Dual Phase Lag Model Research Articles

Causality in non-fourier heat conduction

We present a study of the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and show it obeys Kramers-Kronig relations. In particular, we discuss the Cattaneo-Vernotte and the dual-phase lag models. The constitutive equations are written as a linear response theory and determine the conditions for which the dual-phase lag model does not satisfy Kramers-Kronig relations. An alternative model is presented to describe non-Fourier transport using the similarity with the causal response of viscoelastic materials to avoid this unphysical issue.

Drift–diffusion-Poisson- dual phase lag thermal model with phonon scattering in gate all around field effect transistor

• Phonon scattering effect on Self-heating transistor are investigated. • The impact of temperature-dependent properties are discussed. • A reduction of temperature rise is achieved by using jump boundary condition. • A decrease in temperature is obtained using a temperature-dependent parameters. Gate All Around Field Effect Transistor (GAAFET) is a promising alternative for improving channel control, reducing leakage currents, and bringing down the operational voltage and dynamic power. In the present work, we will attempt to address the self-heating effect in (GAAFET) structure. The finite element approach is used to discretize the Dual-Phase Lag (DPL) heat conduction equation coupled with Poisson and drift-diffusion equations for electrons and holes is performed using the finite element method. Numerical solutions are obtained using the technique of nonlinear Newton–Raphson iteration. This study is also aims to analyze the impact of temperature-dependent (TD) parameters such as thermal conductivity, heat flux phase lag, and volumetric heat capacity on temperature distribution. Further, a temperature jump boundary condition is used at the semiconductor-oxide interface to take into account the phonon scattering phenomenon. In comparison to the constant parameters, the obtained results reveal a decrease in the temporal temperature profile as well as the spatial temperature distribution. Also, the addition of jump boundary conditions causes a reduction in the maximum temperature and heat flux. Thus, the DPL model with proposed TD parameters, including jump temperature boundary condition, is recommended for the investigation of the self-heating effect, which can provide some improvement for the development of GAAFET with good reliability in the device.

The gravitational field effect on a micro-elongated thermoelastic layer under a fluid load with two theories

PurposeThis paper aims to study the gravity effects on a micro-elongated thermoelastic layer under a fluid load, utilizing the Lord–Shulman (L-S) theory and the dual-phase-lag (DPL) model.Design/methodology/approachThe analytical method used was the normal mode which partial differential equations transform into ordinary differential equations.FindingsAluminum epoxy numerical computations are carried out, and the results are graphed. The DPL model and the L-S theory are compared in the complete absence and presence of gravity. Comparisons were also made for three values of and it is observed that the gravity has quite a massive influence on all physical quantities.Originality/valueIn the present paper, the authors shall create the general equation for the energy equation, which includes the two theories (DPL and L-S) as well as the solution of micro-elongated thermoelasticity under fluid load. The problem is pretty important in many dynamical systems.

The thermal response of three-dimensional skin tissue subjected to multiple laser beams

This work investigates the thermal response of the three-dimensional skin model under the multiple laser beams considering the water-related phase change process. The thermal conductivity in the phase change region is assumed as a linear temperature-dependent function. The finite element method is used to obtain the nonlinear thermal response of the three-dimensional skin model in the context of the dual phase lag model. The influences of laser beam’s size, the interval distance and the arrangement layout of laser beams on the temperature are discussed and represented graphically. The results can be used to verify the feasibility and optimization of multiple laser beams.

Thermoelastic analysis of biological tissue during hyperthermia treatment for moving laser heating using fractional dual-phase-lag bioheat conduction

In this paper, a time-fractional dual-phase-lag (DPL) bio-thermoelastic model is presented to solve the thermoelastic response of a biological tissue during hyperthermia treatment by a moving laser heating. To improve the elimination rate of diseased tissue and reduce the side effects to surrounding normal tissue in hyperthermia, it is necessary to study the thermoelastic response of biological tissues under high-speed and high-intensity laser heating. The laser heating process causes a large instantaneous temperature difference and heat flow in the tissue, which leads to abnormal diffusion of heat conduction. The classical Fourier heat conduction model cannot describe this anomalous diffusion phenomenon due to infinite heat propagation velocity. In order to describe anomalous diffusion in tissue, the fractional derivative is introduced into the DPL heat conduction model. In order to solve the elastic deformation of tissue under heating, the biological fractional thermoelastic theory is established by combining the fractional DPL model with one-dimensional thermoelastic theory. The physical significance of the phase lags and fractional order is elucidated. The thermoelastic responses are compared with those based on existing models. Finally, the effects of blood perfusion rate and laser velocity on temperature distribution and thermal stress response during percutaneous laser thermal ablation are analyzed.

Wave scattering of plane wave at the loosely bonded interface of two dissimilar rotating triclinic magneto-thermoelastic media under nonlinear thermoelasticity and DPL model

In the present work, the reflection and transmission of plane waves incident at the loosely bonded interface between two dissimilar anisotropic (triclinic), rotating magneto-thermoelastic media is studied. Four non-linear theories of thermoelasticity namely Classical coupled theory (CL), Lord-Shulman theory (LS), dual-phase-lag (DPL) model and Green-Naghdi theory (GNIII) are employed. Using these theories, the effect of mechanical and thermal bonding parameters on the reflection and refraction coefficients is compared. Moreover, the effect of magnetic field and angular velocity on the reflection and refraction coefficients is discussed with the help of graphs under different thermoelastic theories. Energy partition of reflected and transmitted waves are also carried out which validates the problem.

Dual-phase-lag model on microelongated thermoelastic rotating medium

The dual-phase-lag (DPL) model is applied to study the influence of rotation on a two-dimensional micro-elongated thermoelastic medium problem. Mechanical force along with the layer of the elastic half-space interface and micro-elongated thermoelastic half-space is applied. The analytic expressions for displacement component, temperature distribution, micro-elongational scalar and stress components have been derived and represented graphically. The rotation has been studied in the presence DPL model and Lord-Shulman theory.

Propagation of plane waves of piezo-thermoelastic diffusive medium under the effect of gravity with dual phase lag model

Propagation of plane waves of piezo-thermoelastic diffusive medium under the effect of gravity with dual phase lag model

The thermal injury analysis of skin tissue with a new nonlocal dual phase lag model

Skin burning or skin thermal damage caused by heat from flash fire or contact with hot plates are the most commonly encountered hazards in daily life and industry. In this work, we investigate the temperature distribution and thermal damage of skin tissue under the action of a moving heat source. The governing equations with the moving heat source are formulated in the context of a new nonlocal dual phase lag model and solved by Laplace transformation. The influences of heat source velocity, lagging time, and nonlocal length on the temperature and thermal damage are discussed and represented graphically.

A numerical study of moving boundary problem involving dual phase lag model of heat mass transfer during immersion frying

In this paper, we developed a dual phase lag model of heat mass transfer during immersion frying of foods. This model is a moving boundary problem of a couple system of second order hyperbolic partial differential equations. Modified finite element Legendre wavelet Galerkin method developed for its solution. The discretization in space and then application of Legendre wavelet Galerkin method converts our problem into a coupled system of generalized Sylvester equations. In a particular case, the solution of the present model is compared with exact solution and are approximately the same. L∞ error decreases as Legendre wavelet basis functions increase and strip size decreases. Whole analysis is done in dimensionless form. The effect of variability of moving interface on Fourier number, Luikov number, Posnov number, Kossovitch number, Biot number and relaxation times is discussed in detail.

Memory Response on the Elasto-Thermodiffusive Interaction Subjected to Harmonically Varying Heat Source

Enlightened by the Caputo type of fractional derivative, this research paper is the analysis of a mathematical model of generalized thermoelastic diffusion with memory-dependent derivative (MDD) for an isotropic infinite medium with a cylindrical cavity in the context of dual-phase lag model. The surface of the cavity is traction free and subjected to harmonically heat sources with constant angular frequency of thermal vibration. Laplace transform technique has been used to solve the problem. Later eigenvalue approach is used to obtain the analytical expressions for different physical fields in the transformed domain. Finally to obtain the solutions in the real-time domain, the Riemann-sum approximation method is used. According to the graphical representations corresponding to the numerical results, the effect of heat source speed on temperature, displacement, stress, mass concentration and chemical potential are studied. The effect of memory-dependent parameters, as well as in the absence of MDD on physical quantities are also demonstrated.

Impact of variable thermal conductivity and diffusivity on two temperature fractional thermodiffusive elastic half space with dual phase lags

The motive of current research is to investigate the impact of variable conductivity and diffusivity on the elasto-thermo-diffusive interactions in a 2D half-space under the two temperature fractional dual phase lag model. At the bounding surface of half-space, thermal and concentration loadings are applied. Variable diffusivity and conductivity are assumed to be linearly dependent on concentration and thermodynamic temperature, respectively. Kirchhoff's transformations are taken into consideration to convert the non-linear heat conduction and diffusion equations into a linear form. Then, reduced governing equations are solved by employing the transform technique. The solutions of different physical quantities are presented in a compact form. Numerical simulation is carried out for copper material. A numerical inversion process is adopted to invert the solutions in the original domain. Consideration of two temperature, dual phase lag fractional thermoelasticity to study the transient responses of half space with specific type of loadings augment the novelty of the present work. The results for conductive and thermodynamic temperature, normal stress and mass concentration are plotted to illustrate the impact of variable diffusivity and conductivity, fractional and two temperature parameters. These parameters are observed to have varying degrees of influence on the physical fields.

Thermal lagging effect on heat transport within living biological tissues

Thermal lagging effect on heat transport within living biological tissues is explored in the context of different relaxation mechanisms. The governing equations of temperature rooted the delay effect between heat flux and temperature gradient, as well as non-equilibrium effect between blood vessel and peripheral tissues, are constructed separately via the classic dual-phase lag model (DPL) and generalized dual-phase lag model (GDPL). An analytical procedure based on the Laplace transform technique and its limit theorem is then proposed. The expressions and effective values of phase lags rooted different effect have been derived and further estimated. On this basis, the temperature response of a biological tissue with its boundary exposed to a pulse heat flux is analyzed. The detailed parametric study has been conducted to explore the dependence of these phase lags on tissue structures and their effect on heat transport properties. The results highlight the contributions of the delay effect and non-equilibrium effect in temperature prediction and state that the delay effect is dominated for a larger tissue size. Meanwhile a significant difference has also been observed with the boundary conditions that obey different thermal conduction mechanism.

Lagging heat models in thermodynamics and bioheat transfer: a critical review

The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro and nanosystems and biological tissues. In other words, the results obtained from the classical equations deviate from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inappropriate for modeling heat transport in these cases. There are several techniques for modeling non-Fourier heat conduction. In the present paper, we place our focus on the dual-phase-lag (DPL) approach. The DPL model, as a popular modification of Fourier's law, has already been utilized in numerous situations, such as simulating ultrafast laser heating and heat conduction in carbon nanotubes. There has been a sharp increase in research on non-Fourier heat conduction in recent years. Several studies have been performed in the fields of thermoelasticity, thermodynamics, transistor modeling, and bioheat transport. This review presents the most recent non-Fourier bioheat conduction works and the related thermodynamics background. The various mathematical tools, modeling different thermal therapies, and relevant criticisms and disputes are discussed. Finally, the novel and other possible studies are also presented to provide a better overview, and the roadmap to the future research and challenges ahead is drawn up.

The effect of inclined load and gravitational field on a 2-D thermoelastic medium under the influence of pulsed laser using dual phase lag model

The purpose of this study is to see how inclined loads and the gravitational field affect a two-dimensional thermoelastic medium influenced by thermal loading from a laser pulse in the context of dual-phase lag model. A linear combination of a normal load and a tangential load is assumed for the inclined load. The surface of the bounding plane is heated by a non-Gaussian laser beam. Analytical formulas for several physical quantities have been produced on the transformed domain using the Laplace and Fourier transform techniques as tools. The numerical inversion of the Fourier transforms have been performed analytically whereas numerical inversion of the Laplace transform is carried out using the Zakian method. All physical quantities have been graphically depicted in the dual-phase-lag model (DPL) and Lord-Shulman (L-S) theory to indicate the effect of pulsed laser, gravity and the angle of inclination of the medium.

Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids

AbstractThe nonlocal elasticity together with electro‐magneto thermal dual‐phase‐lag (DPL) model to a transversely isotropic generalized thermoelastic hollow sphere with voids is addressed in radial direction. The governing equations and stress–strain‐displacement relations have been resolved by applying time harmonics technique. The elimination technique is employed to resolve the homogeneous equations to find the unknowns. The unknowns such as dilatation, displacement, voids volume fraction, temperature change, and radial/de‐hoop stresses have been calculated analytically. In order to discover the vibration analysis, the numerical Iteration method has been applied to thermally insulated/isothermal boundary conditions. For computation purpose the software like MATLAB tool has been used. The real parts of generated data obtained from the frequency equations have also been shown graphically to frequency shift and natural frequencies. The effects of DPL model of the theory of generalized transversely isotropic thermoelasticity with voids have been represented with and without the effects of magnetic field for nonlocal/local elastic materials and validated with existing literature.

Analyses of non-Fourier heat conduction in 1-D spherical biological tissue based on dual-phase-lag bio-heat model using the conservation element/solution element (CE/SE) method: A numerical study

Among the various numerical methods in solving the hyperbolic equation systems, methods that are simple, have higher accuracy, and avoid creating unwanted numerical oscillations along with having shorter runtime are preferred. In the present study, two numerical methods, space-time conservation element and solution element (CESE) as well as control volume (CV) method have been utilized to estimate temperature distribution in the spherical living tissue during laser irradiation. The results of the CESE method in simulating the non-Fourier thermal wave of the dual-phase-lag (DPL) model in spherical coordinates have been validated against the available semi-analytical results as well as the results obtained using the CV method. The good correlation between the results proved that the CESE method can be applied accurately in solving the DPL model thermal waves in spherical coordinates. In addition, the advantages of the CESE method over the CV method have been investigated. No numerical oscillations are detected in the temperature distribution obtained by the CESE method during and after exposure. Furthermore, in the same circumstances, in terms of radial grid size, a larger time step can be used in CESE method which reduces runtime. Examining the four non-Fourier models, hyperbolic, wavelike, diffusive, and over-diffusive, shows that the thermal wave occurs only in two of these models, hyperbolic and wavelike, when the phase lag of the heat flux is greater than the phase lag of the temperature gradient. After stopping laser irradiation, the maximum temperature is diffused from the surface of the tissue to its inner layers. The results proved that the speed of thermal wave progression is not only constant in hyperbolic and DPL models but also decreases in different tissues with the passage of time. Regardless of the type of tissue, the wave motion towards the center of the tissue in the hyperbolic model is greater than the DPL model. In addition, studying the thermal wave propagation speed in different tissues indicated that this parameter has a direct relationship with the thermal diffusivity of the tissues. The diffusion property caused by the temperature gradient phase lag in the DPL model is the reason why the wave expansion is greater than the hyperbolic model and why a wider range of the tissue is affected by the laser irradiation.

A dual-phase-lag (DPL) transient non-Fourier heat transfer analysis of functional graded cylindrical material under axial heat flux

A dynamic thermal conduction problem needs a mathematical formulation and solution consisting of cylindrical coordinates of materials for the application of nuclear reactor and/or laser therapeutic when subjected to higher heat fluxes. In this study, dual-phase-lag (DPL) transient non-Fourier heat conduction in a functional graded cylindrical material is analytically solved under axial heat flux condition. Functional Graded Material (FGM) properties are based by exponential low. Governing equations on the model are expressed in 2D cylindrical coordinates and solved by using the separation of variable method. An effect of the heterogeneity coefficient of the material using Fourier method, Cattaneo–Vernote model and the dual phase lag is analyzed. An influence of non-dimensional temperature changes to the Fourier number in the pure and functional material is analyzed. Results showed that DPL model requires less time to meet the steady temperature compared with single-phase-lag (SPL) model. In the FGMs, each model and method tends to have a constant temperature based on the amount of heterogeneity coefficient, and it can be concluded that one of the factors determining the amount of stable temperature is the properties of the material. The current results provide a straightforward multivariate analytical solution of the non-Fourier conduction equation in a finite cylinder, for cylinders with any boundary conditions and, for cylinders with functional graded materials. It was found that negligible issues with the critical points being presented when compared to the Laplace operator method.

Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.

Thermoelastic damping in the size-dependent micro/nanobeam resonator with nonlocal dual-phase-lag heat conduction

Precisely calculating quality factor based on thermoelastic damping (TED) is of great importance for the design and optimization of micro/nano-resonators. With the consideration of size-dependent effects in the thermal and mechanical fields and the non-Fourier (NF) heat conduction effect, analytical expressions of TED in the micro/nanobeam resonator are proposed by adopting the theories of the modified-couple-stress (MCS) model and the nonlocal dual-phase-lag (DPL) model. TED models expressed in the series form and the explicit form are both developed basing on the energy-definition approach. The differences among TED models are discussed. In the simulation, silicon and gold, which are two representative materials with typical intrinsic length-scale quantities and phase-lag times, are selected for illustration. Additionally, the nonlocal thermal length-scale parameter refers to the mean-free-path (MFP) of energy carriers, and the MCS mechanical length-scale parameter is not constant but proportional to the beam thickness. TED results obtained by the classical model and the previous DPL model are also shown for comparison. The peak phenomena of TED spectra including the peak damping and the peak frequency are investigated according to the present simple model. Results reveal that TED in micro/nanobeam resonators is of dependence observably on the effect of nonlocal DPL-NF heat conduction associated with the thermal field, and the quality factor is improved by the MCS mechanical size-dependent effect.