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This investigation is devoted to exhibit the thermal damage of skin tissue exposed to a moving heat source. Modelling of the problem is performed by adopting dual phase lag theory of bio heat transfer in context of memory dependent derivative. Laplace transform technique has been adopted to represent the analytical solutions of temperature and thermal damage of skin tissue. Thermal damages to the tissues are calculated by the extent of the denatured protein employing with the Arrhenius equation. In order to predict the significance of memory dependent derivative approach, computational results of temperature and thermal damage are evaluated in the frame of different kernel functions as well as time-delay. For the purpose of exhibiting the attractiveness of the present model, obtained results are compared with the results corresponding to the absence of memory dependent derivative. Also, the impact of the velocity of moving heat source has been precisely investigated on temperature variation and thermal damage of skin tissue using quantitative results. Authors' believe that this study will be helpful to study the thermal treatment of several diseases such as hyperthermia. [ABSTRACT FROM AUTHOR]

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]

The main concern of this article is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD). Due to the shortcomings of power law distributions in Taylor's series, some other forms of derivatives with few other kernel functions have been proposed. The present literature deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a thermoelastic thick plate in which, the memory-dependent heat transport equation involves the Dual-phase (DP) lag model of generalized thermoelasticity. Employing the Laplace transform and Fourier transforms, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversions of the respective transforms have been carried out using a suitable numerical scheme based on the Fourier series expansion technique. Numerical computations for stress, displacement and temperature within the plate have been carried out and have been demonstrated graphically. The results also demonstrate how the heat source moves with time and influences the thermophysical quantities according to its respective position by that time. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, memory effect and time-delay also. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of dual-phase lag (DPL) theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod is carried out and displayed graphically. The effect of moving heat source speed, time instance, memory-dependent derivative, magnetic-field and nonlocality on temperature, displacement and stress are studied. [ABSTRACT FROM AUTHOR]

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. In this analysis, the bio-heat equation has been studied in the context of a new formulation using Caputo–Fabrizio (CF) heat transport law. The heat equation for this problem involving the Three-Phase (3P)-lag model under two-temperature theory. The Laplace transform technique is implemented to solve the governing equations. The influences of the CF order, the two-temperature parameter and moving heat source velocity on the temperature of skin tissues have been precisely investigated. The numerical inversion of the Laplace transform is carried out using the Zakian method. The numerical outcomes of conductive temperature and thermodynamic temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different CF order to reach effective heating in hyperthermia treatment. Significant effect of thermal therapy is reported due to the effect of CF order, the two-temperature parameter and the velocity of moving heat source as well. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of Lord–Shulman (LS) theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effects of moving heat source speed, time instance, memory-dependent derivative, magnetic field and nonlocality on temperature, stress, and temperature are studied. [ABSTRACT FROM AUTHOR]

This work deals with the study of transient responses in a two‐temperature generalized thermoelastic infinite medium having a cylindrical cavity due to a time‐dependent moving heat source where the conventional Fourier's law of heat conduction is modified by introducing a new Taylor's series expansion using memory‐dependent derivative (MDD). The resulting non‐dimensional equations are applied to a specific problem. A direct approach is introduced to obtain the analytical expressions of the physical quantities in the Laplace transform domain. The inversion of the Laplace transforms are carried out using the methods based on the Fourier series expansion technique. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are presented graphically. The effects of time‐delay and kernel function have been studied on the thermo‐physical quantities. [ABSTRACT FROM AUTHOR]