Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem

Hsu, Pao-Tung

doi:10.1016/j.amc.2005.11.022

Cited by 22 publications

(8 citation statements)

References 16 publications

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“…The Crank-Nicolson method, which is unconditionally stable and second-order accurate, discretizes (20), (21), (18), (22) and (19) as:…”

Section: Numerical Solution Of Direct Problemmentioning

confidence: 99%

“…Concerning inverse problems for bio-heat transfer, a great deal of numerical techniques has been proposed to solve inverse problems for the Pennes' bio-heat model (Bazán et al, 2017;Cao and Lesnic, 2018;Huntul et al, 2018). However, limited attention has been given to inverse problems for the thermal-wave model (Hsu, 2006;Lee et al, 2013;Yang, 2014). For instance, Lee et al (2013) studied the thermal-wave model and determined the unknown surface heat flux of a living skin tissue from temperature measurements sampled over the tissue using the conjugate gradient method (CGM) coupled with the discrepancy principle.…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

Alosaimi

Lesnic

Niesen

2020

HFF

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Purpose This study aims to at numerically retrieve five constant dimensional thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements. Design/methodology/approach The thermal-wave model of bio-heat transfer is used as an appropriate model because of its realism in situations in which the heat flux is extremely high or low and imposed over a short duration of time. For the numerical discretization, an unconditionally stable finite difference scheme used as a direct solver is developed. The sensitivity coefficients of the dimensionless boundary temperature measurements with respect to five constant dimensionless parameters appearing in a non-dimensionalised version of the governing hyperbolic model are computed. The retrieval of those dimensionless parameters, from both exact and noisy measurements, is successfully achieved by using a minimization procedure based on the MATLAB optimization toolbox routine lsqnonlin. The values of the five-dimensional parameters are recovered by inverting a nonlinear system of algebraic equations connecting those parameters to the dimensionless parameters whose values have already been recovered. Findings Accurate and stable numerical solutions for the unknown thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements are obtained using the proposed numerical procedure. Research limitations/implications The current investigation is limited to the retrieval of constant physical properties, but future work will investigate the reconstruction of the space-dependent blood perfusion coefficient. Practical implications As noise inherently present in practical measurements is inverted, the paper is of practical significance and models a real-world situation. Social implications The findings of the present paper are of considerable significance and interest to practitioners in the biomedical engineering and medical physics sectors. Originality/value In comparison to Alkhwaji et al. (2012), the novelty and contribution of this work are as follows: considering the more general and realistic thermal-wave model of bio-heat transfer, accounting for a relaxation time; allowing for the tissue to have a finite size; and reconstructing five thermally significant dimensional parameters.

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“…The Crank-Nicolson method, which is unconditionally stable and second-order accurate, discretizes (20), (21), (18), (22) and (19) as:…”

Section: Numerical Solution Of Direct Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

Alosaimi

Lesnic

Niesen

2020

HFF

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“…Although analytical solutions exist for a few typical cases with simple geometry, general inverse problems for cases with complicated geometry still need resort to numerical methods, such as the finite difference method (e.g. [9,10]), the finite element method (e.g. [11][12][13]), the differential quadrature scheme (e.g.…”

Section: Introductionmentioning

confidence: 99%

A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis

Hematiyan

Khosravifard

Shiah

2015

International Journal of Heat and Mass Transfer

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“…In Hsu (2006) the 3D inverse non-Fourier heat conduction problem are solved by Finite Difference Method and showing excellent results because it is purely diffusive problems. Excellent results are also presented in Yang et all (2002), were one particular integral formulations are presented for 2D and 3D transient potential flow (heat conduction) analysis.…”

Section: Introductionmentioning

confidence: 99%

Error Analysis in the Numerical Solution of 3d Convection-Diffusion Equation by Finite Difference Methods

Romão

Silva

Moura

2009

RETERM

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In this work an error analysis for numerical solution of 3D convectiondiffusionequation by finite difference methods has been done. The backward, the forward and the central difference schemes are applied for three applications: a case with diffusion dominant corresponding to high diffusion coefficients and two cases with convection dominant or with low diffusion coefficients. In the second application the convective coefficients are function only of the diffusion coefficient that in dimensionless form is named Reynolds numbers. In the third application the convective coefficients are function of both the Reynolds number and of the space. The three applications have analytical solutions to facilitate numerical comparisons of the solutions.

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Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem

Cited by 22 publications

References 16 publications

Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis

Error Analysis in the Numerical Solution of 3d Convection-Diffusion Equation by Finite Difference Methods

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