Influence of Grünwald-Letnikow time and space temperature derivative on heat distribution

Authors

  • Tomasz Raszkowski Department of Microelectronics and Computer Sciences, Łódź University of Technology, Poland
  • Agnieszka Raszkowska Department of Microelectronics and Computer Sciences, Łódź University of Technology, Poland
  • Mariusz Zubert Department of Microelectronics and Computer Sciences, Łódź University of Technology, Poland

Keywords:

Dual-Phase-Lag model, Grünwald-Letnikov derivative, heat transfer approximation, Fourier-Kirchhoff modification, fractional order time derivative

Abstract

In this paper the new thermal model called Dual-Phase-Lag model has been investigated. This method is reasonable for nanometric structures which are more and more popular nowadays. However, during its numerical implementation, some problems can occur. Moreover, the simulation process can take a long period of time. Thus, it is needed to find some approximation scheme of the Dual-Phase-Lag model, which provides highly accurate results and simultaneously reduces time of simulation. Due to these reasons, investigation presented in this paper focuses on the determination of the approximation of the Dual-Phase-Lag model based on the Grünwald-Letnikov derivative definition. Moreover, this approximation takes into consideration the time and space derivative at the same time

References

D. Y. Tzou, A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales, Transactions of ASME J. Heat Transfer, 8–16, 1995.

M. Zubert, M. Janicki, T. Raszkowski, A. Samson, P. S. Nowak, K. Pomorski, The Heat Transport in Nanoelectronic Devices and PDEs Translation into Hardware Description Languages, Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les Déformations, vol. LXIV, 69–80, Łódź, 2014.

M. Zubert, T. Raszkowski, A. Samson, P. Zajac, Methodology of determining the applicability range of the DPL model to heat transfer in modern integrated circuits comprised of FinFETs, Microelectronics Reliability, 139–153, 2018.

B. A. Jacobs, A new Grünwald Letnikov derivative from second order scheme, Abstract and Applied Analysis, vol. 2015, 2015.

T. Raszkowski, A. Samson, M. Zubert Investigation of heat distribution using noninteger order time derivative and Dual-Phase-Lag model approximation, Bulletin de la Société des Sciences et des Lettres de Łódź, Série:Recherches sur les Déformations, In press Łódź, 2019.

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Published

2021-08-12

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