Investigation on the bio-heat transfer with the dual-phase-lag effect

Analysis of thermal damage to laser irradiated tissue based on the dual-phase-lag model

The classical model of the Fourier’s law is known as the most common constitutive relation for thermal transport in various engineering materials. Although the Fourier’s law has been widely used in a variety of engineering application areas, there are many exceptional applications in which the Fourier’s law is questionable. This paper gathers together such applications. Accordingly, the paper is divided into two parts. The first part reviews the papers pertaining to the fundamental theory of the phase-lagging models and the analytical and numerical solution approaches. The second part wrap ups the various applications of the phase-lagging models including the biological materials, ultra-high-speed laser heating, the problems involving moving media, micro/nanoscale heat transfer, multi-layered materials, the theory of thermoelasticity, heat transfer in the material defects, the diffusion problems we call as the non-Fick models, and some other applications. It is predicted that the interest in the field of phase-lagging heat transport has grown incredibly in recent years because they show good agreement with the experiments across a wide range of length and time scales.

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary nonhomogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.

https://journals.sagepub.com/doi/pdf/10.1177/0954406212456651

Heat Conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

This work attempts to estimate the phase lag times of a tissue based on the dual-phase-lag model from the experimental data. The inverse dual-phase-lag bioheat transfer problem in the bilayered spherical tissue is studied. The difference between two layers in the thermophysical parameters, geometry effects, and measurement errors of the input data make it hard to be solved. To solve the present problem, a hybrid scheme based on the Laplace transform, change of variables, and the least-squares scheme is proposed. In order to evidence the validity and accuracy of the estimated results, the comparison of the history of temperature increase between the calculated results and the experimental data is made for various measurement locations. The effect of measurement location on the estimated results is also investigated.

Chin-Tse Lin

Papers

Solution of an Inverse Heat Conduction Problem in a Bi-Layered Spherical Tissue