Study on Evaluation of Effective Thermal Conductivity of Unsaturated Soil Using Average Capillary Pressure and Network Model

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.

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An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials

IEEE Transactions on Components and Packaging Technologies ◽

10.1109/tcapt.2008.2001839 ◽

2008 ◽

Vol 31 (3) ◽

pp. 611-621 ◽

Cited By ~ 28

Author(s):

S. Kanuparthi ◽

G. Subbarayan ◽

T. Siegmund ◽

B. Sammakia

Keyword(s):

Thermal Conductivity ◽

Effective Thermal Conductivity ◽

Network Model ◽

Thermal Interface Materials ◽

Thermal Interface ◽

Interface Materials

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AN IMPROVED CONVOLUTION NEURAL NETWORK MODEL TO PREDICT THE EFFECTIVE THERMAL CONDUCTIVITY OF COMPOSITE MATERIALS

10.1615/ihtc16.nmt.022090 ◽

2018 ◽

Author(s):

Hua Bao ◽

Han Wei ◽

Shuaishuai Zhao

Keyword(s):

Neural Network ◽

Thermal Conductivity ◽

Composite Materials ◽

Effective Thermal Conductivity ◽

Network Model ◽

Neural Network Model ◽

Convolution Neural Network

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An Improved Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials

Journal of Electronic Packaging ◽

10.1115/1.4024392 ◽

2013 ◽

Vol 135 (3) ◽

Author(s):

B. Dan ◽

B. G. Sammakia ◽

G. Subbarayan ◽

S. Kanuparthi

Keyword(s):

Thermal Conductivity ◽

Effective Thermal Conductivity ◽

Network Model ◽

Thermal Transport ◽

Volume Fraction ◽

Spherical Particles ◽

Thermal Interface Materials ◽

Interparticle Interactions ◽

Cylindrical Region ◽

Interface Materials

Thermal interface materials (TIMs) are particulate composite materials widely used in the microelectronics industry to reduce the thermal resistance between the device and heat sink. Predictive modeling using fundamental physical principles is critical to developing new TIMs since it can be used to quantify the effect of particle volume fraction and arrangements on the effective thermal conductivity. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30–80%. An efficient random network model (RNM) that captures the near-percolation transport in these particle-filled systems, taking into account the interparticle interactions and random size distributions, was previously developed by Kanuparthi et al. The RNM approach uses a cylindrical region to approximate the thermal transport within the filler particles and to capture the interparticle interactions. However, this approximation is less accurate when the polydispersivity of the particulate system increases. In addition, the accuracy of the RNM is dependent on the parameters inherent in an analytical description of thermal transport between two spherical particles and their numerical approximation into the network model. In the current paper, a novel semispherical approximation to the conductance of the fillers is presented as an alternative to the cylindrical region approximation used earlier. Compared with the cylindrical model, the thermal conductivities of the semispherical model are more closely to the finite element (FE) results. Based on the FE analysis, the network model is improved by developing an approximation of the critical cylindrical region between two spherical particles over which energy is transported. Comparing the RNM results with FE results and experimental data, a linear relationship of the critical parameter with the thermal conductivity ratio and the volume fraction was found that provides a more accurate prediction of the effective thermal conductivity of the particulate TIMs.

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Thermophysical Properties of Biporous Sintered Copper

Heat Transfer, Part B ◽

10.1115/imece2005-82190 ◽

2005 ◽

Cited By ~ 8

Author(s):

Ying-Yu Lin ◽

Tadej Semenic ◽

Ivan Catton

Keyword(s):

Thermal Conductivity ◽

Capillary Pressure ◽

Effective Thermal Conductivity ◽

Thermophysical Properties ◽

Silicone Oil ◽

Pressure Drops ◽

Sintered Copper ◽

Measurement Results ◽

The One ◽

Working Liquid

Thermophysical properties of bidispersed (biporous)-sintered copper are measured. An apparatus to measure effective thermal conductivity of dry samples is built. It is calibrated using bulk samples with known thermal conductivity. Permeability is measured based on flow resistance though the porous samples. Velocity at different pressure drops is measured and the permeability calculated using Darcy’s law. The experiment is performed using silicone oil as working liquid. The error of the method is less than three percent. Capillary pressure for all samples is measured based on amount of liquid that is held by the porous sample. The Young-Laplace relationship is used to relate capillary pressure to effective pore radius. Porosity of the samples is measured using density method. According to the measurement results, effective thermal conductivity of biporous samples is much lower than for comparable monoporous samples. Permeability and porosity of biporous samples are much higher than the monoporous samples. Capillary pressure of the biporous samples is very close to the one measured for the monoporous samples.

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Estimation of Effective Thermal and Mechanical Properties of Particulate Thermal Interface Materials by a Random Network Model

Journal of Electronic Packaging ◽

10.1115/1.4039136 ◽

2018 ◽

Vol 140 (2) ◽

Cited By ~ 2

Author(s):

Pavan Kumar Vaitheeswaran ◽

Ganesh Subbarayan

Keyword(s):

Mechanical Properties ◽

Thermal Conductivity ◽

Effective Thermal Conductivity ◽

Network Model ◽

Random Network ◽

Thermal Interface Materials ◽

Thermal And Mechanical Properties ◽

Thermal Interface ◽

Classical Models ◽

Interface Materials

Particulate thermal interface materials (TIMs) are commonly used to transport heat from chip to heat sink. While high thermal conductance is achieved by large volume loadings of highly conducting particles in a compliant matrix, small volume loadings of stiff particles will ensure reduced thermal stresses in the brittle silicon device. Developing numerical models to estimate effective thermal and mechanical properties of TIM systems would help optimize TIM performance with respect to these conflicting requirements. Classical models, often based on single particle solutions or regular arrangement of particles, are insufficient as real-life TIM systems contain a distribution of particles at high volume fractions, where classical models are invalid. In our earlier work, a computationally efficient random network model (RNM) was developed to estimate the effective thermal conductivity of TIM systems (Kanuparthi et al., 2008, “An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” IEEE Trans. Compon. Packag. Technol., 31(3), pp. 611–621; Dan et al., 2009, “An Improved Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” ASME Paper No. InterPACK2009-89116.) . This model is extended in this paper to estimate the effective elastic modulus of TIMs. Realistic microstructures are simulated and analyzed using the proposed method. Factors affecting the modulus (volume fraction and particle size distribution (PSD)) are also studied.

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