An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

Shrivastava, Devashish; Roemer, R. B.

doi:10.1016/j.ijheatmasstransfer.2005.04.005

Cited by 21 publications

(6 citation statements)

References 41 publications

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“…. , N , the solutionT l (x, s) that satisfies Equations (10) and (12) is obtained by applying the separation of variables technique to the modified Helmholtz equation (10) [34] in the form of the following infinite series:…”

Section: Superposition Solutionmentioning

confidence: 99%

“…Solution (19) for problem (ii) satisfies Equations (10) and (12) due to the linearity of the problem. The unknown coefficients X l n (s) in series (20) should be chosen such that the boundary conditions (13) and (14) are satisfied.…”

Section: Superposition Solutionmentioning

confidence: 99%

“…This paper presents a numerical method for solving the transient heat conduction problem of a two-dimensional medium containing multiple circular inhomogeneities, cavities and point sources. This problem has applications in the areas of heat conduction in composite materials [1][2][3][4][5][6], die casting and molding [7][8][9], heat exchange between blood tissue and embedded blood vessels [10] and heat exchange between the earth and buried pipes [11]. Additionally, due to the mathematical equivalence of transient heat conduction [12] and transient groundwater flow [13], the method can be applied to transient groundwater flow problems [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

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SUMMARYA two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two-and threedimensional problems demonstrates the effect of the dimensionality.

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Section: Superposition Solutionmentioning

confidence: 99%

Section: Superposition Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

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“…The simplifications result in overestimation of the cooling effects of the blood and thus underestimation of the resultant heating in deep tissue for a given power. The conventional Pennes BHTE has been criticized by several researchers due to its unrealistic assumption of constant blood temperature, and several improvements have been proposed . Also, there exists no experimental validation of the results of this model for MRI applications.…”

Section: Introductionmentioning

confidence: 99%

In vivo radiofrequency heating in swine in a 3T (123.2-MHz) birdcage whole body coil

et al. 2013

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Purpose To study in vivo radiofrequency (RF) heating produced due to power deposition from a 3T (Larmour frequency = 123.2 MHz), birdcage, whole-body coil. Methods The RF heating was simulated in a digital swine by solving the mechanistic generic bioheat transfer model (GBHTM) and the conventional, empirical Pennes bioheat transfer equation for the following two cases: (1) when the porcine head was in the isocenter, and (2) when the porcine trunk was in the isocenter. The simulation results were validated by making direct fluoroptic temperature measurements in the skin, brain, simulated hot regions, and rectum of ten swine (Case 1, N= 5, mean animal weight = 84.03 ± 6.85 kg, Whole-body average SAR = 2.65 ± 0.22 W/kg; Case 2, N= 5, mean animal weight = 81.59 ± 6.23 kg, Whole-body average SAR = 2.77 ± 0.26 W/kg) during one hour of exposure to a turbo spin echo sequence. Results The GBHTM simulated the RF heating more accurately compared to the Pennes equation. In vivo temperatures exceeded safe temperature thresholds with allowable SAR exposures. Hot regions may be produced deep inside the body, away from the skin. Conclusion SAR exposures to produce safe temperature thresholds may need re-investigation.

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“…Furthermore, in the context of bio-heat transfer modeling of tissue convection within parallel vessels has been considered in many contributions, e.g. [42,44,16,32].…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical analysis of counter-flow parallel convective exchangers considering axial diffusion

Dichamp

Gournay

Plouraboué

2017

International Journal of Heat and Mass Transfer

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We perform a systematic analysis of heat transfer in a counter-current three dimensional convective exchanger, when the inlet/outlet influence is fully taken into account. The analysis, carried out for constant fluid properties, considers the various influences of the fluid/solid conductivity, the imposed convection, inlet/outlet far-field conditions, and lateral boundary conditions. Using a generalized Graetz mode decomposition which permits to consider, both transverse and longitudinal diffusion influence in the exchanger as well as in the inlets/outlets, we put forward several salient generic features of convection/conduction heat transfer. In all cases we found an optimal Péclet number for the cold or hot effectiveness. Even if, as expected, the larger the Péclet the larger the Nusselt number, high transfer performances are found to be poorly efficient and/or to necessitate non-compact elongated exchangers. Performance degradation arising at high Péclet number are found to be related to ''convective leaks" taking place within outlets. A fully developed regime occurs at large Péclet and/or for long exchangers, which is fully determined by the first eigenvalue of the generalized Graetz mode decomposition, which is an extension of classical Graetz analysis. Numerical results are found consistent with a generalized linear relation between effectiveness and the number of heat transfer units asymptotically established in the convection dominated regime. This study opens new perspectives for micro-heat exchangers where moderate convection provides the best effectiveness and compactness. This contribution is also useful for giving reference solutions to counterflow exchangers with realistic inlet/outlet boundary conditions.

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An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

Cited by 21 publications

References 41 publications

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

In vivo radiofrequency heating in swine in a 3T (123.2-MHz) birdcage whole body coil

Theoretical and numerical analysis of counter-flow parallel convective exchangers considering axial diffusion

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