Thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction

Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction are investigated analytically and numerically. The corresponding dispersion relation is a sixth-order algebraic equation, governed by six non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter, the ratio between extensional and torsional moduli, the Fourier number, and the dimensionless thermal relaxation. The behavior of the solutions is discussed from two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxation on the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wave celerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered. However, with large wavenumbers, the solutions behave differently depending on the thermal relaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from the classical result of the speed of second sound.