Dual-phase-lag heat conduction in a furnace wall made of functionally graded materials

In this article, the transient heat transfer in a furnace wall, which is made of functionally graded materials (FGMs), is investigated based on the hyperbolic-type dual-phase-lag (DPL) heat conduction model to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the furnace wall are assumed to vary following a power-law form along the radial direction with arbitrary non-homogeneity indices. For simplicity, the values of the phase lags are taken constant. A semi-analytical solution for the temperature field is obtained in the Laplace domain. The transformed temperature solution is inverted to the physical quantity by using numerical inversion of the Laplace transform. A comparison between the hyperbolic-type DPL model and thermal wave model in the temperature responses of the furnace wall is made. Effects of different phase-lag values on the behavior of heat transfer are also investigated.