Thermoelastic waves in a helix with parabolic or hyperbolic heat conduction

Of concern is the steady-state thermoelastodynamics of a helix, whose material is governed by a coupled thermoelastic model. Heat transfer follows either a parabolic (Fourier) or a hyperbolic (Maxwell–Cattaneo) rule. As a result, in the one-dimensional setting, there are three coupled differential equations that lead to a fast (primarily axial) and a slow (primarily torsional) wave. Particularly for harmonic motions, we find that the thermal diffusivity and the relaxation time (of the Maxwell–Cattaneo model) have minor effects, whereas the thermoelastic coupling constant is dominant—it speeds up these waves—and overall there is damping. Additionally, we review and note differences from solutions of equations governing plane harmonic waves in a non-centrosymmetric, thermoelastic micropolar continuum in three dimensions.