ORIGINAL Heat conduction and heat wave propagation in functionally graded thick hollow cylinder base on coupled thermoelasticity without energy dissipation S. M. Hosseini Æ M. Akhlaghi Æ M. Shakeri Received: 28 August 2007 / Accepted: 26 February 2008 / Published online: 14 March 2008 Ó Springer-Verlag 2008 Abstract In this paper, heat wave propagation and cou- pled thermoelasticity without energy dissipation in functionally graded thick hollow cylinder is presented based on Green–Naghdi theory. The material properties are supposed to vary as a power function of radius across the thickness of cylinder. The cylinder is considered in axi- symmetry and plane strain conditions and it is divided to many sub-cylinders (layers) across the thickness. Each sub- cylinder is considered to be made of isotropic material and functionally graded property can be created by suitable arrangement of layers. The Galerkin finite element method and Newmark finite difference method are employed to solve the problem. The time history of second sounds and displacement wave propagation are obtained for various values of power function. Computed results agree well with the published data. 1 Introduction Functionally Graded Materials (FGMs) are a new genera- tion of composites where the volume fractions of the FGM constituents vary gradually from one surface to the other. These kinds of materials give a non-uniform microstructure with continuously graded macro-properties. The most important of its applications is in high temperature condi- tions. Therefore, determination of temperature field or thermo-elasticity analysis is an important topic for them. In the recent years vibration, dynamic analysis of FGMs and wave propagation analysis have been studied by researchers. A number of research works have been carried out in the steady-state thermoelastic [1, 2], and transient thermo- elastic [3, 4], and wave propagation problems. A computational method was presented to investigate SH wave in FGM plates by Han et al. [5]. The material properties were assumed to be a quadratic function in the thickness direction. A novel spectral element was presented to study the wave propagation behavior in FGM beams subjected to high frequency impact loads by Chakraborty et al. [6]. The propagation of stress waves in FGMs was studied numerically by means of the theory of laminated composite wave–propagation algorithm by Berezovski et al. [7]. There are some works on wave propagation problems by using multilayer modeling of FGM. The better rule-of-mixture called as SBS method for FGMs has been used in FG plates [8], FG cylinders [9, 10] and FGPM cylinders [11]. A two-dimensional numerical simulation model for the elastodynamic wave propagation in two linear elastic, isotropic, joint half-spaces was presented by Vollmann et al. [12]. They considered that the border between the two half-spaced was graded in a way, which the values of elastic properties and the densities vary smoothly from one half-space to the other. The vibration and dynamic analysis of functionally graded cylinders was studied by authors [13]. The mean velocity of radial stresses wave propagation, natural frequency and dynamic S. M. Hosseini Mechanical Engineering Department, Khorasan Research Institute of Sciences and Food Technology, P.O. Box 91735-139, Mashhad, Iran M. Akhlaghi (&)  M. Shakeri Mechanical Engineering Department, Amirkabir University of Technology, P.O. Box 15875-4413, Hafez Avenue, Tehran, Iran e-mail: ma@profmehdi.com; makhlagi@cic.aut.ac.ir 123 Heat Mass Transfer (2008) 44:1477–1484 DOI 10.1007/s00231-008-0381-9