Transient non-Fourier thermal interactions of two parallel cracks in porous metal foam

Abstract

Experimental evidence shows heat conduction in the porous media would be non-Fourier under specific circumstances. The novelty of this research lies in considerations of the non-Fourier effect and the interactions of two parallel thermally insulated cracks in the porous metal foam. The transient propagation characteristics are examined by utilizing the Dual-phase-lag model, which incorporates the certain time required to establish local thermal equilibrium between the solid framework and surrounding pores. Fourier transform and Laplace transform are employed to solve the mathematical model simulating a porous strip subjected to abrupt thermal shock. After reducing the problem to two groups of singular integral equations, the transient temperature distributions and heat flux intensity factors are determined with the help of numerical Laplace inversion. Numerical calculations are carried out to evaluate the impacts of crack positions, the relative density, phase lags, and two crack lengths on the thermal characteristics, which would contribute to a thorough understanding of the ultrafast process of porous materials operating in extreme conditions.

Keywords

• Dual-phase-lag model
• Crack
• Fourier transform
• Laplace transform
• Singular integral equations
• Porous material