Thermoelastic interactions in rotating media with diffusion and multi-phase-lag heat conduction under nonlocal theory

Purpose The purpose of this study is to investigate a rotating diffusive nonlocal thermoelastic medium under the multi-stage-lags model. Design/methodology/approach Laplace–Fourier method was introduced for solving the problem to obtain the expressions of field quantities are obtained. Using numerical computations with the computer in the context of software like MATLAB, the analytical findings have been authenticated. Findings The displacement components, temperature, mass concentration field and stresses are performed by numerical computations for suitable material and explained by displaying the graphs. Comparisons are made to highlight the impact of nonlocality, rotation and phase-lags parameters on the physical fields that indicate to the strong impact for the external parameters on the phenomenon and agree with the results obtained when the new parameters neglected. Originality/value The originality of this work lies in developing a unified mathematical model that simultaneously incorporates rotation, diffusion, nonlocal elasticity and multi-phase-lag heat conduction. While previous studies have considered these effects separately or in limited combinations, the current model provides a more comprehensive description of thermoelastic interactions by accounting for both spatial nonlocality and temporal phase-lag effects. This coupling allows for a more accurate representation of wave propagation and thermal behavior in advanced materials, particularly at micro- and nano-scales.