Interaction of mechanical, temperature and diffusion fields in a solid cylinder subjected to transient heating
DOI:
https://doi.org/10.7242/1999-6691/2026.19.1.2Keywords:
thermomechanodiffusion, phase-lag effects, relaxation of heat and diffusion flows, unsteady problems, Green's functions, Laplace transform, Fourier series, Bessel functionsAbstract
The article examines the phenomena caused by the mutual influence of mechanical, temperature and diffusion fields in a continuous orthotropic multicomponent cylinder under the action of unsteady external perturbations set on the cylinder surface. The cylinder does not experience volumetric perturbations. It is assumed that the physico-mechanical processes occurring in the cylinder depend only on the radial coordinate. The mathematical formulation involves a system of coupled nonstationary thermodiffusion equations in a cylindrical coordinate system. The employed heat and mass transfer model accounts for the finite velocity of thermal and diffusion wave propagation. The kinematic relations for thermal and diffusion flows are constructed based on the generalized Lord–Shulman theory. The proposed algorithm for solving a polar-symmetric problem is based on the integral representation of the desired fields in the form of time-dependent convolutions of Green's functions and the functions, describing surface thermomechanodiffusion perturbations. The Green's functions are found by applying the time-domain Laplace transform and the Fourier–Bessel series expansion, which makes it possible to reduce the initial boundary value problem to a system of linear algebraic equations with respect to the coefficients of the Fourier series. The solutions of this system are rational functions, and therefore the inverse Laplace transformation is carried out analytically using the theory of residues and tables of operational calculus. Using a three-component cylinder as an example, a numerical analysis of the interaction between mechanical, temperature and diffusion fields under external unsteady thermal action is performed and the obtained results are compared with the solutions to known problems of thermoelasticity and mechanodiffusion. The effect of the finite velocity of propagation of thermal and diffusion fluxes on the kinetics of heat and mass transfer in continuous media under different types of external thermal load is investigated.
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