Solution of hyperbolic bioheat transfer problems by numerical green's functions: the ExGA-linear &amp;#952; method

Loureiro, Felipe dos Santos; Wrobel, L.C.; Mansur, Webe João

doi:10.1590/s1678-58782012000400006

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…Green's function [171] Ghazanfarian and Abbassi [92,93] and Ghazanfarian and Shomali [94] have extended the mentioned three-level finite difference scheme to higher dimensions for Cartesian coordinates. Similar to the original method, in these two studies, a weighted time average is used to stabilize the results of the numerical method.…”

Section: Finite Difference Methodsmentioning

confidence: 99%

“…The numerical scheme is developed to overcome the mathematical difficulties induced by the difference between two layers in the relaxation times, strong nonlinearity of the interfacial boundary condition, the radiative boundary condition at the interface, and a singularity at the center axis. A time-domain formulation called the explicit Green's approach (ExGA) linear θ method for the solution of the bioheat equation is presented [171]. Starting from the hyperbolic bioheat equation, which includes the parabolic special case, the linear method is incorporated into the standard ExGA time marching scheme.…”

Section: Hybrid Methodsmentioning

confidence: 99%

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

2015

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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.

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Section: Finite Difference Methodsmentioning

confidence: 99%

Section: Hybrid Methodsmentioning

confidence: 99%

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

2015

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“…(17). Actually, the convolution integral is dealt with analytically considering a type of time variation for the heat load vector and the only error is due to the use of an approximate Green's matrix given by Eq.…”

Section: Convolution Integralmentioning

confidence: 99%

The Explicit Green’s Approach with stability enhancement for solving the bioheat transfer equation

Loureiro¹,

Mansur²,

Wrobel³

et al. 2014

International Journal of Heat and Mass Transfer

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The aim of this paper is to propose a strategy for performing a stability enhancement into the Explicit Green's Approach (ExGA) method applied to the bioheat transfer equation. The ExGA method is a time-stepping technique that uses numerical Green's functions in the time domain; these functions are here computed by the FEM.Basically, a new two nonequal time substeps procedure is proposed to compute Green's functions at the first time step. This is accomplished by adopting the standard explicit Euler scheme and an optimized procedure to yield the best stability constraint, allowing a reduction into the number of time steps without loss of accuracy. In addition, the concept of local numerical Green's functions is introduced and explored aiming at reducing the computational effort of nodal Green's functions calculation. Two examples are presented in order to show the potentialities of the proposed methodology, one to illustrate the accuracy and another applied to skin burn simulations.

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