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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]

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]

Significant variations are observed over the working temperature range of the various engineering problems such as designing the structures heated by sudden heat flux in engineering. At that time, major variations in the coefficient of the thermal conductivity of the material are observed. Electrical conductivity is also found to be directly dependent on the thermal conductivity. Therefore, present problem enlightens the influence of the variable thermal conductivity and electrical conductivity inside a half space medium permeated by the magnetic field in context of dual phase lag thermoelasticity. Thermal shock has been applied to the non-traction boundary of the medium. Analytical solutions are calculated by adopting Laplace transform technique. Physical fields such as conductive temperature, displacement as well stress of the medium are evaluated in time-domain numerically by using a suitable method of numerical inversion of Laplace transform. Further, to predict the utility of the present model, computational results are compared to the corresponding results of heat conduction model with single phase lag (Lord and Shulman model). By examining the numerical results that have been graphically represented, significant differences have been attributable to the studied fields due to the variable thermal conductivity and different heat conduction models. [ABSTRACT FROM AUTHOR]

Presence of phase lags is found to be very efficient for predicting the realistic outcomes of the real world problems. The concept of phase lags exhibits the finite speed of thermal waves which is contrary to the concept of paradox of heat conduction. Present work is devoted to investigate the role of phase lags in the problem of magneto thermoelasticity with moving heat source inside a half-space medium. The governing equations are being developed in the context of generalized thermoelasticity involving three phase lags. A thermal shock has been applied on the traction free boundary of the medium. The Laplace transform technique has been employed for finding the analytical solutions. Physical variables such as temperature, displacement as well as stress have been determined in the time-domain. Computational results have been derived to predict the influence of the effective parameters such as phase lags and velocity of the heat source on the physical variables at different values of time. [ABSTRACT FROM AUTHOR]

The present article focuses on the new meticulous model based on the postulate of memory-dependent derivatives to analyze the thermo-mechanical interactions inside the nano-beam-based machined resonators. Also, the size effect on dynamic responses of thermoelastic vibrations of homogeneous and isotropic nano-beam is considered. The fundamental expressions are formulated in the frame of non-local generalized thermoelasticity with paired relaxation times by operating the results of Euler-Bernoulli beam theory, non-local effect, and memory-dependent derivative. The proposed model is applied to study the nano-beam-based machined resonator subjected to the ramp-type heating and exponentially decaying time-dependent load. Closed-form solutions of the physical fields are examined by applying the Laplace transform mathematical mechanism. However, the coherence of the new thermal conductivity framework, a collation has been bestowed among the results obtained in the presence or absence of the memory-dependent derivative; also, the size effect is analyzed on the significant parameters of nano-beam such as deflection, temperature, displacement as well as bending moment. Moreover, the prominent influence of the distinct affecting parameters such as constituents of memory-dependent derivative (kernel function and time delay) and ramping time parameter with an applied load on the physical fields have been investigated with the help of quantitative results. [ABSTRACT FROM AUTHOR]

The present study is concerned with the analysis of the existence of magnetic field in micro-beam resonators in the context of generalized thermoelasticity with single relaxation time. MEMS are mostly set in permanent magnetic fields. Two dissimilar cases, with different boundary conditions (First: simply supported and isothermal, Second: clamped and isothermal) of micro-beam resonators, have been discussed. In the first case, magneto-thermoelastic damping has been analyzed by the vibration responses of deflection and thermal moment, which are obtained by the Laplace transform method along with the finite Fourier sine transform method, while in the second case, the magneto-thermoelastic damping has been characterized by the vibration frequency through normal mode analysis. Therefore, the present study highlights the influence of magnetic field in the vibration responses of deflection as well as thermal moment of the micro-beam resonators in both cases separately. Size dependency of micro-beam resonators has been observed. The analytic result shows that the amplitude of deflection and thermal moment is attenuated for the coupled magneto-thermoelasticity. [ABSTRACT FROM AUTHOR]

The present study is concerned with the investigation of the transient responses of a half-space medium with the variable material properties in the context of dual phase lag thermo-elasticity. The boundary of the medium is subjected to thermal shock. Further, the bounding surface is considered to be heated by a non-Gaussian laser beam. Kirchhoff transformation and the Laplace transform technique have been adopted to obtain the analytical solutions. Graphical results of the field components such as non-dimensional conductive temperature, non-dimensional displacement as well as non-dimensional stress have been achieved and illustrated for the different values of time and variable thermal conductivity. Significant results are obtained and it is believed that these results may support in designing the structures heated by a non-Gaussian laser beam in engineering. [ABSTRACT FROM AUTHOR]

The present work is devoted to the study of the propagation of magneto-thermoelastic waves generated by a thermal shock in a finitely conducting elastic half-space. Three phase lag (TPL) theory of thermoelasticity has been applied to account for the interaction among the elastic, thermal and magnetic fields. Mechanical load and thermal shock has been applied on the boundary of the medium. Laplace transform technique on time has been used to obtain the solutions. By considering an illustrative example, numerical results have been computed to explore the physics of the problem. The results for the TPL model have been compared with those for the dual phase lag theory. The study reveals that the distribution of temperature, displacement and stress for the TPL model are significantly different from those of the two phase lag models, as the time progresses until the steady state is reached. [ABSTRACT FROM AUTHOR]