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

Abstract

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.

Thermo‐viscoelastic behavior in an infinitely thin orthotropic hollow cylinder with variable properties under the non‐Fourier MGT thermoelastic model

“…In this problem under study we will assume that the thermal coefficients 𝐾 and 𝐾 * and the specific heat 𝐶 𝐸 are linearly temperature-dependent, while the parameter 𝑘, (𝑘 = 𝐾∕(𝜌𝐶 𝐸 ) will be taken into consideration as a constant value. The thermal coefficients 𝐾 are assumed to be in the following form [30,43]…”

“…Ilioushin and Pobedria [24] investigated the principle of thermoviscoelasticity as well as the solutions to certain thermoviscoelasticity boundary value problems. Several investigations related to the theory of thermoviscoelasticity have been presented in the literature for example, in [25][26][27][28][29][30][31][32][33][34].…”

Solution of Moore–Gibson–Thompson Equation of an Unbounded Medium with a Cylindrical Hole

“…In the context of several mechanical aspects of the flux, this theory started with a third-order differential equation. The MGT thermoelastic model has led to a significant increase in the range of researchers devoted to this theory [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma

“…This theory began with a third-order differential equation created in the context of fluid mechanics. Since the introduction of the MGT theory [ 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], many researchers have devoted their efforts to studying this new model.…”

“…In the recent decade, many researchers have focused on using different hyperthermia approaches to apply distinct bioheat models in cancer therapy [ 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 ]. Numerical and analytical approaches have been used to solve mathematical models, and certain adjustments have been made.…”