Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model

Ramos, Anderson and Campelo, Anderson and Freitas, Mirelson and Kovács, Róbert Sándor (2024) Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model. JOURNAL OF THERMAL STRESSES, 47 (9). pp. 1262-1276. ISSN 0149-5739

Text RamEtal24.pdf - Published Version Restricted to Repository staff only Download (1MB) | Request a copy

Abstract

In the literature, one can find numerous modifications of Fourier’s law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme’s stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics.

Actions (login required)

Edit Item