Dual Phase Lag Equation Research Articles

Application of different variants of the BEM in numerical modeling of bioheat transfer problems.

Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.

Numerical Simulation of Thermal Damage to Living Biological Tissues Induced by Laser Irradiation Based on a Generalized Dual Phase Lag Model

A generalized dual phase lag (DPL) bioheat model based on the nonequilibrium heat transfer in living biological tissues is applied to investigate thermal damage induced by laser irradiation. Comparisons of the temperature responses and thermal damages between the generalized and classical DPL bioheat model, derived from the constitutive DPL model and Pennes bioheat equation, are carried out in this study. It is shown that the generalized DPL model could predict significantly different temperature and thermal damage from the classical DPL model and Pennes bioheat conduction model. The generalized DPL equation can reduce to the classical Pennes heat conduction equation only when the phase lag times of temperature gradient (τ T ) and heat flux vector (τ q ) are both zero. The effects of laser parameters such as laser exposure time, laser irradiance, and coupling factor on the thermal damage are also studied.

Transient Temperature Response of Pulsed-Laser-Induced Heating for Nanoshell-Based Hyperthermia Treatment

This paper aims to address the transient phenomenon in pulsed-laser-induced heating for nanoshell-based hyperthermia. Within the framework of dual phase lag model, the transient temperature with the relaxation behavior involved was compared with that based on Fourier's law. The temporal variation of temperature is investigated under the irradiation of pulsed laser, as well as continuous-wave (CW) laser. A semianalytical solution of 1-D nonhomogenous dual phase lag equation in spherical coordinates is presented. The results show that the transient temperature with relaxation behavior considered is generally higher than that predicted by a classical diffusion model. The magnitude of difference depends on pulsewidth, duty cycle, and repetition rate. The maximal transient temperature is as high as 350 times the steady-state temperature in a CW case. The biological effect caused by the overheating in a short period needs to be studied further.

Fast Transient Thermal Analysis of Gold Nanoparticles in Tissue-Like Medium

Gold-nanoparticle-based hyperthermia has attracted considerable attention in the recent ten years in cancer treatment. In hyperthermia-based cancer treatment, in order to produce efficient thermal therapy yet without excessive heat damage to human body, besides the steady-state thermal condition, the transient thermal response is of vital importance. As part of theoretical research associated with nanoparticle-mediated hyperthermia therapy for cancer treatment, the transient heat transfer process of laser interacting with gold nanoparticle in tissue-like medium is investigated. Within the framework of dual-phase-lag (DPL) model, this paper focuses on the microscopic heat transfer performance of a gold nanoparticle in a surrounding medium. A semianalytical solution of 1-D nonhomogenous DPL equation in spherical coordinates is presented for a heat transfer process with a constant laser heat source and a short-pulsed laser heating source. Results show that the transient temperature calculated by DPL model greatly exceeds that predicted by the classical diffusion model, with either a constant source or a pulsed source. This phenomenon is mainly attributed by the phase lag of heat flux in the surrounding tissue.

Effect of boundary phonon scattering on Dual-Phase-Lag model to simulate micro- and nano-scale heat conduction

In this paper, one-dimensional heat conduction within a thin slab for Knudsen numbers more than 0.1 is implemented using the Dual-Phase-Lag (DPL) model including phonon scattering boundary condition. The Dual-Phase-Lag equation is solved with a stable and convergent finite difference scheme. Also the Laplace transformation technique is employed to solve DPL equation analytically. The results show that in the smaller values of Knudsen number, the results of the DPL model lay very close to the solution of the Boltzmann equation. Also, it is shown that moving towards the steady state, the DPL model reduces to the Cattaneo and Vernotte (CV) model and has results more accurate than the Ballistic-Diffusive Equations (BDE). It is also shown that the temperature distribution is closer to the results of Boltzmann equation relative to the heat flux distribution. Due to the simplicity of derivation of the DPL model formulation and its possibility for developing to higher dimensions, using the DPL model with new boundary condition is recommended to simulate nano- and micro-scale heat conduction. To investigate the accuracy of the DPL model, its results are compared with the results obtained from BDE model, and Boltzmann equation.

Notable physical anomalies manifested in non-Fourier heat conduction under the dual-phase-lag model

In this study, a number of notable physical anomalies concerning non-Fourier heat conduction under the dual-phase-lag (DPL) model are observed and investigated. It is found that, during the transient heat transfer process, the over-diffusion mode predicts a “hyper-active” to “under-active” transition in thermal behavior. The main cause behind it lies in the time-varying effect of τT (the phase lag of the temperature gradient) on the thermal response. Also, change of polarity in reflected thermal waves can be observed when a constant-temperature boundary is involved, which hints that a heating process may be followed by a spontaneous cooling effect. A fairly strong connection is present between the τT-induced dispersive effect and an unusual thermal accumulation phenomenon in an on–off periodic heating process. Furthermore, a paradox involving a moving medium is detected in the DPL model, which can be solved by replacing the temporal partial derivatives in the DPL equation with the material derivatives. During the process of analysis, a high-order characteristics-based TVD scheme is relied on to provide accurate and reliable numerical simulations to the DPL heat conduction equation under various initial-boundary conditions.

An alternative discretization and solution procedure for the dual phase-lag equation

We describe an alternative numerical treatment of the dual phase-lag equation often used to account for microscale, short-time heat transport. The approach consists of an undecomposed formulation of the partial differential equation resulting from Taylor expansion with respect to lag times of the original delay partial differential equation. Trapezoidal integration in time and centered differencing in space provide an accurate discretization, as demonstrated by comparisons with analytical and experimental results in one dimension, and via grid-function convergence tests in three dimensions. For relatively fine 3-D grids the approach is approximately six times faster than a standard explicit scheme and nearly three times faster than an implicit method employing conjugate gradient iteration at each time step.