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Enlightened by the memory dependent derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a rod in the context of three-phase lag theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod were fixed, and heat is insulated. Employing Laplace transform as a tool, the problem was transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain was obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod was carried out and displayed graphically. The effect of the moving heat source speed, time instance, memory dependent derivative, magnetic field and nonlocality on temperature, displacement, and stress was studied. Finally, three animated were added for easy understanding of the effect of moving the heat source on the studied fields. As per authors concern, the concept of the animated has been presented for the first time in this kinds of literature till now. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a functionally graded thermoelastic rod being enlightened by the memory-dependent derivative. This article investigates the transient phenomena due to the influence of an induced magnetic field of constant intensity and due to the presence of a moving heat source of constant velocity in the context of three-phase lag model of generalized thermoelasticity. Employing the Laplace and the Fourier transforms as tool, the problem has been constructed in the transformed domain. The inversions of the Fourier transform have been carried out using residual calculus whereas the numerical inversions of the Laplace transform have been performed employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod are carried out and have been demonstrated graphically. The results also demonstrate how the nonhomogeneity parameter and the speed of the moving heat source influence the thermophysical quantities. It is observed that the temperature, thermally induced displacement, and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, nonhomogeneity, and memory effect also. [ABSTRACT FROM AUTHOR]

In this retrospective study, the understanding of heat transport and temperature variations on the tissues of the patients with recurrent cervical cancer subjected to chemoradiation or neoadjuvant chemotherapy followed by surgery and radiotherapy has been studied in the light of Caputo–Fabrizio (CF) bio-heat transport law, in the context of Lord–Shulman (LS) model. The skin tissue is subjected to prescribed temperature and both ends of the tissue are thermally insulated. Laplace transform technique is implemented to solve the governing equations. The influences of CF order and moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The thermal injuries to the tissue are assessed by the denatured protein range using the current formulation in which the numerical inversion of the Laplace transform is carried out using Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different orders of CF derivative to reach effective heating in hyperthermia treatment. [ABSTRACT FROM AUTHOR]

The vibration analysis of elastic medium is very important along with the miniaturization of the device and wide application of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Due to these, size-dependent thermoelastic model have been introduced for higher order simple material to adopt both the size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free energy. Keeping this in mind, the present analysis reports the effect of ultra-short-pulsed laser heating in coupled thermoelastic vibration of a microscale ribbon resonator. The heat transport law of the current problem is defined by incorporating the three-phase-lag heat transport law in the context of Caputo–Fabrizio (CF) derivative. Finite sinusoidal Fourier and Laplace transform techniques have been employed to determine the lateral vibration of the ribbon and the temperature increment within the microscale ribbon. The result provides the direction how the nonlocality and size-dependence can control the vibration analysis and some excellent predictive capability have been demonstrated due to the presence of energy absorption depth and the order of CF derivative also. [ABSTRACT FROM AUTHOR]

The model of the equations of generalized thermoelasticity based on the Lord–Shulman's theory with nonlocal elasticity effect is used to study the photothermal waves in a semiconducting medium. The exact expressions for the displacement components, temperature, carrier density, and stress components are obtained by using normal mode analysis. Numerically simulated results are obtained and presented graphically for silicon. The comparisons are shown graphically to explore the effects of the time and the elastic nonlocal parameter on the different physical quantities. [ABSTRACT FROM AUTHOR]

The vibration of elastic micro-beam is of major significance due to wide applications of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Accordingly, the size-dependent thermoelastic model has been developed to deal with higher-order simple material to adopt both size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free-energy. This survey demonstrates the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale resonator, in which, the non-local heat transport equation is drafted in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer in the context of two-temperature theory. Laplace transform and finite sinusoidal Fourier transform techniques have been employed to determine the lateral vibration of the beam and the scaled thermal moment within the beam. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Specific attention is paid to study the effect of thermal non-local parameter, energy absorption depth, memory-dependent derivative, the two-temperature parameter and delay time also. [ABSTRACT FROM AUTHOR]

A new gadolinium(III)-based coordination polymer (CP), [Gd(3,5-pydc)1.5(CO2)0.5(H2O)4]·3H2O (1, where 3,5-pydc = 3,5-pyridinedicarboxylate), has been successfully synthesized using a slow diffusion method at room temperature. Single-crystal X-ray diffraction study of 1 confirmed its one-dimensional ladder-like structure. The Gd3+ ions are in a distorted tricapped trigonal prismatic geometry. Two types of 3,5-pydc ligands are present in the structures: in one case, the pyridine nitrogen remains vacant, whereas in the other case, the pyridine nitrogen is coordinated with CO2 to form zwitterionic carbamate. The phase purity of 1 has been confirmed by powder X-ray diffraction, thermogravimetric analysis and IR spectroscopic studies. The aqueous dispersion of compound 1 exhibits weak luminescence emission at 385 nm upon excitation at 270 nm. To explore the ligand-sensitized metal-centred luminescence, we have prepared a composite by mixing the CP with Tb3+ ions (Tb@1). The formation of the composite has been confirmed by IR spectroscopic studies in the solid state. The composite showed excellent ligand-sensitized metal-centred luminescence. We have utilized this luminescence property for the sensing of anions in aqueous media. The composite shows luminescence quenching behaviour in the presence of Cr2O72−, CrO42−, and NO2−, with high sensitivity, and their limits of detection are 147 ppb, 142 ppb and 20 ppb, respectively. Selectivity experiments show that the detection of these three anions is highly selective in the presence of other common anions. Detailed experimental studies suggest that the preferable interaction of the three anions with the Tb3+ ions inside the composite and the reduction of the excitation energy are probably responsible for the quenching behaviour. [ABSTRACT FROM AUTHOR]

This study proposes a computationally efficient approach about the dynamic response of a homogeneous, transversely isotropic, thermoelastic micro-beam resonator subjected to time-dependent thermal loading. Due to the shortcomings of power law distributions in fractional derivatives, the usage of some other forms of derivatives with few other kernel functions are proposed. With this motivation, the heat transport equation is defined in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer which is modeled based on Euler-Bernoulli beam theory. The beam is assumed to be clamped-clamped conditions on its axial ends. Employing the Laplace transform technique, the analytical solutions have been obtained. Further, incorporating residual calculus, the inversion of the transformed solutions are performed. The analytical expressions for the deflection has been computed numerically for a Silicon micro-beam using Maple software. The new approach is able to portray material heterogeneities and the non-locality of the new kernel allows the full describing of the memory within structure and media with different scales, which cannot be described by classical fractional derivative and also that of the memory-dependent derivative. [ABSTRACT FROM AUTHOR]