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Functionally graded materials are widely used in the aerospace, nuclear, and aviation industries because of their exceptional properties. The progressive and continuous variation in elastic and thermal characteristics across its surfaces reduces thermal stress within the material and increases its endurance. To study how functionally gradient thermoelastic nanobeams interact with abrupt heat in the context of nonclassical thermoelasticity with phase delays, this study introduces a new mathematical model incorporating memory-dependent derivatives. A heat transfer equation based on memory-dependent derivatives with two delay times can be formulated by combining Eringen's assumptions, the Hamiltonian principle, and Euler–Bernoulli's theory. The analytical solutions for the domains of the system were obtained in the field of the Laplace transform. The distributions of physical fields such as temperature, displacement, deflection, and flexural moment were found numerically using an approximation algorithm. Through the discussion of the computational results and the graphical figures, the effects of effective parameters such as kernel functions, time delay, and nonlocal quantum were indicated. Moreover, a comparison of the current thermal conductivity model with existing classical and nonclassical thermal conductivity models was established to confirm the proposed model. [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]

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]

The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains. [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]

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 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]