On a generalized non-local two-temperature heat transfer DAE modeling/simulation methodology for metal-nonmetal thermal inter-facial problems

• Published in: International journal of heat and mass transfer 2019-08, Vol.138, p.508-515
• Main Authors: Xue, Tao, Zhang, Xiaobing, Tamma, Kumar K.
• Format: Article
• Language: English
• Subjects: Algebra; Computer simulation; Differential algebraic equation; Differential equations; Domains; Electron phonon interactions; Electron-phonon interaction; Electronic devices; Heat; Heat transfer; Heat transmission; Mathematical models; Metal-nonmetal thermal interface; Ordinary differential equations; Phonons; Thermodynamic properties; Time integration; Two-temperature theory
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2019.04.067

•A generalized two-temperature theory is proposed for the metal-nonmetal thermal contact.•The proposed model is nonlocal in both space and time.•The thermal contacts with perfect/imperfect interfaces are formulated in DAE framework. With the increasing demand of electronic devices at micro-/nano-scales, the numerical modeling of metal-nonmetal thermal inter-facial problems is one of the most important and necessary aspects for the design of these devices at small scales; particularly the non-local and non-Fourier thermal behaviors play a vital role. This work exploits a generalized two-temperature heat transfer model to describe the metal-nonmetal thermal contact, in which the electron-phonon interaction dominates the thermal behavior in the metal whereas only phonon transport dominates the thermal behaviors in the nonmetal; and the heat energy between the metal and the nonmetal domains are transferred only by phonons. The non-locality in space and time of this generalized two-temperature theory is first mathematically proved with rigor. A generalized computational strategy based on this non-local two-temperature model is then formulated in the framework of differential algebraic equations instead of classical ordinary differential equations, where the thermal interface conditions are treated as algebraic equations. The proposed formulation allows considering the complex thermal inter-facial phenomena involving a large range of scale effects and Fourier/nonFourier thermal behaviors in both the metal and the nonmetal domains. The novel unified time integration of GS4-1 DAE Index 2 is exploited to solve the resulting differential-algebraic system and to predict the thermal behaviors between many thermal flux models without extra computational cost.