A Counter Current Vascular Network Model of Heat Transfer in Tissues

1996 ◽  
Vol 118 (1) ◽  
pp. 120-129 ◽  
Author(s):  
H. W. Huang ◽  
Z. P. Chen ◽  
R. B. Roemer

A fully conjugated blood vessel network model (FCBVNM) for calculating tissue temperatures has been developed, tested, and studied. This type of model represents a more fundamental approach to modeling temperatures in tissues than do the generally used approximate equations such as the Pennes’ BHTE or effective thermal conductivity equations. As such, this type of model can be used to study many important questions at a more basic level. For example, in the particular hyperthermia application studied herein, a simple vessel network model predicts that the role of counter current veins is minimal and that their presence does not significantly affect the tissue temperature profiles: the arteries, however, removed a significant fraction of the power deposited in the tissue. These more fundamental models can also be used to check the validity of approximate equations. For example, using the present simple model, when the temperatures calculated by the FCBVNM are used for comparing predictions from two approximation equations (a simple effective thermal conductivity and a simple Pennes’ bio-heat transfer equation formulation of the same problem) it is found that the Pennes’ equation better approximates the FCBVNM temperatures than does the keff model. These results also show that the “perfusion” value (W˙) in the Pennes’ BHTE is not necessarily equal to the “true” tissue perfusion (P˙) as calculated from mass flow rate considerations, but can be greater than, equal to, or less than that value depending on (1) how many vessel levels are modeled by the BHTE, and (2) the “true” tissue perfusion magnitude. This study uses a simple, generic vessel network model to demonstrate the potential usefulness of such fully conjugated vessel network models, and the associated need for developing and applying more complicated and realistic vascular network models. As more realistic vascular models (vessel sizes, orientations, and flow rates) are developed, the predictions of the fully conjugated models should more closely model and approach the true tissue temperature distributions, thus making these fully conjugated models more accurate and valuable tools for studying tissue heat transfer processes.

Author(s):  
Devashish Shirvastava ◽  
Robert B. Roemer

This work presents the first numerical validation/sensitivity study of a new bio-heat equation, the tissue convective energy balance equation (TCEBE) in an unheated tissue with a simple but physiologically realistic 3D arterial blood vessel network. The validation of the TCEBE is performed by comparing its predictions of the tissue temperature field with the predictions of a test case in which the 3D conduction energy equation is solved in the tissue and the 1D convective energy equation is solved in the embedded blood vessel network. To perform the sensitivity analysis of the TCEBE, the effects of size of the vessels, and the inlet temperature of arterial blood on the tissue temperature distribution are presented. The relationship between the Pennes’ perfusion related term and the true tissue perfusion has also been investigated. Results show that 1) the TCEBE has a potential to replace the Pennes’ equation as a new, more accurate bio-heat equation, and 2) the Pennes’ perfusion related term is dominated by the heat transfer from larger vessels through their overall heat transfer coefficients, i.e. their ‘UA’ values, and the effect of true tissue perfusion on Pennes’ perfusion related term is negligible.


Geothermics ◽  
2017 ◽  
Vol 67 ◽  
pp. 76-85 ◽  
Author(s):  
Chulho Lee ◽  
Li Zhuang ◽  
Dongseop Lee ◽  
Seokjae Lee ◽  
In-Mo Lee ◽  
...  

Author(s):  
Ayushman Singh ◽  
Srikanth Rangarajan ◽  
Leila Choobineh ◽  
Bahgat Sammakia

Abstract This work presents an approach to optimally designing a composite with thermal conductivity enhancers (TCEs) infiltrated with phase change material (PCM) based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In present study, TCEs are in the form of a honeycomb structure. TCEs are often used in conjunction with PCM to enhance the conductivity of the composite medium. Under constrained composite volume, the higher volume fraction of TCEs improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. The present work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated trade-off. In this study, the total volume of the composite and the interfacial heat transfer area between the PCM and TCE are constrained for all design points. A benchmarked two-dimensional direct CFD model was employed to investigate the thermal performance of the PCM and TCE composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the PCM and TCE has been developed. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.


2009 ◽  
Vol 38 (11) ◽  
pp. 2218-2223 ◽  
Author(s):  
Alex Sandro Campos Maia ◽  
Roberto Gomes da Silva ◽  
João Batista Freire de Souza Junior ◽  
Rosiane Batista da Silva ◽  
Hérica Girlane Tertulino Domingos

The objective of the present study was to assess the effective thermal conductivity of the hair coat (k ef, mW.m-1.K-1) of Holstein cows in a tropical environment, as related to conduction and radiation in the absence of free convection. The average k ef was 49.72 mW.m-1.K-1, about twice the conductivity of the air (26 mW.m-1.K-1) and much less than that of the hair fibres (260 mW.m-1.K-1). The low k ef values were attributed mainly to the small cross area of individual hairs, ρef/ρf (17.2% and 21.3% for black and white hairs, respectively). White coats were denser, with longer hairs and significantly higher k ef (53.15 mW.m-1.K-1) than that of the black hairs (49.25 mW.m-1.K-1). The heritability coefficient of the effective thermal conductivity was calculated as h²=0.18 the possibility was discussed of selecting cattle for increased heat transfer through the hair coat.


2019 ◽  
Vol 141 (1) ◽  
Author(s):  
Yuntao Cui ◽  
Yujie Ding ◽  
Shuo Xu ◽  
Yushu Wang ◽  
Wei Rao ◽  
...  

Gallium-based liquid metal (LM) inherits excellent thermophysical properties and pollution-free characteristics. However, it has long been a fatal problem that LM would cause serious corrosion and embrittlement on the classical substrate made of aluminum alloys in constructing chip cooling device. Here, anodic oxidation treatment was introduced on processing the aluminum alloy aiming to tackle the corrosion issues. The prepared anodic oxidation aluminum (AAO) coatings were composed of nanopore layers and barrier layers on a high-purity alumina matrix that were manufactured electrochemically. According to the measurement, the effective thermal conductivity of the anodized aluminum alloy increases with the total thickness of sample increasing. When the total thickness L exceeds 5 × 10−3 m, effects of the porous media on effective thermal conductivity are negligible via model simulation and calculation. It was experimentally found that aluminum alloy after surface anodization treatment presented excellent corrosion resistance and outstanding heat transfer performance even when exposed in eutectic gallium–indium (E-GaIn) LM over 200 °C. The convective heat transfer coefficient of LM for anodized sample reached the peak when the heat load is 33.3 W.


2016 ◽  
Vol 846 ◽  
pp. 500-505
Author(s):  
Wei Jing Dai ◽  
Yi Xiang Gan ◽  
Dorian Hanaor

Effective thermal conductivity is an important property of granular materials in engineering applications and industrial processes, including the blending and mixing of powders, sintering of ceramics and refractory metals, and electrochemical interactions in fuel cells and Li-ion batteries. The thermo-mechanical properties of granular materials with macroscopic particle sizes (above 1 mm) have been investigated experimentally and theoretically, but knowledge remains limited for materials consisting of micro/nanosized grains. In this work we study the effective thermal conductivity of micro/nanopowders under varying conditions of mechanical stress and gas pressure via the discrete thermal resistance method. In this proposed method, a unit cell of contact structure is regarded as one thermal resistor. Thermal transport between two contacting particles and through the gas phase (including conduction in the gas phase and heat transfer of solid-gas interfaces) are the main mechanisms. Due to the small size of particles, the gas phase is limited to a small volume and a simplified gas heat transfer model is applied considering the Knudsen number. During loading, changes in the gas volume and the contact area between particles are simulated by the finite element method. The thermal resistance of one contact unit is calculated through the combination of the heat transfer mechanisms. A simplified relationship between effective thermal conductivity and loading pressure can be obtained by integrating the contact units of the compacted powders.


2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Swaren Bedarkar ◽  
Nurni Neelakantan Viswanathan ◽  
Nidambur Bharatha Ballal

Heat transfer in packed beds and their thermal response have been of great interest for scientists and engineers for the last several years, since they play a crucial role in determining design and operation of reactors. Heat transfer of a packed bed is characterised through lumped parameter, namely, effective thermal conductivity. In the present studies, experiments were performed to investigate the thermal conductivity of a packed bed in radial direction. The packed bed was formed using iron ore particles. To determine the effective thermal conductivity a new transient methodology is proposed. The results obtained were compared with the models proposed by ZBS and Kunii and Smith.


Sign in / Sign up

Export Citation Format

Share Document