A Size-Dependent Non-Fourier Heat Conduction Model for Magneto-Thermoelastic Vibration Response of Nanosystems

This study proposes a new fractional model to show how heat transfers through nanomaterials by considering the thermoelastic vibration of one-dimensional nanostructures via nonlocal elasticity theory. Size-dependent properties of materials can either give a very high thermal conductivity or explain the heat transfer mechanism in large-scale integrated circuits, which improves the quality of thermoelectric devices. The modified heat conduction model includes two-phase lags and higher-order proportional Caputo fractional time derivatives. By applying the dual-phase lag approach, it can be shown that the energy equation can be simplified to regulate the heat transfer rate to the crystal lattice in nanostructured models. The suggested model is employed to investigate the magneto-thermoelastic interactions in a nonlocal solid that undergoes time-dependent periodic heat generation. The sensitivity of various material parameters, such as nonlocal parameters, higher-order derivatives, and fractional operators, is explored in depth for the considered physical fields.