Fundamental Theorems and Wave Dynamics in Rotating Thermoelastic Diffusion with Multi-Phase Delays and Temperature-Dependent Properties

The current study uses a novel mathematical formulation of temperaturedependent thermoelastic diffusion with multi-phase delays in a rotating frame of reference (TDMR). Higher order time derivatives are included for the diffusing mass flux, the gradient of chemical potential, the gradient of temperature, and the TDMR model of heat flow vector in Fourier’s and Fick’s laws. The fundamental theorems (energy, uniqueness, reciprocity, and variational criterion) are examined using the preliminary equations for the simulated model TDMR. Reciprocity theorem applications are taken for particular scenarios including body forces, heat sources, and chemical potential sources. It has been noted that the variational criteria and these theorems are mostly influenced by the field variables’ susceptibility and the variations in the parameters of higher-order temporal derivatives. The two-dimensional example of the assumed model’s planar wave propagation is also provided. Four connected longitudinal waves have been identified: the primary (P) wave, secondary (S) wave, thermal (T) wave, and chemical potential (CP) wave. Wave properties such as phase velocity and attenuation coefficient are estimated numerically and displayed visually. A few special examples are also investigated and connected with the established outcomes. This work provides a foundation for further research into basic issues in thermoelastic continua under various physical field factors. Numerous applications in material science, geomechanics, soil dynamics, and the electronic sector can be made of the current findings.OPEN ACCESS Received: 22/02/2025 Accepted: 11/04/2025 Published: 30/06/2025