Search

Understanding the biothermal response of skin tissue exposed to electromagnetic (EM) radiation and variable thermal fields is crucial for mitigating risks associated with such exposures. This knowledge can empower the development of safe and efficacious evidence‐based treatments for various skin conditions within the medical field. This study employs the fourth‐order Moore–Gibson–Thomson (MGT) concept to establish a theoretical framework for biothermal analysis. This investigation aims to elucidate the biothermal response of skin tissues to EM radiation. The developed model facilitates the prediction of thermal reactions within human skin and the subsequent evaluation of bioheat transfer efficiency in biological tissues. The proposed model is implemented on a one‐dimensional representation of a skin layer and incorporates the effects of an induced electric field and a time‐harmonic heat source. Additionally, a linear dependence of metabolic heat generation on tissue temperature is considered. By employing Laplace transforms, the analytical solutions for tissue temperature are presented. The derived analytical solutions are compared with established theories to assess the accuracy of the proposed model. The results reveal that the modified MGT bioheat transfer model predicts lower temperatures compared to the conventional Pennes model, attributable to the incorporation of the thermal relaxation time constant. [ABSTRACT FROM AUTHOR]

In this article, a thermomagnetic viscoelastic nonlocal model has been introduced that incorporating the nonlocal elasticity theory of Eringen and the Kelvin–Voigt type. In the heat conductivity equation, the dual-phase-lag thermoelastic model (DPL) has been used to account for microstructural effects caused by high-rate heat transfer processes. The proposed DPL thermoelastic model illustrates the effects of material deficiencies and the thermomechanical relationship due to the extremely rapid heating. Within the framework of the nonlocal DPL model, a one-dimensional magneto-thermoelastic problem of half-space whose surface is exposed to an instantaneous heat source and magnetic field has been studied. With the eigenvalue approach technique and Laplace transform method, analytical solutions for the studied physical fields are provided. The transformed expressions to the field quantities are reversed into the physical domain by applying Zakian's algorithm. The effects of the nonlocal parameter, the viscosity and the applied heat source have been shown graphically on the differences in the fields within the medium. [ABSTRACT FROM AUTHOR]

Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier's equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors. [ABSTRACT FROM AUTHOR]

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions. [ABSTRACT FROM AUTHOR]

This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder's thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure. [ABSTRACT FROM AUTHOR]

The present study examines the lateral thermal vibrations of a nanobeam subjected to an axial motion while being influenced by a sinusoidal thermal load. The partial differential equation describing the system was obtained using the extended Hamiltonian principle. Also considered were the Euler‐Bernoulli (EB) beam, the nonlocal couple stress theory, and Eringen's nonlocal elasticity model. This type of axially moving beam has multiple applications in design, including industrial, civil, structural, chemical, and computer engineering. The Laplace transform technique is utilized to translate partial differential equations into a thermoelastic differential equation of the sixth order. This study investigates the impact of nanobeam size and velocity on thermo‐mechanical characteristics. To explore the impacts of axial velocity, pulse width, nonlocal index, material length scale coefficient, and phase lag coefficients on the examined studied fields, such as lateral vibration and temperature change for the moving nanobeam are calculated. The specified factors were discovered to impact the flexibility and dynamic response of the nanobeam substantially. [ABSTRACT FROM AUTHOR]

Mathematical models and numerical simulations are used to analyse and predict the behaviour of porous materials under coupled mechanical and thermal loading conditions in poroelastic thermoelastic studies. This field is crucial in understanding and designing systems involving porous media where mechanical and thermal factors are important. For this reason, this work aims to provide a theoretical study of porous elastic materials surrounded by a magnetic field using the dual phase lag (DPL) model of thermoelasticity. The significance of this study lies in its diverse range of applications across several engineering, and geophysical disciplines, encompassing soil mechanics, geomechanics, petroleum engineering, and civil engineering. An investigation was conducted on an indefinitely long, porous, solid circular cylinder subjected to a constant magnetic field to demonstrate the proposed theoretical framework. The outer surface of the cylinder was thermally shocked and maintained free from any stress or traction. To solve the problem, Laplace transforms and their inverse methods are used. Numerical examples of excess pore water pressure, temperature, displacement, induced magnetic field, and thermal stresses are given at different medium sites. Finally, graphical representations were created to depict the results of field variables across different thermal delays and porosity estimates. [ABSTRACT FROM AUTHOR]

Abstract In order to describe the photothermal dynamic behavior of viscoelastic semiconductor materials, the authors of this work propose a fractional modification of the Kelvin-Voigt type. The generalized Mittag-Leffler function method with two parameters was utilized as the non-local, nonsingular kernel of the Goufo-Caputo fractional operator, which is similar to the AB fractional derivative. Also, a new concept of photovoltaic heat transfer has been developed to describe the process of photothermal heating in semiconductors, in which light energy is converted into thermal energy by absorption. This unique model is grounded in the theoretical framework of the Moore-Gibson-Thompson (MGT) equation, and it offers additional insights into the underlying process of light sensitive heat transfer, as well as the intricate interaction between heating signals, elasticity, and plasma. As a direct application of the proposed model, the photothermal interactions that occur when an infinitely rotating semiconductor material with a cylindrical hole is subjected to a laser thermal flux and immersed in a constant axial magnetic field have been investigated. These findings may have implications for developing optically absorbent nanostructures and their use in photothermal energy generation. For this reason, the comparison of modified photoelasticity models with spherical derivatives and classical models applied to semiconducting materials seems interesting. [ABSTRACT FROM AUTHOR]

This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected to an electrical power source was employed to generate heat. In addition, the influence of an ultra‐short‐pulsed laser on the vibration of a microbeam is studied, taking into account its heating effect. The microbeam system variables were analyzed after solving the mathematical equations by applying the Laplace transform technique. Graphs showing how different inputs affect different mechanical fields, such as Winkler substrate stiffness, voltage, electrical resistance, and temperature modulus pulses, are also presented. An increase in the Winkler modulus and the shear modulus of the foundation was found to decrease the amount of deflection and axial deformation in the microbeams. The increased beam stiffness has resulted in this decrease. [ABSTRACT FROM AUTHOR]

When designing mechanical equipment, it's important to consider the photothermal impacts in addition to mechanical ones. This is because photothermal effects can have a significant influence on equipment performance. In this paper, a new theory of thermo-photoelasticity is presented that explains the processes of photoelectron carriers and heat transport in homogeneous and isotropic viscoelastic semiconductor materials. The proposed model combines fourth-order Moore–Gibson–Thompson (MGT) thermoelasticity with the coupled plasma equation. We also include the viscoelastic linear Kelvin–Voigt model, which represents the viscous nature of matter, as part of the model derivation process. We study the problem of a thermoelastic semiconductor medium with stable elastic properties and its traction-free surface exposed to heat flux in the form of laser pulses. To provide analytical solutions for all the variables studied, we use the normal mode approach as the methodology. Furthermore, we estimate the effects of laser pulse rise time, viscosity, and thermal parameters on all fields studied with the help of some comparisons displayed in different illustrations. [ABSTRACT FROM AUTHOR]

In this study, the Moore–Gibson–Thompson (MGT) concept of thermal conductivity is applied to a two-dimensional elastic solid in the form of a half-space. This model was constructed using Green and Naghdi's thermoelastic model to address the infinite velocity problem of heat waves. It has been taken into account that the free surface of the medium is immersed in an electromagnetic field of constant intensity, undergoes thermal shock, and rotates with a uniform angular velocity. The governing equations of a modified version of Ohm's law account for the impact of temperature gradients and charge densities. By using the method of normal mode analysis, an analytical representation of the studied physical fields was obtained. The effect of rotation and the modulus of modified Ohm's law on the responses of the field distributions examined is discussed, along with accompanying graphical representations. Other thermoelastic models have been compared with the results of the proposed system when the relaxation time is ignored. [ABSTRACT FROM AUTHOR]

The objective of this work is to improve an appropriate generalized thermoelastic heat transport framework. In the proposed model, the mathematical heat transfer equation is characterized by the fourth-order Moore-Gibson-Thompson (MGT) equation. Construction of the system equation in Green-Naghdi type III model involves the addition of the phase lag delay coefficient up to the second degree. This proposed model is advantageous because it is compatible with observable physical processes and allows speed reduction as heat waves travel within the solid. The presented model can also be used to derive a number of alternative models of thermoelasticity as special cases. The Hall current influence is considered to analyze the magneto-thermoelastic couplings in an infinite conducting viscoelastic medium with a cylindrical cavity under a strong magnetic field propagating along the cavity axis. It is assumed that the viscoelastic material of the medium is Kelvin-Voigt type. Also, in contrast to many cases where the thermal conductivity factor remains unchanged, it is considered that this coefficient varies with changes in temperature. To solve the system of equations, the Laplace transform methodology is used. The studied fields are shown schematically, and the implications of viscosity and thermal fluctuation are explained. Moreover, tabular representations of numerical data are provided, and the suggested model is validated via comparison with the existing frameworks. • Development of a proper generalized thermoelastic heat transfer framework. • The fourth-order Moore-Gibson-Thompson (MGT) equation is used. • The Hall current influence is considered for the magneto-thermoelastic couplings. • Laplace transform method is employed to solve the system of equations. • Thermal conductivity factor varies with changes in temperature. [ABSTRACT FROM AUTHOR]

Optical and photo-thermal effects have emerged in many fields, including thermal characterization, spectroscopy, transportation, and non-destructive examinations. In this study, the Moore-Gibson-Thompson (MGT) thermoelastic model is used to explore the photo-thermal coupling of an isotropic, homogeneous, semiconducting and thermomagnetic solid. The heat conduction law is modified to include the time derivative of fractional order and theoretically formulate the system of governing equations. Using the extended Mittag–Leffler functions as nonsingular kernels, the Atangana and Baleanu derivatives considers the features of fractional derivatives. As measured by an external reference frame, it is taken into account that the medium rotates with a constant angular velocity about the axis of symmetry. The cavity boundaries undergo thermal shock and time-varying heat flux. It has been shown that the Laplace transform method is a powerful technique for solving such problems that link the plasma and heat transfer with phase delays. It is finally aimed to describe the numerical results for changes in carrier density as a function of time and radial distance, temperature increment, strain, thermal stresses, and displacement using a photo-induced carrier with different values of physical relaxation time and fractional operator. [ABSTRACT FROM AUTHOR]

By laminating piezoelectric and flexible materials during the manufacturing process, we can improve the performance of electronic devices. In smart structure design, it is also important to understand how the functionally graded piezoelectric (FGP) structure changes over time when thermoelasticity is assumed. This is because these structures are often exposed to both moving and still heat sources during many manufacturing processes. Therefore, it is necessary to conduct theoretical and experimental studies of the electrical and mechanical characteristics of multilayer piezoelectric materials when they are subjected to electromechanical loads and heat sources. Since the infinite speed of heat wave propagation is a challenge that classical thermoelasticity cannot address, other models based on extended thermoelasticity have been introduced. For this reason, the effects of an axial heat supply on the thermomechanical behavior of an FGP rod using a modified Lord-Shulman model with the concept of a memory-dependent derivative (MDD) will be explored in this study. The exponential change of physical properties in the direction of the axis of the flexible rod will be taken into account. It was also assumed that there is no electric potential between the two ends of the rod while it is fixed at both ends and thermally isolated. Applying the Laplace transform method, the distributions of the physical fields under investigation were calculated. The obtained results were compared to those in the corresponding literature with varying heterogeneity values, kernel functions, delay times, and heat supply speeds. It was discovered that the studied physical fields and the dynamic behavior of the electric potential are weakened by increasing the inhomogeneity index. [ABSTRACT FROM AUTHOR]

This work aims to theoretically analyze the nonuniform heat transfer through a micropolar miniature half-space by investigating the magneto-thermo-viscoelastic interactions. To examine the micromechanical coupling and the influence of thermo-mechanical relaxation, a higher-order two-phase-lag thermoelastic concept and a viscoelastic model of Kelvin–Voigt type are considered. The theoretical framework has been extended to incorporate the Eringen's nonlocal model to include the small-scale effects. The so-called Hall effect occurs in a conductive material when it is subjected to a high magnetic field orthogonal to the direction of the current traveling through it. Without nonlocality and viscoelastic effects, it is possible to achieve different types of generalized theories of thermoelasticity. The governing equations are developed and numerically solved using Laplace transforms. The Laplace transform is then inverted numerically using a method based on Fourier series expansion, and then the numerical values of physical fields are presented. The consequences of variations in nonlocality, viscoelasticity and the Hall effect are finally demonstrated and a comparison between the findings of this study and those for the generalized thermoelastic models are reported. [ABSTRACT FROM AUTHOR]

The increase in electric potential occurs when the temperatures of electrically conductive or semiconductive materials change, known as the Seebeck effect. In this paper, the Moore-Gibson-Thompson heat equation model was constructed for an extended theory of thermomagnetic elasticity to show how this phenomenon affects flexible materials. As a result of the Seebeck effect, the impacts of thermal gradients and charge density, as well as those of Fourier's law and current density, are incorporated into Ohm's law. This model has been used to study what would happen to an unbounded thermoelastic solid material when exposed to a uniform magnetic field and a continuous thermal line. To address the problem, we combined the Laplace and Hankel transformational methods with the potential function technique. The numerical inversions of the investigated physical fields in the space–time domain were obtained using an accurate and well-proven Laplace transform inversion algorithm. Graphs are used to represent the numerical data, and the results have been analyzed. In addition, the effect of thermoelectric sensitivity and the coefficient that relates current density to heat flux density was measured. [ABSTRACT FROM AUTHOR]

According to the concept of small polar thermoelasticity, rotational and translational motions of elastic materials can cause aggregate deformations, temperature changes, and microcycles. This theory is used to study atomic and molecular vibrations and the deformation of solids due to changes in temperature and other energetic forces. The current study investigates the two-dimensional electromagnetic micropolar thermoelasticity of an elastic medium whose surface is heated by a heat source and influenced by a transverse magnetic field. This work combines the higher-order dual phase lag model with the two-temperature theory to address this investigation. Using the normal mode approach to the system equations, we have calculated the temperature normal force stress, displacements, and tangential couple stress in the physical domain. The corresponding expressions of the studied fields are provided, and corresponding graphical examples are also provided. Numerical comparisons were made to investigate the effects of the discrepancy index, the Hall current, and higher-order derivatives. It is concluded from the present contribution that some advanced thermoelastic systems deserve study. [ABSTRACT FROM AUTHOR]

This article introduces a new model that can be used to describe elastic thermal vibrations caused by changes in temperature in elastic nanobeams in response to transverse external excitations. Using the idea of nonlocal elasticity and the dual-phase lagging thermoelastic model (DPL), the coupled equations of motion and heat transfer were derived to explain small-scale effects. Additionally, modified couple stress theory (MCST) and Euler–Bernoulli (EB) beam assumptions were considered. The proposed theory was verified by considering the thermodynamic response of nanobeams moving horizontally at a constant speed while one end is subjected to a periodic thermal load. The system of governing equations has been solved numerically with the help of Laplace transforms and one of the tested evolutionary algorithms. The effects of changing the nonlocal modulus, the magnitude of the external force, and the length scale parameter on the system fields were investigated. It is also shown how the behavior of the thermal nanobeam changes depending on the phase delay factors in addition to the horizontal velocity of the beam. To determine this model's accuracy, its results were compared with the results of the classical continuity model and thermoelastic concepts. The numerical results show that when the nanobeam moves, the length scale can change the studied thermal and mechanical vibration wave patterns and physical fields. Additionally, during thermally stimulated vibrations, thermodynamic effects that have implications for the dynamic design and performance improvement of nanostructures must be considered. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Thermo-magnetic interaction in a viscoelastic micropolar medium by considering a higher-order two phase-delay thermoelastic model." The correction addresses some typos and errors in the original article. It corrects the units of certain parameters, fixes a misprint in an equation, and clarifies the definitions of dimensionless parameters. The authors state that the corrected formulas for these parameters are valid when substituting the system parameters. The correction notice concludes with a declaration of no conflict of interest and a note from the publisher. [Extracted from the article]

This study highlights the introduction of a new mathematical model for functionally graded thermoelastic nanobeams (FGNB) which contains a free choice of the kernel function and time delay. The basic equations that govern the proposed model have been constructed on the basis of Hamilton's principle, Euler-Bernoulli's assumptions, Eringen's theory and three-phase-lag memory dependent heat conduction. The FGNB is due to a heat flux depending on time. The nanoscale beams can be regarded as non-homogeneous composite structures and typically vary from the ceramic at the bottom of the beam to the metal on the top with a continuous structural transmission along with the thickness of the beam. Utilizing the Laplace integral transform, the problem is solved analytically. The variations in moment distribution, temperature, displacement and deflection are illustrated graphically for the various kernel functions, time delays, the influence of the nonlocal parameter, and periodic pulse. Compared with the current thermoelastic models, the implications of the present model are discussed. [ABSTRACT FROM AUTHOR]

In this study, the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage are investigated. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore–Gibson–Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler–Bernoulli microbeams is provided with the support of visco-Pasternak's base with three parameters. Using the Laplace transform method, an approximation of an analytical solution is found for the field variables being examined. A comparison was made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature. [ABSTRACT FROM AUTHOR]

By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be addressed using classical thermoelasticity, extended thermoelasticity models have been derived. The thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a moveable axial heat source is considered in this paper, utilizing the dual-phase-lag (DPL) heat transfer model. It was supposed that the physical characteristics of the FG rod varied exponentially along the axis of the body. Both ends hold the rod, and there is no voltage across them. The Laplace transform and decoupling techniques were used to obtain the physical fields that have been analyzed. A range of heterogeneity, rotation, and heat source velocity measures were used to compare the results presented here and those in the previous literature. [ABSTRACT FROM AUTHOR]

This paper introduces size-dependent modeling and investigation of the transverse vibrational behavior of rotating thermoelastic nanobeams by means of nonlocal elasticity theory. In the formulation, a model of thermal conductivity with two-phase delays (DPL) was utilized. By incorporating the interactions between phonons and electrons, this model took into account microstructural influences. Also, we have employed the state-space approach and Laplace transform approach to solve the governing equations, which were developed in the context of the nonlocal Eringen model. The nanobeam material is subjected to a changeable temperature field produced by the graphene tape attached to the nanobeam and connected to an electrical source. In addition, the nanobeam material is fully encompassed by an axially applied magnetic field. It has been revealed how coefficients such as the rotational angular velocity of the nanobeam, nonlocal coefficient, voltage, electrical resistance, and applied magnetic field influence its behavior. [ABSTRACT FROM AUTHOR]

In this article, a modified Moore–Gibson–Thompson heat transfer equation with a memory-dependent derivative is utilized to investigate the thermoelastic interaction induced by non-Gaussian lasers in an infinitely elastic nonlocal medium. A memory-based derivative is also examined, and it was discovered to be superior at predicting the pattern of real-life challenges. This finding is part of the conviction that is currently analyzed. The idea of a memory-dependent derivative is attractive since it has some peculiarities. These characteristics include remarkable components as the kernel function and time lag, both of which can be freely selected according to the specifications of the problem. In addition, the non-local concept of Eringen was utilized in the research project so that the small-scale influence could be understood. Using the Laplace transform as a method, analytical–numerical solutions to problems involving thermo-physical fields, such as dimensionless temperature and deformation, as well as nonlocal physical stress, can be analyzed and compared. Numerical solutions have been used to explore the influence of memory-dependent derivative components such as the kernel function and the time delay coefficient on the studied domain variables of the medium. The computational outcomes of the studied fields are also used to find out the role of the non-local index. [ABSTRACT FROM AUTHOR]

Functionally gradient materials (FGM) in nanobeams are interesting issues in the theory of elasticity and thermoelasticity regarding thermal and mechanical stress. These advanced heat-resistant materials are used as structural components in contemporary technology. The thermoelastic interactions in functionally graded nanobeams (FGN) have been studied in this article. The basic equations that control the introduced model have been established based on the Euler–Bernoulli beam concept, Eringen's theory, and the two phase-lag fractional heat conduction model. The heat equation has been modeled and fractionalized into a new formula that includes nonsingular and nonlocal differential operators. The physical properties of the nanobeam vary in graded according to its thickness. The FGN nanobeam is subject to a time-dependent and periodically varying heat flow. The differential equations are analyzed analytically in the Laplace transform field. The responses in the nanobeam are graphically depicted for various fractional-order values, the influence of the nonlocal parameter and the periodic frequency of the heat flux. The results show that the gap between classical and nonlocal theories widens with increasing nonlocal parameters and decreasing nanobeam length. [ABSTRACT FROM AUTHOR]

The term "optical thermoelasticity" is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters. [ABSTRACT FROM AUTHOR]

On the basis of the analysis of thermoelastic motion, the current research develops a novel model of modified thermoelasticity. The rotating long hollow cylinders with fixed surfaces are considered in a generalized Moore–Gibson–Thompson thermoelastic model (MGTTE) framework, including the modified Ohm's law. The cylinders are made of a thermoelastic material that rotates at a uniform rotational speed and is elastic in the transverse direction. The set of equations for the MGT heat conduction in the new model is built under the influence of the electromagnetic field by including a delay time in the context of Green–Naghdi of the third kind (GN-III). The inner boundary of the hollow cylinder is not only restricted but also sensitive to heat loading. The outer surface, on the other hand, is also restricted but insulates the heat. The Laplace transform method is utilized to deal with the differential equations produced in the new domain and transfer the problem to the space domain. The Dubner and Abate method is used to compute dynamically and graphically depict the theoretical findings for an isotropic transverse material. After comparing the results of several thermoelastic theories, the implications for the electromagnetic field are discussed. [ABSTRACT FROM AUTHOR]

This article proposes a photothermal model to reveal the thermo-magneto-mechanical properties of semiconductor materials, including coupled diffusion equations for thermal conductivity, elasticity, and excess carrier density. The proposed model is developed to account for the optical heating that occurs through the semiconductor medium. The Moore–Gibson–Thompson (MGT) equation of the fourth-order serves as the theoretical framework to establish the photothermal model. It is well-known that the optical and heat transfer properties of such materials behave as random functions of photoexcited-carrier density; therefore, the current model is remarkably more reliable compared to the earlier closed-form theories which are limited to a single form. The constructed theoretical framework is able to investigate the magneto-photo-thermoelastic problems in a semiconductor medium due to laser pulse excitation as a case study. Some parametric studies are used to exhibit the impact of thermal parameters, electromagnetic fields, laser pulses and thermoelectric coupling factors on the thermomagnetic behavior of physical variables. Finally, several numerical examples have been presented to draw the distributions of the examined field variables. [ABSTRACT FROM AUTHOR]

The current work presents a theoretical framework to analyze the nonlocal thermoelastic model with a general kernel function for memory-based derivatives by incorporating two-time delays. The introduced model aims at studying the thermomechanical response of rotating size-dependent nanobeams. The nonlocal elasticity theory and the generalized heat conduction model with phase delays are utilized to formulate the problem. In the proposed model, the thermal conductivity is expected to vary linearly with temperature and the system is excited by a variable harmonic heat source by considering the time-dependent exponential decaying load. To this end, the semi-analytical solutions for the transverse and axial displacements, thermodynamic temperature and bending moment are examined using the Laplace transform method. The effects of the nonlocal parameter and various loading conditions are also investigated and discussed. Finally, it is demonstrated that how the linear variation of thermal conductivity could affect the performance of the considered system. [ABSTRACT FROM AUTHOR]

The small size and clever design of nanoparticles can result in large surface areas. This gives nanoparticles enhanced properties such as greater sensitivity, strength, surface area, responsiveness, and stability. This research delves into the phenomenon of a nanobeam vibrating under the influence of a time-varying heat flow. The nanobeam is hypothesized to have material properties that vary throughout its thickness according to a unique exponential distribution law based on the volume fractions of metal and ceramic components. The top of the FG nanobeam is made entirely of ceramic, while the bottom is made of metal. To address this issue, we employ a nonlocal modified thermoelasticity theory based on a Moore–Gibson–Thompson (MGT) thermoelastic framework. By combining the Euler–Bernoulli beam idea with nonlocal Eringen's theory, the fundamental equations that govern the proposed model have been constructed based on the extended variation principle. The fractional integral form, utilizing Atangana–Baleanu fractional operators, is also used to formulate the heat transfer equation in the suggested model. The strength of a thermoelastic nanobeam is improved by performing detailed parametric studies to determine the effect of many physical factors, such as the fractional order, the small-scale parameter, the volume fraction indicator, and the periodic frequency of the heat flow. [ABSTRACT FROM AUTHOR]

This work gives some results and develops the derivation of memory dependence heat conduction model with dual phase-lags using the modified definition of the fractional derivative of Caputo and higher-order memory-dependent derivative (MDD). The introduced model was derived by improving the heat conduction equation replacing the conventional Fourier's law and generalizing some of the previous models. As an application of the proposed model, we will consider an infinite thermoelastic long annular cylinder whose inner surface is thermally insulated and restricted, while the exterior surface is due to thermal shock and traction free. The numerical results of the physical fields are shown graphically against the position, and the effects of some basic parameters on them are estimated. Theoretical analysis and mathematical results confirm that the selection of an appropriate kernel, time delays and memory response can affect the turbulence in the thermal fields. [ABSTRACT FROM AUTHOR]

In this research, two alternative approaches to fractional derivatives, namely Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional operators, are used to propose a generalized model of thermoelastic heat transfer of a rigid cylinder with thermal characteristics. The proposed model can be constructed by combining the DPL model with phase delays and the two temperature theories. It will be taken into account that the solid cylinder has variable physical properties. It was also assumed that the surface of the cylinder is penetrated by a continuous magnetic field and is regularly exposed to thermal loading from a continuous heat source. The numerical solutions of the studied physical fields in the AB and CF fractional derivative cases were derived using the Laplace transform method and are compared visually and tabularly and discussed in detail. [ABSTRACT FROM AUTHOR]

The main objective of this work is to study the homogeneous thermoelastic interactions in an isotropic hollow thin cylinder immersed in an electric–magnetic field using the linear Moore–Gibson–Thompson theory of thermoelasticity, taking into account the generalized Ohm's law. The MGT system of thermoelastic equations for the new model is created by incorporating a relaxation period in the Green–Naghdi type III framework. In addition, the Maxwell equations that investigate the effect of the electromagnetic field are presented. While the outer surface of the hollow cylinder is thermally insulated and free of traction, the interior surface is both free of traction and subject to thermal shock. To convert the problem to the space domain only, the Laplace transform methodology is used to solve the governing equations generated in the transformed domain. The theoretical results are computed dynamically and are graphically displayed for a transversely isotropic material using the Honig and Hirdes approach. A comparison of findings based on different (classical and generalized) thermoelastic theories is provided, followed by a discussion on the impact of the applied electromagnetic field. [ABSTRACT FROM AUTHOR]

By considering the Moore–Gibson–Thompson (MGT) equation, the current work introduces a modified fractional photothermal model. The construction model is based on the proportional Caputo fractional derivative, which is a new definition of the fractional derivative that is simple and works well. In addition, the theory of heat transfer in semiconductor materials was used in the context of optical excitation transfer and plasma processes. The proposed model was used to investigate the interaction of light and heat within a magnetized semiconductor sphere rotating at a constant angular speed. The Laplace transform was used to obtain solutions for optical excitation induced by physical field variables. Using a numerical method, Laplace transforms can be reversed. The figures show the effects of carrier lifetime, conformable fractional operator, and rotation on thermal and mechanical plasma waves, which are shown in the graphs. The theory's predictions were compared and extensively tested against other existing models. [ABSTRACT FROM AUTHOR]

In this work, we extend the modification of the generalized theories of thermoelasticity and photothermal. In this context, a new model has been derived based on the Moore-Gibson-Thompson (MGT) equation and combining the two models of thermoelasticity with one relaxation time (Lord-Shulman) and the theory of Green-Naghdi of the third type (GN-III). One of the most important features of the proposed model is that it predicts limited speeds of thermal signals and photovoltaic waves. The proposed model has been applied to examine the interactions between plasma, thermal, and elastic processes within a solid semiconductor sphere. It was taken into account that the sphere rotates with a constant angular velocity around its axis, is surrounded by an external magnetic field, and is also subjected to thermal shock. The singularities encountered in different physical fields have been addressed in the center and poles of the sphere. The influence of rotation and carrier lifetime parameters on different physical properties of semiconductor materials has been graphically displayed and explained using the Laplace method. [ABSTRACT FROM AUTHOR]

The current paper is concerned with a new size-dependent thermoelastic model where the constitutive and the motion equations are modified. The governing equations of the introduced model are derived based on the generalized dual-phase-lag thermoelastic model and non-local elasticity theory. Additionally, the present work is an attempt to investigate a thermoelastic interaction in an infinite medium with a cylindrical cavity based on the proposed model. The cavity surface is traction free and exposed to a time-dependent moving heat source. The analytical formulas for the field quantities are obtained first in the Laplace transform domain. To find the inverse Laplace transform into the physical quantities, a numerical technique is performed. The numerical results are discussed in different cases to highlight the effect of the size -scale parameter and the speed of the heat source on the studied thermo-physical fields. [ABSTRACT FROM AUTHOR]

An advanced model is developed to analyze the thermoelastic vibrations of a nonlocal isotropic solid medium subjected to a pulsed heat flux using Caputo–Fabrizio fractional derivative heat conduction. The mathematical model of an infinite isotropic and homogeneous medium is obtained by applying nonlocal elasticity theory and fractional calculus using single kernels with generalized thermoelasticity. The Laplace transform technique is employed to numerically solve the fundamental equations under the corresponding boundary conditions of the problem. A detailed parametric study is performed to examine the effects of increasing laser pulse duration as well as fractional and nonlocal order coefficients on thermoelastic waves of the medium. It can be emphasized that the higher temperature will reduce the thermal conductivity. It is also notable that some special cases and previous thermoelastic models can be reduced from the present model. [ABSTRACT FROM AUTHOR]

This investigation aims to employ a modified fractional two-phase thermal conductivity (DPL) model to elucidate the influence of temperature variations on the thermophysical properties of human skin tissue. The model incorporates the fractional Atangana–Baleanu (AB) derivative operator, characterized by its non-local and non-singular kernel. This specific choice enables the model to capture non-local effects and memory phenomena within the context of skin tissue thermal conductivity. A segment of human skin tissue is subjected to a ramp-type thermal load for analysis using the modified fractional two-phase DPL model. The investigation focuses on the exterior surface, with the opposing surface assumed to be thermally insulated and free of external mechanical interactions. The governing equations are employed within the Laplace transform domain to describe and solve for the thermophysical response of the skin tissue. Subsequently, a parametric study is conducted to elucidate the influence of phase delays, fractional order, and the ramp heating profile on the behavior of the tissue under various scenarios. [ABSTRACT FROM AUTHOR]

In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen's non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian's computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined. [ABSTRACT FROM AUTHOR]

Many challenges in different applied fields of research, such as materials science, viscoelasticity, biological sciences, physics, and mechanical engineering, require the study of derivative operators using single singular or nonsingular kernels. Atangana and Baleanu (AB) constructed a novel fractional derivative without a singular kernel based on the extended Mittag–Leffler function to overcome the singular kernel problem seen in previous definitions of fractional‐order derivatives. In this article, we provide a novel mathematical thermoelastic heat conduction model that includes the fractional AB derivative operators. In addition, the Moore–Gibson–Thompson (MGT) equation has been incorporated into the proposed heat transport model. The proposed model has been applied to study an infinite orthotropic material with a cylindrical aperture, and the thermal conductivity coefficient of the body depends on the temperature change. The Laplace transform approach has been used to solve the system of governing partial differential equations (PDEs). To assess the validity of the proposed model and for the purposes of comparison, the numerical results have been depicted in figures as well as in tables. [ABSTRACT FROM AUTHOR]

Long hollow cylinders are commonly utilized in various technological applications, including liquid and gas transmission. As a result, its value is growing, becoming increasingly important to many research efforts. Compared with thermal isotropic homogeneous cylinders, thermo-viscoelastic orthotropic cylinders have less relevant data. In this paper, a thermoelastic fractional heat conduction model was developed based on the Moore-Gibson-Thompson equation to examine the axial symmetry problem of a viscoelastic orthotropic hollow cylinder. Atangana and Baleanu derivative operators with nonsingular and nonlocal kernels were used in constructing the fractional model. The thermal properties of the cylinder materials are assumed to be temperature-dependent. The Laplace transform is applied to solve the system of governing equations. The numerical calculations for temperature, displacement, and stress components are performed by the effect of fractional order, rotation, and changing thermal properties of the cylinder. The results showed that due to the presence of fractional derivatives, some properties of the physical fields of the medium change according to the value of the fractional order. [ABSTRACT FROM AUTHOR]

This work aims to assess the response of viscoelastic Kelvin–Voigt microscale beams under initial stress. The microbeam is photostimulated by the light emitted by an intense picosecond pulsed laser. The photothermal elasticity model with dual-phase lags, the plasma wave equation and Euler–Bernoulli beam theory are utilized to construct the system equations governing the thermoelastic vibrations of microbeams. Using the Laplace transform technique, the problem is solved analytically and expressions are provided for the distributions of photothermal fields. Taking aluminum as a numerical example, the effect of the pulsed laser duration coefficient, viscoelasticity constants and initial stress on photothermal vibrations has been studied. In addition, a comparison has been made between different models of photo-thermoelasticity to validate the results of the current model. Photo-microdynamic systems might be monolithically integrated on aluminum microbeams using microsurface processing technology as a result of this research. [ABSTRACT FROM AUTHOR]

In the presented work, a modified fractional Kelvin–Voigt model (KVM) is introduced to explain the time-dependent behavior of viscoelastic materials based on thermo-viscoelasticity theory and fractional calculus. The fractional KVM involves mechanical viscoelastic parameters and differential operators of fractional orders. In addition, the governing system equations are constructed within the framework of generalized thermoelasticity with three different delay times (TPL). The resulting derived model is used to study the thermo-viscoelastic interactions in a rotating transversely hollow cylinder under the influence of thermal loads and due to a magnetic field of constant intensity. The system of equations is solved, and solutions for non-dimensional physical quantities such as temperature, radial displacement, and thermal stresses are derived by applying the Laplace transform technique. To assess the influences of fractional order, relaxation factors and delay time parameters using different models of thermo-viscoelasticity in the presence and absence of fractional orders, several comparisons are made in tables and figures. Finally, according to the discussion of the numerical results, the prominent role of these parameters in the propagation behavior of mechanical and thermal waves is revealed. [ABSTRACT FROM AUTHOR]

Photothermal spectroscopy is a method of measuring the optical absorption and thermal properties of semiconductor materials using high-sensitivity spectroscopic techniques. Heating occurs due to light, which is absorbed but not dissipated by emission. In this paper, a new model is provided that can be used to understand the process of optical thermal transfer and the interaction between elastic plasma waves and heat. The proposed photothermal model is described by the Moore–Gibson–Thompson heat equation. Using the proposed model, the thermal and photoacoustic effects in an infinite isotropic and homogeneous body with a cylindrical cavity of semiconductor material crossed into a fixed magnetic field and subjected to high-intensity laser heat flux were investigated. The inner surface of the cavity is considered to be traction-free, and the carrier density is photogenerated by a laser pulse heat flux that decays exponentially. The numerical calculations for the components of thermal stresses, displacement, temperature field, and carrier density are obtained using the Laplace transform approach. The propagation of heat, elastic, and plasma waves, as well as the distributions of each investigated field, were examined and explained. The comparison is also used to see how different thermal response features, such as thermal relaxation, laser pulse duration, and lifetime, affect the thermoelastic response. [ABSTRACT FROM AUTHOR]

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered. [ABSTRACT FROM AUTHOR]

The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. The equations of the heat conduction and the mass diffusion have been modified by using Taylor's series of time-fractional order. In this new model, the Fourier and the Fick laws have been modified to include a higher time-fractional order of the heat conduction vector, the gradient of temperature, the diffusing mass flux and the gradient of chemical potential. We adopted the definitions of Caputo and Jumarie; for time-fractional derivatives. The work of Nowacki; Sherief, Hamza, and Saleh; and Aouadi; are deduced as limit cases from the current investigation. Applying this formulation, we have discussed a thermoelastic-diffusion problem for a half-space exposed to thermal and chemical shock with a permeable material in contact with the half-surface. We discussed the sensitivity of the different physical parameters in all studied fields in detail and the results are presented graphically as well as in tabular forms. [ABSTRACT FROM AUTHOR]

Rotating micromachined beams are one of the most practical devices with several applications from power generation to aerospace industries. Moreover, recent advances in micromachining technology have led to huge interests in fabricating miniature turbines, gyroscopes and microsensors thanks to their high quality/reliability performances. To this end, this article is organized to examine the axial dynamic reaction of a rotating thermoelastic nanobeam under a constant‐velocity moving load. Using Eringen's nonlocal elasticity in conjunction with Euler–Bernoulli theory and Hamilton's principle, the governing equations are derived. It is assumed that the nanobeam is affected by thermal load and the boundary condition is simply supported. The Laplace transform approach is employed to solve the partial differential equations. A numerical example is presented to analyze the effects of the nonlocal parameter, rotation speed and velocity of the static moving load on the dynamic behavior of the system. The numerical results are graphically illustrated and analyzed to recognize the variations of field variables. Finally, in some special cases, our results are compared to those reported in the literature to demonstrate the reliability of the current model. [ABSTRACT FROM AUTHOR]

The current paper has been presented to illustrate the thermoelastic vibration of a rotating microbeam based on generalized thermoelasticity theory, taking into account Euler–Bernoulli's assumptions. Using Hamilton's principle, the equation of motion of the initially stressed rotating microbeams has been derived. The microbeam is exposed to femtosecond laser pulses and sinusoidal varying heat. The Laplace transform technique is applied to obtain an analytical solution to the field variables. The influence of properties of various parameters, such as axial load, laser pulse duration, angular velocity, and material variation on the thermal and elastic waves of the rotating microbeam has been displayed graphically and discussed in detail. [ABSTRACT FROM AUTHOR]

The objectives of this article are to present a mathematical model that uses Eringen's nonlocal elasticity theory to describe the free vibratory motion of rotating nanoscale beams. The Euler–Bernoulli beam theory, Eringen's nonlocal elasticity theory, and generalized thermoelasticity with phase-lags are used to derive the system of equations for rotating thermoelastic nanobeams. The studied nanobeam is subjected to ramp-type heating and to a significantly exponentially decaying load. The analytical solution was derived using the Laplace transform method, and the transformation of the converted fields was performed by applying the residue calculus. The numerical results of the physical fields under investigation are collected and displayed graphically. The impacts of nonlocal parameters, different types of loads, and ramping-time parameters in addition to rotation were studied and analyzed. [ABSTRACT FROM AUTHOR]