The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous two-temperature thermoelastic solid half-space in the context of Lord and Shulman theory of generalized thermoelasticity. The governing equations of a two-temperature generalized thermoelastic medium are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The speed of Rayleigh wave is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter. 1. Introduction Lord and Shulman [1] and Green and Lindsay [2] extended the classical dynamical coupled theory of thermoelasticity to generalized thermoelastic theories. These theories treat heat propagation as a wave phenomenon rather than a diffusion phenomenon and predict a finite speed of heat propagation. Ignaczak and Ostoja-Starzewski [3] explained in detail the above theories in their book Thermoelasticity with Finite Wave Speeds. The representative theories in the range of generalized thermoelasticity are reviewed by Hetnarski and Ignaczak [4]. Wave propagation in thermoelasticity has many applications in various engineering fields. Some problems on wave propagation in coupled or generalized thermoelasticity are studied by various researchers, for example, Deresiewicz [5], Sinha and Sinha [6], Sinha and Elsibai [7, 8], Sharma et al. [9], Othman and Song [10], Singh [11, 12], and many more. Gurtin and Williams [13, 14] proposed the second law of thermodynamics for continuous bodies in which the entropy due to heat conduction was governed by one temperature, that of the heat supply by another temperature. Based on this law, Chen and Gurtin [15] and Chen et al. [16, 17] formulated a theory of thermoelasticity which depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature . The two-temperature theory involves a material parameter . The limit implies that , and the classical theory can be recovered from two-temperature theory. The two-temperature model has been widely used to predict the electron and phonon temperature distributions in ultrashort laser processing of metals. According to Warren and Chen [18], these two temperatures can be equal in time-dependent problems under certain conditions, whereas and are generally different in particular problems involving wave propagation. Following Boley and Tolins [19], they studied the wave
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