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

  • 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

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Published
2021-08-12
Section
Articles