Effect of thermal wave propagation on thermoelastic behavior of functionally graded materials in a slab symmetrically surface heated using analytical modeling

Design and development of FGMs as the heat treatable materials for high-temperature environments with thermal protection require understanding of exact temperature and thermal stress distribution in the transient state. This information is primary tool in the design and optimization of the devices for failure prevention. Frequently FGMs are used in many applications that presumably produce thermal energy transport via wave propagation. In this study, transient non-Fourier temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined. Hyperbolic heat conduction equation in terms of heat flux is used for obtaining temperature profile. Separation of variables scheme based on the variation of parameters is implemented to solve the non-homogenous thermoelastic problem in which any arbitrary temperature distribution can be employed. Physical properties are assumed to vary exponentially in the media and the problem is analyzed for different mechanical boundary conditions. Furthermore effect of the material inhomogeneity, thermal relaxation time and the Fourier number on the stress distribution, temperature variation and jumps is investigated. Parallel computation is used to present the fully converged numerical results. Findings indicate the non-Fourier heat conduction has significant influence on the dynamic temperature and stress field. Based on the results it is suggested that in the design of FG structures against failure under thermal loading and heat treatability, the hyperbolic model is more appropriate than the classical Fourier model.