Phase Lag Of Temperature Gradient Research Articles

A semi-analytical method of three-dimensional dual-phase-lagging heat conduction model

With the development of picosecond laser technology, the dual-phase-lagging (DPL) model is more suitable to describe the heat transfer problem with micro-scale effect and micro-time effect. In this paper, a three-dimensional dual-phase-lagging heat transfer model for picosecond laser processing is established. Then Fourier transform (FT) and Laplace transform (LT) are used to derive the frequency response functions (FRFs) of the problem in the frequency domain, and the inverse Laplace transform (ILT) and discrete-convolution fast Fourier transform (DC-FFT) algorithm are used to solve the temperature field. The calculation accuracy of this method is verified and the effect of phase lag constants on temperature field is studied. The results show that the semi-analytical method has a high accuracy for solving the dual-phase-lagging heat conduction model, and the phase lag of heat flux will affect the heating rate in the heating stage, and the phase lag of temperature gradient will delay the formation of temperature field. The effect of phase lag constants on temperature-time history is investigated and the related phenomena are explained by using the two-step heat transfer theory. This semi-analytical method provides a new approach to solve the problem of three-dimensional dual-phase-lagging heat transfer.

Comparative analysis of thermal damage to laser-irradiated breast tumor based on Fourier conduction and non-Fourier heat conduction models: A numerical study

In recent decades, laser technology has been widely used in surgeries and thermal therapies. To ensure patient safety and enhance therapeutic effectiveness in laser applications, it is crucial to accurately analyze burn injuries during the treatment process. In this study, a bioheat transfer model that includes the effects of metabolic heat generation, capillary blood vessels, and relaxation times of heat flux and temperature gradient was developed to study the non-Fourier heat conduction behavior in 2-D spherical breast tumor during the laser hyperthermia process. By employing different heat conduction models and the Arrhenius burn integration, the temperature distribution and laser-induced thermal damage to tumors were obtained. The progression of burn injury in time and the effect of various parameters on it were investigated. It was observed that the DPL model provides more reliable results in comparison with the CV model in predicting thermal damage to bio-tissue when non-Fourier effects are taken into consideration. The results showed that increasing heat flux phase lag leads to severe thermal damage, earlier onset of empyrosis, and wider and deeper burn injury. However, a greater phase lag of temperature gradient results in lower and superficial thermal damage, milder burn, later onset of empyrosis, and smaller burned area. The effect of laser power density on the onset time of different degrees of burn and their sensitivity to input power were investigated, and the results were represented graphically. Finally, investigation of wave propagation in various tissues revealed that the wave propagation speed is not constant and reduces as time increases.

Propagation and reflection of plane waves in biological tissue based on nonlocal TPL thermoelasticity

The investigation for propagation and reflection of plane waves is carried out based on three-phase-lag (TPL) thermoelasticity with the aids of Eringen's nonlocal theory in a special medium - biological tissue. The scalar and vector potential functions of Helmhotz decomposition are adopted to obtain the propagation speeds, attenuation coefficients and reflection coefficients of plane waves analytically. There are two sets of dispersive attenuated longitudinal waves whose speeds of propagation are associated with angular frequency, and independent transverse elastic shear wave which exhibits no attenuation. It is found that the blood perfusion rate has few effects on wave propagation speed and attenuation coefficient and the phase lag of temperature gradient is negligible in present configuration. The effects of working angular frequency, nonlocal parameters, phase lag times, reflecting thermal boundaries and the type of incident waves on the propagation speeds, attenuation coefficients and reflection coefficients of harmonic waves are discussed and investigated graphically.

Thermoelastic behavior of skin tissue induced by laser irradiation based on the generalized dual-phase lag model.

This paper analyzes the thermoelastic responses of skin tissue during laser irradiation based on a generalized dual-phase-lag (DPL) model. The method of separation of variables is utilized to obtain the analytical solutions for thermal and mechanical responses. The influences of some crucial parameters on temperature, displacement and stress evolutions are discussed, including the phase lag of heat flux, the phase lag of temperature gradient and the phase lag of laser pulse, the coupling factor between tissue and blood, the porosity of tissue, the equivalent diameter of tissue and the diameter of blood vessels. The generalized DPL bio-heat transfer model predicts different results from those by the classical DPL model and Pennes model. The equivalent diameter of tissue affects the coupling factor between tissue and blood, while the diameter of blood vessels mainly affects the porosity of tissue.

On a multi-phase-lag model of coupled thermoelasticity

Various qualitative properties of the dual/three-phase-lag heat equations are discussed. A refined model of coupled thermoelasticity is formulated to consider three delay times: a phase-lag of heat flux, a phase-lag of temperature gradient, and a phase-lag of thermal displacement gradient. Three special cases are considered to deal with all the considered models in the literature. In the first case one can obtain the simple and Tzou's dual-phase-lag, Lord–Shulman and the classical models. The Green–Naghdi type II model of generalized thermoelasticity without energy dissipation is obtained in the second case. Case 3 is devoted to considering the Green–Naghdi type III model. As an application, a unified form to a multi-phase-lag model is presented to yield all the preceding models as well as the Green–Lindsay generalized thermoelasticity model. A validation example is provided to discuss the coupled solution for photothermal semiconducting isotropic beam. Some illustrative flowcharts and plots are added and concluding remarks are presented.

Thermal damage in three-dimensional vivo bio-tissues induced by moving heat sources in laser therapy

The thermal damage of a three-dimensional bio-tissue model irradiated by a movable laser beam was studied in this work. By employing the DPL biological heat conduction model and Henriques’ thermal damage assessment model, the distribution of burn damage of vivo human tissue during laser therapy was analytically obtained. The influences of laser moving velocity, laser spot size, phase lags of heat flux and temperature gradient were discussed. It was found that the laser moving speed and the laser spot size greatly influence the thermal damage degree by affecting the energy concentration degree. The increases of the laser moving speed and laser spot size can enlarge the irradiated region and reduce the burn degree. A greater phase lag of temperature gradient led to lower accumulation of thermal energy and lower burn degree. However, the increment of heat flux phase lag leads to the thermal energy accumulation and more serious burn degree in the irradiated region.

Numerical study of dual-phase-lag heat conduction in a thermal barrier coating with a hybrid method

In this study, the dual-phase-lag (DPL) heat conduction model is applied to study the non-Fourier heat transfer in a thermal barrier coating (TBC) structure subjected to heat flux on the exterior of the coating. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods in conjunction with hyperbolic shape functions is used to solve the hyperbolic heat conduction equations in the linearized form of DPL model. The transformed nodal temperatures are inverted to the physical quantities using numerical inversion of the Laplace transform. Parametric studies of properties of the substrate and the coating on the temperature distributions in the TBC are performed. A comparison between the present study and other work in the literature using the thermal wave model is also made. The results also show that the phase lag of heat flux tends to induce thermal waves with sharp wave fronts separating heated and unheated zones in the structure, while the phase lag of temperature gradient results in non-Fourier diffusion-like conduction and smooths the sharp wave fronts by promoting conduction into the medium.

Non-Fourier heat conduction in a thin gold film heated by an ultra-fast-laser

Based on the dual-phase-lagging (DPL) heat conduction model, the Cattaneo-Vernotte (CV) model and the improved CV model we investigate the one-dimensional heat conduction in gold films with nano-scale thickness exposed to an ultra-fast laser heating. The influence of system parameters on the temperature field is explored. We find that for all the non-Fourier heat conduction models considered in this work, a larger Knudsen number normally leads to a higher temperature. For the DPL model, the large ratio of the phase lag of temperature gradient to the phase lag of heat flux reduces the maximum temperature and shortens the time for the system to reach its steady state. The CV model and the improved CV model lead to the similar thermal wave behavior of the temperature field, but the thermal wave speeds for these two models are different, especially for large Knudsen numbers. When the phase lag of temperature gradient is smaller, the difference between the DPL model and the improved CV model is not significant, but for the large phase lag of temperature gradient the difference becomes quite significant, especially for the large Knudsen number. In addition, the effect of the surface accommodation coefficient, which is a parameter in the slip boundary condition, on the temperature field of the gold film heated by ultra-fast laser pulses is investigated based on the DPL model.

Heat conduction in nanofluids: Structure–property correlation

We examine numerically the effects of particle-fluid thermal conductivity ratio, particle volume fraction, and particle morphology on nanofluids effective thermal conductivity and phase lags of heat flux and temperature gradient, for six types of nanofluids containing sphere, cube, hollow sphere, hollow cube, slab-cross and column-cross nanoparticles, respectively. The particle’s radius of gyration and the non-dimensional particle-fluid interfacial area are found to be two characteristic parameters for the effect of particles’ geometrical structure on the effective thermal conductivity. The nanoparticles with larger values of these two parameters can change fluid conductivity more significantly. Due to the enhanced particle-fluid interfacial heat transfer, the nanofluid effective thermal conductivity can practically reach the Hashin–Shtrikman bounds when the particle-phase connects to form a network and separates the base fluid into a dispersed phase. The particle aggregation can effectively affect the effective thermal conductivity when the separation distance among particles is smaller than about one fifth of the particles’ dimension. For the nanofluids considered in the present work, the phase lags of heat flux and temperature gradient scale with the square of particle dimension and range from 10 −11 s to 10 −7 s; the effect of cross-coupling between the heat conduction in the fluid and particle phases is weak; the phase lag of temperature gradient is larger than that of heat flux such that the heat conduction in them is diffusion-dominant and their effective thermal conductivity can be well predicted by the predictive models developed in the present work based on the classical diffusion theory for two-phase systems.

A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model

The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.

Study of heat transfer in multilayered structure within the framework of dual-phase-lag heat conduction model using lattice Boltzmann method

The effect of the phase lag of temperature gradient, τ T , on the transmission–reflection phenomenon, induced by a pulsed thermal energy passing the interface of a two-layered structure, within the framework of dual-phase-lag based heat conduction equation is studied numerically by the lattice Boltzmann (LB) method. An extended LB equation, with truncation error of order two, and a numerical solution procedure are developed for the solution of the governing equation and the derived interfacial boundary condition. Results show that the interface reflects a negative followed by a positive waveform when the pulsed thermal wave propagates from the media with lower τ T into the media with higher τ T and vice versa if the wave propagates from higher into lower τ T media. These special phenomena which have not been presented in the available literatures are unable to be predicted in the framework of hyperbolic heat conduction equation.