Abstract

We consider one-dimensional lattice and nonlocal heat diffusion problems. Some experimental, numerical and analytical works have shown significant deviations from Fourier’s law in the case of problems dealing with temporal and spatial microscales. Hence, we propose a study based on a one-dimensional Cattaneo–Vernotte thermal lattice. Some exact analytical solutions based on the method of separation of variables and the use of trigonometric series are formulated for this spatially discrete diffusion problem. The discrete thermal lattice model is compared to a nonlocal continuous Cattaneo–Vernotte model. The length scale for the nonlocal equation is calibrated from the lattice spacing, by applying a continualization method to the lattice heat equation. Then, an error analysis is performed to study the efficiency of the nonlocal model with respect to the local one. It is concluded that the Cattaneo–Vernotte thermal lattice response may be efficiently approximated by a continuous nonlocal Cattaneo–Vernotte heat equation.

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