Integro-differential form of the first-order dual phase lag heat transfer equation and its numerical solution using the Control Volume Method

• Autorzy: Ciesielski M. , Mochnacki B. , Majchrzak E.

Identyfikatory

DOI

10.24423/aom.3555

• Języki publikacji: EN

Abstrakty

EN

The start point of the dual phase lag equation (DPLE) formulation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. This type of equation can be used (among others) to describe the heat conduction processes proceeding in micro-scale. Depending on the number of components in the development of the generalized Fourier law into a power series, one can obtain both the first-order DPLE and the second-order one. In this paper the first-order dual phase lag equation is considered. The primary objective of this research is the transformation of DPLE differential form to the integro-differential one supplemented by the appropriate boundary-initial conditions. The obtained form of the differential equation is much simpler and more convenient at the stage of numerical computations – the numerical algorithm based on the three-time-level scheme reduces to the two-time-level one. To find the numerical solution, the Control Volume Method is used (the heating of thin metal film subjected to a laser beam is considered). The choice of the numerical method was not accidental. The method has a simple physical interpretation ensuring the preservation of the local and global energy balances. To our knowledge, it has not been used so far in this type of tasks. In the final part of the paper the examples of numerical simulations are presented and the conclusions are formulated.

Słowa kluczowe

EN

micro-scale heat transfer; dual phase lag model; integro-differential equation; Control Volume Method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2020
• Tom: Vol. 72, nr 5
• Strony: 415--444
• Opis fizyczny: Bibliogr. 46 poz., rys.

Twórcy

autor

Ciesielski M.

• Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa, Poland

autor

Mochnacki B.

• University of Occupational Safety Management, Bankowa 8, 40-007 Katowice, Poland

autor

Majchrzak E.

• Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland

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