thermoelasticity, type-III thermoelasticity, frequency equation, waveguide, wavenumber, wave mode, azimuthal number, heat interchanging

The article is devoted to the study of cross-coupled type-III generalized thermoelastic waves propagation via a long cylindrical waveguide. The sidewall of the waveguide is assumed free from tractions and permeable to heat. The analysis is carried out in the framework of coupled generalized theory of GNIII-thermoelasticity consistent with the basic thermodynamic principles. The theory combines both possible mechanisms of heat transfer: thermodiffusion and wave. TypeIII generalized thermoelasticity includes classical thermoelasticity (GNI/CTE) and the theory of hyperbolic thermoelasticity (GNII) as limiting cases. The GNII-theory can be formulated as a field theory [1-3] and differential field equations are of hyperbolic analytical type. Closed solution of the coupled GNIII-thermoelasticity equations satisfying the required boundary conditions on the surface of waveguide including convective heat interchanging condition is obtained. For a given azimuthal number a numerical analysis of frequency equation is given. A scheme of frequency equation roots localization is proposed and wavenumbers of the coupled thermoelastic waves of the first and seventh azimuthal numbers are computed. A numerical study of the coupled thermoelastic waves of the 70th azimutal number is also discussed