A peridynamic model for non-Fourier heat transfer in orthotropic plate with uninsulated cracks

Abstract

In this paper, the transient temperature response of a cracked plate under thermal shock is investigated. To eliminate the problems caused by the assumption of infinite heat propagation speed, the non-Fourier heat transfer theory is adopted. A peridynamic model is developed to consider the non-Fourier effect, the orthotropy of thermal conductivity, and the crack thermal resistance. This model avoids the spatial derivative and is efficient to analyze the problems with discontinuities. Based on the Kapitza thermal resistance model, a thermal resistance bond is proposed to deal with the uninsulated crack. The explicit and implicit discrete schemes of peridynamic formulation are presented to solve the temperature field. The model is verified by the analytical solution and excellent agreements are obtained. For the non-Fourier phenomenon observed in bismuth, numerical examples are presented for analyzing the effects of crack thermal resistance, crack orientation angle, and multi-crack distribution on non-Fourier heat transfer.