Simulation of non-Fourier heat conduction in discontinuous heterogeneous materials based on the peridynamic method

Abstract

Discontinuous heterogeneous materials, such as rocks and concrete, exhibit non-Fourier heat conduction. To predict this type of conduction behavior in discontinuous materials, a bond-based peridynamic heat conduction model based on the peridynamic theory was derived by introducing the dual-phase-lag model. The model was verified by the results obtained using other numerical methods. The Weibull distribution function was introduced to describe the heterogeneity in the thermal conductivity. The heat conduction in a plate with two pre-existing cracks under thermal shock was simulated. The effects of phase lag and heterogeneity were discussed. The results showed that the heat transfer rate is mainly controlled by the phase lag ?q of the heat flux. When ?q remains unchanged, the heat transfer rate increases with the increase in the phase lag ?T of the temperature gradient. The influence of cracks on the temperature field is mainly reflected in the area near the crack end. Although the temperature in the local area may be positively correlated with ?T in the short term, the long-term influence of the factor becomes increasingly weaker. The proposed method has a wide application prospect in simulating non-Fourier?s heat conduction in discontinuous heterogeneous materials.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

“…Currently, numerical methods for solving transient heat conduction equations are broadly classified into two categories: mesh-based methods, including finite difference method (FDM) [1,2], finite element method (FEM) [3,4], Finite Volume Method [5,6], and Boundary Element Method (BEM) [7]; and meshless methods, such as the generalized finite difference method [8,9], smoothed particle hydrodynamics method (SPH) [10], meshless local Petrov-Galerkin method (MLPG) [11][12][13][14], meshless local radial basis function-based differential quadrature (RBF-DQ) [15], peridynamics (PD) [16,17], and peridynamic differential operator (PDDO) [18,19]. Based on time discretization, these methods can be divided into explicit and implicit schemes.…”