This paper aims to develop a physically interpretable nonlocal method for transient heat diffusion in cracked media with imperfect thermal interfaces.
A peridynamic-differential-operator-based heat-diffusion formulation is constructed by replacing the local Laplacian with a second-order nonlocal differential operator. Zero-thickness cracks are represented through a projected-normal series-resistance relation that maps interfacial thermal resistance to the transmission factor of crack-intersected bonds using the material thermal conductivity and the local crack-normal projection of the bond length. The method is assessed using analytical benchmarks, comparisons with finite element method solutions and a localized heat-source problem.
The finite-resistance benchmark confirms that the formulation reproduces the analytical temperature jump and heat-flux continuity. For the finite-resistance double-crack validation case, the monitoring-point history agrees closely with the independent reference solution obtained using the finite element method, yielding a root-mean-square error of 0.084 °C. In the localized heat-source problem, finite-resistance and insulating cracks reduce the downstream temperature by 19.6% and 48.1%, respectively. They also decrease the finite-time cumulative heat-removal efficiency from 0.037 for the intact plate to 0.029 and 0.018, respectively, while the final energy-balance errors remain below 1.0%.
The methodological contribution is the projected-normal series-resistance mapping from interfacial thermal resistance to crack-bond transmission for prescribed zero-thickness cracks. The formulation is further used to quantify transient downstream thermal shielding, source-side heat retention and finite-time heat-removal degradation under imperfect crack-interface conditions.
