classical equivalent impedance network allows to compute efficiently the thermal behaviour of multilayered slabs with internal heat sources whatever the time and the thermophysical properties. This approach is applied in order to simulate heat transfer in three different multilayered materials with heat sources. These simulations show the capability of such a methodology to simulate time and space multiscale heat diffusion problems.

Mots clés: Heat source; Multilayer materials; Numerical simulation; Thermal quadrupoles

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

Jérôme Pailhès, Christophe Pradere, Jean-Luc Battaglia, Jean Toutain, Andrzej Kusiak, et al.. Thermal quadrupole method with internal heat sources. International Journal of Thermal Sciences, 2012, 53, pp.49-55. ⟨10.1016/j.ijthermalsci.2011.10.005⟩. ⟨hal-01020781⟩