2019/10/21 by Róbert Kovács, Kovács, Róbert, Patrizia Rogolino +1
Engineering · Mathematics · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Nanofluid Flow and Heat Transfer #Numerical methods in inverse problems #Statistical Mechanics (cond-mat.stat-mech) #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1910.09175
openalex publication_date 2019/10/21 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The second law of thermodynamics is a useful and universal tool to derive the\ngeneralizations of the Fourier's law. In many cases, only linear relations are\nconsidered between the thermodynamic fluxes and forces, i.e., the conduction\ncoefficients are independent of the temperature. In the present paper, we\ninvestigate a particular nonlinearity in which the thermal conductivity depends\non the temperature linearly. Also, that assumption is extended to the\nrelaxation time, which appears in the hyperbolic generalization of Fourier's\nlaw, namely the Maxwell-Cattaneo-Vernotte (MCV) equation. Although such\nnonlinearity in the Fourier heat equation is well-known in the literature, its\nextension onto the MCV equation is rarely applied. Since these nonlinearities\nhave significance from an experimental point of view, an efficient way is\nneeded to solve the system of partial differential equations. In the following,\nwe present a numerical method that is first developed for linear generalized\nheat equations. The related stability conditions are also discussed.\n