Non-Fourier fractional heat conduction in two bonded dissimilar materials with a penny-shaped interface crack

Abstract

This paper studies a generalized non-Fourier fractional heat conduction problem of a bi-material with a penny-shaped interface crack under sudden heat flux shock. The Hankel transform and Laplace transform are employed to solve an initial-boundary value problem associated with a time-fractional partial differential equation. Closed-form temperature field and the dynamic intensity factors of heat flux and temperature gradient near the front of a penny-shaped crack are obtained in the Laplace transform domain. Numerical results in the time domain are obtained by using a numerical inversion of the Laplace transform. Two cases of a cracked homogeneous platinum and a bi-material composed of platinum and quartz glass with an interface crack are analyzed to show the effects of fractional order, crack size and material properties on the temperature change and the intensity factors of heat flux and temperature gradient. Obtained results based on the non-Fourier fractional order heat conduction are compared with those using the hyperbolic heat conduction graphically. It is found that transient temperature gradient and heat flux exhibit the inverse-square-root singularity near the crack front, and their intensity factors depend on the bi-material property. Moreover, the temperature in magnitude on the crack face of platinum is much smaller than that on the crack face of quartz glass. The heat flux is continuous across the interface, while the temperature gradient is discontinuous across the interface. Transient response of temperature, its gradient, and heat flux for the case of fractional order is noticeable for the earlystage of application of sudden heat flux.