TY - JOUR

T1 - On a generalized non-local two-temperature heat transfer DAE modeling/simulation methodology for metal-nonmetal thermal inter-facial problems

AU - Xue, Tao

AU - Zhang, Xiaobing

AU - Tamma, Kumar K.

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

KW - Differential algebraic equation

KW - Electron-phonon interaction

KW - Metal-nonmetal thermal interface

KW - Two-temperature theory

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U2 - 10.1016/j.ijheatmasstransfer.2019.04.067

DO - 10.1016/j.ijheatmasstransfer.2019.04.067

M3 - Article

AN - SCOPUS:85064431606

VL - 138

SP - 508

EP - 515

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

ER -