Ramp-type Heating Research Articles

The Heat Transfer in Skin Tissues Under The General Two-Temperature Three-Phase-Lag Model of Heat Conduction with a Comparative Study

In this paper, a new and more general model of heat conduction that depends on the drift velocity due to thermomass motion assumption will be established and will be applied to the skin tissue. Four different heat conduction models will be incorporated into a unified equation of heat conduction: the Pennes, Vernotte-Cattaneo, dual-phase-lag of Tzou, and the general two-temperature three-phase-lag of Youssef. The governing partial differential equations of the general two-temperature three-phase-lag model of bioheat conduction will be implemented and solved directly in the domain of the Laplace transformation. The numerical solutions of the Laplace transform will be calculated by executing the Tzou iteration formula. The ramp-type heat on the surface of the skin tissue will be considered as thermal loading. The conductive and dynamic temperature increment reactions have been studied and discussed with different values of ramp-time heat, characteristic length, and drift velocity parameters. The novelty of this work is to introduce some comparisons of the four under-studied bioheat conduction models and show the differences between them in the figures. The numerical results show that the ramp-time heat, drift velocity, and characteristic length parameters have major impacts on the increment of both dynamical and conductive temperature distributions.

Varying Thermal Conductivities of Microelongated Excited Electron-Hole Optical Waves in Semiconductors Subjected to Ramp-Type Heating

Varying Thermal Conductivities of Microelongated Excited Electron-Hole Optical Waves in Semiconductors Subjected to Ramp-Type Heating

The Influence of the Caputo Fractional Derivative on Time-Fractional Maxwell’s Equations of an Electromagnetic Infinite Body with a Cylindrical Cavity Under Four Different Thermoelastic Theorems

This paper introduces a new mathematical modeling of a thermoelastic and electromagnetic infinite body with a cylindrical cavity in the context of four different thermoelastic theorems; Green–Naghdi type-I, type-III, Lord–Shulman, and Moore–Gibson–Thompson. Due to the convergence of the four theories under study and the simplicity of putting them in a unified equation that includes these theories, the theories were studied together. The bunding plane of the cavity surface is subjected to ramp-type heat and is connected to a rigid foundation to stop the displacement. The novelty of this work is considering Maxwell’s time-fractional equations under the Caputo fractional derivative definition. Laplace transform techniques were utilized to obtain solutions by using a direct approach. The Laplace transform’s inversions were calculated using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions were obtained numerically and represented in figures. The time-fractional parameter of Maxwell’s equations has a significant impact on all the mechanical studied functions and does not affect the thermal function. The time-fractional parameter of Maxwell’s equations works as a resistance to deformation, displacement, stress, and induced magnetic field distributions, while it acts as a catalyst to the induced electric field through the material.

State-Space Approach to the Time-Fractional Maxwell’s Equations under Caputo Fractional Derivative of an Electromagnetic Half-Space under Four Different Thermoelastic Theorems

This paper introduces a new mathematical modelling method of a thermoelastic and electromagnetic half-space in the context of four different thermoelastic theorems: Green–Naghdi type-I, and type-III; Lord–Shulman; and Moore–Gibson–Thompson. The bunding plane of the half-space surface is subjected to ramp-type heat and traction-free. We consider that Maxwell’s time-fractional equations have been under Caputo’s fractional derivative definition, which is the novelty of this work. Laplace transform techniques are utilized to obtain solutions using the state-space approach. Laplace transform’s inversions were calculated using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions were obtained numerically and are illustrated in figures. The time-fraction parameter of Maxwell’s equations had a major impact on all the studied functions. The time-fractional parameter of Maxwell’s equations worked as resistant to the changing of temperature, particle movement, and induced magnetic field, while it acted as a catalyst to the induced electric field through the material. Moreover, all the studied functions have different values in the context of the four studied theorems.

Effect of Rotation in a Semiconductor Medium Under Photothermal Theory with Ramp Type Heating

Effect of Rotation in a Semiconductor Medium Under Photothermal Theory with Ramp Type Heating

Magnetic field and initial stress on a rotating photothermal semiconductor medium with ramp type heating and internal heat source

This manuscript addresses a significant research gap in the study by employing a mathematical model of photo thermoelastic wave propagation in a rotator semiconductor medium under the effect of a magnetic field and initial stress, as well as ramp-type heating. The considered model is formulated during the photothermal theory and in two-dimensional (2D) electronic-elastic deformation. The governing equations represent the interaction between the primary physical parameters throughout the process of photothermal transfer. Computational simulations are performed to determine the temperature, carrier density, displacement components, normal stress, and shear stress using the application of Lame’s potential and normal mode analysis. Numerical calculations are carried out and graphically displayed for an isotropic semiconductor like silicon (Si) material. Furthermore, comparisons are made with the previous results obtained by the others, as well as in the presence and absence of magnetic field, rotation, and initial stress. The obtained results illustrate that the rotation, initial stress, magnetic field, and ramp-type heating parameter all have significant effects. This investigation provides valuable insights into the synergistic dynamics among a magnetization constituent, semiconducture structures, and wave propagation, enabling advancements in nuclear reactors' construction, operation, electrical circuits, and solar cells.

Biomechanical response of skin tissue under ramp-type heating by incorporating a modified bioheat transfer model and the Atangana–Baleanu fractional operator

Biomechanical response of skin tissue under ramp-type heating by incorporating a modified bioheat transfer model and the Atangana–Baleanu fractional operator

The photothermal interaction of a viscothermoelastic semiconducting ceramic solid sphere under the Green–Naghdi heat conduction model

This work introduces a new mathematical model for viscothermoelastic semiconducting solid spheres of ceramic materials considering the photothermal interaction using three types of the Green–Naghdi heat conduction model. The outer surface of a solid sphere is loaded thermally using ramp-type heat as a boundary condition. Following that, Laplace transforms and their inversion forms have been applied. The figures show that the mechanical relaxation time and ramp-time heat parameters have significant effects on the increase in carrier density and temperature, in addition to strain, displacement, the average of principal stresses, and the strain-energy density. The energy produced by viscothermoelastic semiconducting materials based on photothermal interaction may be controlled by the ramp-time heat parameter. The novelty of this work is to test the three types of the Green–Naghdi heat conduction model and apply the model to zirconia, a ceramic material.

Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating

Fractional order of refined Lord–Shulman model for a 1D thermoelastic response of skin tissue due to ramp-type heating

Thermoelastic diffusion in a half space due to fractional order theory

Based on the theory of fractional thermoelastic diffusion, a two dimensional problem for thermoelastic half space is considered. The upper surface of the half space is taken to be traction free and subjected to ramp type heating. Integral transform technique and a direct approach method are used to obtain the solution in the transformed domain. Numerical inversion techniques are used to obtain the inverse double transforms. The effect of Tempered-Caputo fractional derivative is studied. Numerical results are discussed and represented graphically.

Implementation of Legendre wavelet method for the size dependent bending analysis of nano beam resonator under nonlocal strain gradient theory

The bending analysis due to thermoelastic loading in nanoscale materials is primarily determined by the physical aspect of the material and the modeling of structures. This paper examines the prediction of bending characteristics of the Euler-Bernoulli beam using Moore-Gibson-Thompson (MGT) thermoelasticity theory in conjunction with nonlocal strain gradient theory (NSGT). The coupled equations for dimensionless deflection and temperature change with ramp-type heating boundary conditions are formulated and solved using the Laplace transform method and the wavelet approximation method. The stiffness softening and hardening effects due to nonlocal and length-scale parameters are assessed, and their discrepancies are discussed. Findings further reveal that the impact of the thermal relaxation parameter on deflection and temperature is negligible. Moreover, the different aspect ratios of the beam's structure depict the prominently behavior of structural simulations in bending.

Elasto-thermoelectronic diffusion waves with changing thermal conductivity and thermal heating of microtemperature semiconductor

This paper presents a theoretical investigation of linear thermal conductivity temperature-dependent coupled elasto-thermoelectronic diffusion (ETD) waves in a micro-temperature semiconductor, specifically focusing on the effects of photo-excited processes. The governing equations are formulated for a semi-infinite silicon wafer, which serves as a semiconductor material. The explicit study of the strong coupling between the equations governing elastic wave transport, carrier (plasma) transport, and thermal wave transport is conducted in the presence of microtemperature influence. The electron–hole interaction is obtained within the framework of the ETD theory. Laplace transform is used to resolve the governing equations in a non-dimensional framework for thermoelastic and electronic deformation in one-dimensional (1D) scenarios. The present study employs the proposed model to analyze the impact of ramp-type heating on a stationary plane of unbounded semiconductor material. Thermoelastic electronic coupling is found to be affected by the presence of variable thermal conductivity and microtemperature parameters.

Three-field mixed hp-finite element method for the solution of the Guyer–Krumhansl heat conduction model

On the basis of numerous experimental studies the Guyer–Krumhansl heat conductivity model can be considered as one of the most promising theoretical models to simulate the low temperature processes and the thermal behavior of such complex structures as materials with inhomogeneities and interfaces, as well as porous materials. However, the classical h-version finite element methods do not provide convergent and accurate results for the solution of the Guyer–Krumhansl heat conductivity model. In recent paper, a new three-field variational formulation is derived treating the temperature, the heat flow and its current density as independent variables. Both the temperature- and the heat flow boundary condition are weakly imposed, i.e., built in the variational form.Based on this variational background, a new, hp-version mixed finite element method is constructed. The h- and p-convergence behaviors of the temperature and the heat flow are analyzed on the transient region for two representative model problems: (i) a rapid heating process with exponentially changing rate and (ii) a ramp-type heating process. The relative and absolute errors are measured in maximum norm. From the computational experiments it follows that the mixed hp-finite element method gives reliable, robust (uniformly stable) results not only for the h- but also for the p-approximation in the case of both the temperature and the heat flow.

The influence of the mechanical damage on a viscothermoelastic nanobeam due to ramp-type heating under Green-Naghdi theory type-II

The main object of this work is to analyze viscothermoelastic homogeneous and isotropic nanobeams under the effect of mechanical damage. A Green-Naghdi type-II model of thermoelasticity has been constructed under simply supported conditions. Moreover, the Laplace transforms have been applied for the governing differential equations. Tzou iteration method with approximation has been applied to calculate the Laplace inverse transforms. The numerical results are presented and validated for use in a viscothermoelastic rectangular nanobeam of silicon nitride when it has been thermally loaded by ramp-type heating and simple support. The numerical results have been demonstrated in different figures to stand on the effects of the mechanical damage variable, mechanical relaxation times parameters, and ramp-time heat parameter on all the studied functions. We conclude that the effect of the mechanical damage variable, ramp-time heating parameter, and mechanical relaxation times parameters are highly influential on all the studied functions and thermomechanical waves.

Propagation of plane waves in nonlocal semiconductor nanostructure thermoelastic solid with fractional derivative due to ramp-type heat source

In this paper, propagation of thermoelastic waves in semi-conducting nanostructure medium is studied. First, the governing equations are formulated with the help of coupled nonlocal elasticity theory, thermoelastic three-phase-lag model, and equation of motion. Heat equation with fractional order is incorporated to study thermal effects on the propagation of wave. The problem is solved using Fourier series and Laplace transform to obtain the exact expressions of physical fields. The distributions of the nondimensional carrier density and stresses are obtained and illustrated graphically. The effects of nonlocal parameter, fractional order parameter, and time parameter on these wave characteristics are concerned and discussed in detail. Some semiconductor materials as Silicon (Si) and Germanium (Ge) are used to make the numerical simulation and some comparisons in different thermal memories are made.

Thermal and fracture analysis of collinear interface cracks in graded coating systems under ramp-type heating

Ceramic based thermal barrier coatings are extensively employed to shield critical engineering components from harsh temperature environments, where the typical Fourier's law may not be able to provide an accurate assessment of the physical process. This work adopts a more generalized heat conduction approach to reveal the thermal and fracture interaction mechanism of two collinear interface cracks in orthotropic functionally graded thermal coating systems by dual-phase-lag theory. The heating rate of the imposed thermal loading on the exterior bounding surface is modeled by ramp-type function, where the ramping period is comparable to the certain time spent for building the local thermal equilibrium within composites. The methods of Fourier transform and Laplace transform in conjunction with the singular integral equations are applied to solve the complex transient thermoelastic problem. Parametric investigations are conducted to investigate the impacts of ramping time, thermal lags, nonhomogeneous parameters, and crack spacing on the thermal and fracture characteristics. According to the maximum hoop stress criterion, higher fracture risk is discovered with the approaching of collinear interface cracks.

The vibration of a nanobeam under generalized thermoviscoelasticity theory based on thermomass motion subjected to ramp-type heat

The vibration of a nanobeam under generalized thermoviscoelasticity theory based on thermomass motion subjected to ramp-type heat

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

In this work, a novel mathematical model of thermoelastic, homogenous, isotropic, and infinite medium with a spherical cavity has been constructed. Under the hyperbolic two-temperature Green-Naghdi theory of thermoelasticity type-I and type-III with fractional-order strain, the governing equations have been established. The bounding surface of the cavity has been thermally loaded by a ramp-type heat and is connected to a rigid foundation which prevents volumetric strain. Different values of the fractional-order and two-temperature parameters have shown numerical results for the dynamical and conductive temperature increment, strain, displacement, and average of principal stresses, which are graphically applicable to all the functions studied. The fractional-order parameter has significant effects on stress and strain distributions, while it has a limited effect on the dynamical and conductive temperatures increment. The hyperbolic two-temperature parameter has significant effects on all studied functions based on Green-Naghdi models of type-1 and type-II. Moreover, the ramp-time heat parameter has a significant impact on all the studied functions under all the studied models of thermoelasticity.

The vibration of a nanobeam subjected to constant magnetic field and ramp-type heat under non-Fourier heat conduction law based on the Lord-Shulman model

In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of the Lord-Shulman thermoelastic theorem which contains the non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using the Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Studying the Thermoelastic Waves Induced by Pulsed Lasers Due to the Interaction between Electrons and Holes on Semiconductor Materials under the Hall Current Effect

In the present work, the interaction between electrons and holes in semiconductor materials is investigated. According to the excitation process, the optical-elastic-thermal-diffusion (OETD) process is considered when the medium is exposed to a strong magnetic field and laser pulses. Photo-elastic and photo-electronics deformations are taken into account when the Hall current impact appears due to the magnetic field pressure on the semiconductor medium. Due to the complexity of the model, the governing equations that describe the system in one dimension (1D) are studied. Mathematical transformations (Laplace transform) were used to simplify the equations to obtain the physical quantities under study which were affected by laser pulses. To obtain complete solutions, some conditions were obtained from the free surface as well as from a mechanical ramp type and pulse heat flux, and then numerical transformations were applied using the inverse Laplace transform. Under the influence of several variables in this question, the results were explained graphically for silicon (Si) material and the results were analyzed in terms of their physical significance.