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The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

This study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity.

The concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials.

It has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form.

The outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

The purpose of this paper is to establish a two-dimensional model of Green–Lindsay theory for micropolar magneto-thermoelastic medium to study the photothermal effect. The model is used to study the coupling between elastic waves and plasma waves generated due to thermal changes in a micropolar elastic medium.

Normal mode analysis is used to obtain the analytical solutions of the governing equations.

Effects of magnetic field, micropolarity, photothermal and time are highlighted on various physical fields such as stresses, temperature, displacement and carrier density. The above physical fields also conform to the boundary conditions. It is further observed that all the physical quantities become zero outside some bounded region of space, thus confirming the notion of generalized theory of thermoelasticity.

The values of physical fields are computed numerically using MATLAB software considering material constants for silicon. Furthermore, the effects are depicted graphically and analyzed accordingly. The study is valuable for the analysis of thermoelastic problems involving magnetic field, micropolarity and elastic deformations.

The purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing piezoelectric layers.

A unit cell shall be taken into account for the simulation of BNNT's volume fraction. A rectangular micromechanical model is used to obtain the mechanical properties of unit cell of piezoelectric fiber-reinforced composite (PFRC). The three-dimensional (3D) elasticity method is presented to provide the relationship between displacements and stresses. The one-dimensional differential quadrature method (1D-DQM) and the state-space methodology are combined to create the semi-analytical technique. The state-space approach is utilized to implement an analytical resolution in the thickness direction, and 1D-DQM is used to implement an approximation solution in the radial direction. The composite consists of a polyvinylidene fluoride (PVDF) matrix and BNNTs as reinforcement.

A study on the PFRC is carried, likewise, the coefficients of its properties are obtained using a micro-electromechanical model known as the rectangular model. To implement the DQM, the plate was radially divided into sample points, each with eight state variables. The boundary situation and DQM are used to discretize the state-space equations, and the top and bottom application surface conditions are used to determine the natural frequencies of the plate. The model's convergence is assessed. Additionally, the dimensionless frequency is compared to earlier works and ABAQUS simulation in order to validate the model. Finally, the effects of the thickness, lateral wavenumber, boundary conditions and BNNT volume fraction on the annular plate's free vibration are investigated. The important achievements are that increasing the volume fraction of BNNTs increases the natural frequency.

The micromechanical “XY rectangle” model in PFRC along with the three-dimensional elasticity model is used in this literature to assess how the piezoelectric capabilities of BNNTs affect the free vibration of polymer-based composite annular plates under various boundary conditions.

This paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.

The analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.

Computational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.

The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.

This investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.

This study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of the involute arc cylindrical gear considering friction coefficient.

The influences of fractal dimension, fractal roughness and surface modification coefficient on the TCC of the rough surface were studied.

The results indicate that increasing the fractal dimension or reducing the fractal roughness enhances the TCC of the rough surface, and raising the surface correction coefficient contributes to this improvement.

In this work, the novelty of the work is that the authors first established a novel fractal model of TCC of the involute arc cylindrical gear considering friction coefficient. The achievements of this study provide some theoretical basis for the investigation of the TCC of the involute arc cylindrical gear.

The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.