Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Using the Laplace transform, the governing partial differential equations have been converted to the space-domain, and then solved analytically to obtain the distributions of the field quantities. Numerical computations are shown graphically to verify the effect of memory presence, graded material properties, time-delay, Kernel function, and the thermo-piezoelectric response on the physical fields.

Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load

A theoretical nonlocal thermoelastic model for studying the effects of the thermal conductivity variability on a rotating nanobeam has been described in the present article. The theory of thermal stress is employed using the Euler–Bernoulli beam model and generalized heat conduction with phase lags. It is believed that the thermal conductivity of the current model varies linearly according to temperature. Due to variable harmonic heat, the considered nanobeam excited and was subjected to a time-varying exponential decay load. Using the Laplace transform process, the analytical solutions for displacement, deflection, thermodynamic temperature and bending moment of rotating nanobeams are provided in final forms and a numerical example has been taken to address the problem. A comparison of the stated results was displayed and additionally, the influences of non-local parameters and varying load were analyzed and examined. We also investigate how the linear changes in the temperature of physical properties can influence both the static and dynamic responses to the rotating nanobeam.

Emergence of Non-Fourier Hierarchies

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs, and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier’s law for room-temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermo-mechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier’s law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.