## 1 Introduction
[13] proposed a method combining thermoelastic theory and the semi-analytical finite element method to study the effects of uniform and non-uniform thermal effects on phase velocity, group velocity, etc. Based on the Fourier expansion approach of [PERSON]'s generalized theory, [PERSON] et al. [14] examined the wave propagation properties of a generalized thermoelastic solid cylinder of any cross-section. The propagation of thermoelastic waves in an infinite-length hollow cylinder was studied by [PERSON] et al. [15]. In the meantime, [PERSON] et al. [16] used [PERSON]'s boundary integral approach, which is based on the first kind of Fredholm integral equations, to study the three-dimensional dispersion problem of thermoelastic waves. Based on experimental data, [PERSON] et al. [17] examined the temperature sensitivity of group velocity in aluminum alloy plates and examined how various temperatures affected Lamb waves. [PERSON] et al. [18] investigated the dispersion characteristics of guided waves in multilayer composite cylinders as well as thermoacoustic-elastic effects. Using [PERSON]'s gradient and the generalized thermoelastic theory of GN, [PERSON] et al. [19, 20, 21] numerically solved the thermoelastic wave propagation characteristics of a functional gradient plate. They then expanded the application of this method to a curved spherical plate and hollow cylinders for the circumferential thermoelastic guided wave propagation problems. Following that, to investigate the guided wave propagation problem in fractional-order thermoelastic plates, [PERSON] et al. [22] developed a modified Legendre polynomial approach based on the fractional-order thermoelastic theory. [PERSON] et al. [23] investigated thermoelastic Lamb waves in functional gradient nanoplates using the integral form of the modified nonlocal theory. [PERSON] et al. [24] and [PERSON] et al. [25] solved and analyzed the propagation characteristics of circumferential guided waves in a Lamb wave in a fractionally thermoelastic multilayer plate and in a fractionally viscoelastic hollow cylinder, respectively, based on the thermoelastic theoretical model of fractional order. [PERSON] et al. [26] investigated thermoelastic waves in rods with rectangular cross-sections based on the GL thermoelastic theory using modified bi-orthogonal Legendre polynomials. [PERSON] et al. [27] studied the propagation characteristics of transient ultrasonic guided waves generatedby concentrated heating on the outer surface of an infinitely anisotropic hollow cylinder. Based on the LS generalized thermoelastic theory, [PERSON] et al. [28] studied the longitudinal guided waves of fractional order thermoelastic inhomogeneous hollow cylinders based on adiabatic boundary conditions by using the analytical Legendre polynomial series method. Most of the above studies involve plate structures, and most of the studies on thermoelastic waves in hollow cylinders focus on the propagation characteristics of circumferential guided waves, with fewer studies on the propagation characteristics of thermoelastic guided waves in the longitudinal direction. Longitudinal guided waves have a high potential for use in pipeline inspection due to their propagation properties, which are particularly sensitive to circumferential faults. This study investigates the propagation characteristics of longitudinal thermoelastic waves in an orthotropic anisotropic hollow cylinder using the GN generalized thermoelastic model. In the first part, the thermoelastic guided wave dispersion model with temperature field is established by coupled thermodynamic equations. In the second part, the phase velocity dispersion curves of the longitudinal guided wave in an orthotropic anisotropic hollow cylinder as well as the displacements of the plasmas and the temperature variations are numerically computed, and the influences of the diameter-to-thickness ratio as well as the reference temperature on the dispersion characteristics are analyzed.