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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]

The primary focus of the present contribution is to develop a new system of differential equations describing the nonlocal thermoelasticity theory. The problem deals with the thermoelastic interaction in a nonhomogeneous thermoelastic layer induced by absorbing penetrating laser radiation throughout its volume. The heat conduction equation has been formulated in the context of memory dependent three-phase lag model. The surfaces of the layer are thermally insulated and free of traction. Employing the integral Laplace transform technique, the solutions of the field quantities have been achieved in the transformed domain. The corresponding solutions in the space–time domain have been derived using the numerical inversion of the Laplace transform by Riemann-sum approximation technique. The numerical estimates of the field quantities have been depicted graphically to address the effects of nonlocality and memory effects on the temperature profile, displacement and stress components. The effect of the delay time, nonhomogeneity and various choices of linear and nonlinear kernel functions in the heat transport law have also been reported. [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]

The present article is aimed at studying the effect of an induced magnetic field in an initially stressed homogeneous, isotropic, thermoelastic half-space. The corresponding mathematical modeling has been formulated in the context the memory-dependent heat transport equation in the context of three-phase lag model of generalized thermoelasticity involving two-temperature theory. The bounding plane of the medium is subjected to different types of prescribed temperature and variable mechanical loading. Employing the Laplace transform, the analytical results for the distributions of the thermophysical quantities have been derived and the corresponding vector-matrix differential equation is solved with the help of state space approach. The numerical inversion of the Laplace transform is carried out with the help of an efficient and pragmatic algorithm based on the Riemann-sum approximation technique. Numerical computations for a copper material is performed and have been demonstrated graphically. The result provides a motivation to investigate the problem and draw conducting remarks due to the influence of the magnetic field, memory effect and time-delay parameter also. [ABSTRACT FROM AUTHOR]

The objective of the present study is to formulate the bio-heat model to study the variations of temperature profile and thermal damages within a spherical living tissue subjected to a thermal therapy, whose outer surface is thermally insulated. The heat conduction equation is formulated in the context of convolution-type Dual-phase (DP) lag memory-dependent derivative, having kernels to be power functions, from which, the Lord–Shulman model can be obtained as a particular case. The Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and effect of time-delay parameters on the temperature of skin tissues and the thermal injuries are precisely demonstrated. The thermal injuries of the tissue are assessed by the denatured protein range. The numerical inversion of the Laplace transform is performed with the help of Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated to identify an appropriate therapy to select different kernel functions for effective heating in hyperthermia treatment. Significant effect of the thermal therapy is reported due to the effect of delay time also. [ABSTRACT FROM AUTHOR]

The analysis of fracture 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. With this motivation, the present study is now formulated to provide the nonlocal phenomena of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is subjected to prescribed temperature and stress. The governing equations have been solved on employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm's integral equation of the first kind. The Bellman method has been used to compute numerical inversion of the Laplace transform. The result provides the direction how the nonlocality and size-dependence can control the fracture and what is the significant effect of various kernel functions and the effect of memory is also reported. [ABSTRACT FROM AUTHOR]

In the present analysis, the bio-heat equation has been studied in the context of memory responses which is defined in the form of convolution having kernels as power functions. The heat transport equation for this problem involving the memory-dependent derivative on a slipping interval in the context of Dual-phase (DP) lag model, which is used to study the thermal damage within the graded spherical skin tissue during the thermal therapy, whose outer surface is thermally insulated. Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and time-dependent 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 method. 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 kernel functions to reach effective heating in hyperthermia treatment. The significant effect of the thermal therapy is reported due to the effect of nonhomogeneity and delay time also. [ABSTRACT FROM AUTHOR]

In this paper, a general solution for the propagation of plane waves in the generalized piezo-thermoelastic medium for the two-dimensional problem under the different thermoelastic theories is investigated. We have included Lord-Shulman (L-S) and dual-phase lag (DPL) and three-phase lag (TPL) theories. The normal mode analysis is used to obtain the exact expressions for the considered variables. The results of the physical quantities have been illustrated graphically to study the effect of different kernel of memory dependent derivative along with memory dependent derivative is not used, the effect of delay times of memory dependent derivative for three-phase-lag (TPL) and finally comparisons between (L-S), (DPL) and (TPL) theories have been made in all the distribution. [ABSTRACT FROM AUTHOR]

This article highlights on the study of coupled plasma, thermal and elastic waves within an orthotropic infinite semiconducting medium in context of photothermal transport process having a spherical cavity under two-temperature theory. The memory-dependent heat transport equation for the present problem is involving the two-temperature dual-phase (DP) lag model of generalized thermoelasticity. The inner boundary of the cavity is stress free and is subjected to an exponentially decaying pulse. Moreover, the carrier density is prescribed on the boundary in terms of the recombination velocity. Employing the Laplace transform as tool, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversion of the Laplace transform is carried out using a suitable scheme based on the Riemann-sum approximation technique. Numerical computations for an orthotropic semiconductor are performed and have been demonstrated graphically. The results also demonstrate the effect of coupling between plasma, thermal and elastic waves due to the presence of several kernel functions and response of memory effect. Also, significant differences on the thermophysical quantities are revealed due to the influence of two-temperature parameter, memory effect and time-delay parameter. [ABSTRACT FROM AUTHOR]

This present study deals with a novel mathematical model of generalized thermoelasticity in a fiber-reinforced, isotropic unbounded thermoelastic solid due to the presence of a continuous line heat source under the influence of magnetic field. The derivative is defined in an integral form of a common derivative on a slipping interval by incorporating memory-dependent heat transfer. Employing both Laplace and Hankel transforms as tools, analytical results for distributions of different fields have been derived with the help of potential function approach. The inversion of Hankel transform is performed analytically, whereas the numerical inversion of Laplace transform is carried out employing Zakian method and the method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory to exhibit the significance of the kernel functions and the time-delay parameter is constructed. The significant differences of the two different numerical schemes have also explained. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of reinforcement and magnetic field. Also, significant differences due to the choice of linear and nonlinear kernels in the heat equation is elaborated. [ABSTRACT FROM AUTHOR]