Formulation of the boundary and initial conditions supplementing the dual-phase lag models
Year: 2025
Type: article
Abstract: In the paper the mathematical and numerical models of heat transfer processes basing on the dual-phase lag equation - DPLE (the energy equation with two delay times) is considered. This type of equation is, as a rule, applied for mathematical description of thermal processes taking place in the microdomains (microscale heat transfer) and also for the modeling of problems associated with the heat transfer in biological tissue domains, what follows from the specific tissue structure.The primary goal of the considerations presented in this paper is to show the correct form of boundary conditions supplementing DPL equation (equations). Presented in literature the solutions of different DPLE variants are obtained using the classical form of boundary conditions (as in the Fourier equation), which is not completely correct. In this paper the proper mathematical form of the Neumann, Robin and continuity conditions taking into account the non-zero values of lag times is presented.The second part of the paper is devoted to the numerical aspects of solving the problems basing on the mathematical description formulated in this way. At the stage of computations the finite difference method (FDM) in an implicit scheme is applied (1D and axially-symmetrical problems are considered). The results of numerous simulations are shown, including a comparison of solutions using the classical approach to boundary-initial conditions and the approach presented in this paper.
Authors: Ewa Majchrzak, Bohdan Mochnacki
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415788726