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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]

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]

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]

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]

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]

Simple Summary: Heat transport in biological tissue is mediated through a variety of phenomenological processes, involving tissue heat exchange, blood-tissue convection, blood perfusion or advection and diffusion across microvascular beds, and metabolic heat production. In recent years, many physicians and engineers have taken an interest in applying computational and mathematical techniques to model biological systems. The objective of the current paper is to provide an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time. The suggested model is used to examine heat transport in biological tissues as an infinite concentric spherical region during magnetic fluid hyperthermia. This method is used to investigate the influence of heat generation through heat treatment on a skin tumor a spherical layered structure. The present model can explain the effect of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences including transfer, metabolism support, blood perfusion, and other similar treatments. Hyperthermia therapy is now being used to treat cancer. However, understanding the pattern of temperature increase in biological tissues during hyperthermia treatment is essential. In recent years, many physicians and engineers have studied the use of computational and mathematical models of heat transfer in biological systems. The rapid progress in computing technology has intrigued many researchers. Many medical procedures also use engineering techniques and mathematical modeling to ensure their safety and assess the risks involved. One such model is the modified Pennes bioheat conduction equation. This paper provides an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time by incorporating in it the (MGT) equation. The suggested model examines heat transport in biological tissues as forming an infinite concentric spherical region during magnetic fluid hyperthermia. To investigate thermal reactions caused by temperature shock, specifically the influence of heat generation through heat treatment on a skin tumor [AEGP9], the Laplace transformation, and numerical inverse transformation methods are used. This model was able to explain the effects of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences, transfer, metabolism support, and blood perfusion. Comparison of the numerical results of the suggested model with those in the literature confirmed the validity of the model's numerical results. [ABSTRACT FROM AUTHOR]

The current study investigates thermophotovoltaic interactions using a new mathematical model of thermoelasticity established on a modification of the Green–Naghdi model of type III (GN-III). The basic equations, in which the heat transfer is in the form of the Moore–Gibson–Thompson (MGT) equation, are derived by adding a single delay factor to the GN-III model. The impact of temperature and electrical elastic displacement of semiconductors throughout the excited thermoelectric mechanism can be studied theoretically using this model. The proposed model was used to investigate the interactions between the processes of thermoelastic plasma in a rotating semiconductor solid sphere that was subjected to a thermal shock and crossed to an externally applied magnetic field. The influence of rotation parameters on various photothermal characteristics of silicon solid was presented and explored using the Laplace technique. [ABSTRACT FROM AUTHOR]