A Three-Dimensional Analytical Model for the Effective Thermal Conductivity and Porosity in High-Porosity Metal Foam Using a Nonisotropic Unit Cell

2010 ◽  
Vol 17 (3) ◽  
pp. 257-270 ◽  
Author(s):  
M. Haghighi ◽  
Norollah kasiri
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Analytical Model ◽  
Metal Foam ◽  
Three Dimensional ◽  
Unit Cell ◽  
High Porosity

Characterization of High Porosity Open-Celled Metal Foam Using Computed Tomography

2004 ◽  
Author(s):  
Eric N. Schmierer ◽  
Arsalan Razani ◽  
Scott Keating ◽  
Tony Melton
Keyword(s):  
Heat Transfer ◽  
Computed Tomography ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Surface Area ◽  
Metal Foam ◽  
Three Dimensional ◽  
Metal Foams ◽  
High Porosity ◽  
Interfacial Surface

High porosity metal foams have been the subject of many investigations for use in heat transfer enhancement through increased effective thermal conductivity and surface area. Convection heat transfer applications with these foams have been investigated for a large range of Reynolds numbers. Common to these analyses is the need for quantitative information about the interfacial surface area and the effective thermal conductivity of the metal foam. The effective thermal conductivity of these metal foams have been well characterized, however little investigation has been made into the actual surface area of the foam and its dependence on the foam pore density and porosity. Three-dimensional x-ray computed tomography (CT) is used for determining interfacial surface area and ligament diameter of metal foam with porosities ranging from 0.85 to 0.97 and pore densities of 5, 10, 20, and 40 pores per inch. Calibration samples with known surface area and volume are utilized to benchmark the CT process. Foam results are compared to analytical results obtained from the development of a three-dimensional model of the high porosity open-celled foam. The results obtained are compared to results from previous investigations into these geometric parameters. Results from calibration sample comparison and analysis of the foam indicate the need for additional work in quantifying the repeatability and sources of error in CT measurement process.

Study of Micro-Structure Based Effective Thermal Conductivity of Graphite Foam

2016 ◽  
Author(s):  
Yue Chai ◽  
Xiaohu Yang ◽  
Xiangzhao Meng ◽  
Qunli Zhang ◽  
Liwen Jin
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Analytical Model ◽  
Geometric Model ◽  
Three Dimensional ◽  
Heat Sinks ◽  
High Porosity ◽  
Geometry Model ◽  
Graphite Foam

As a new type of functional material, porous graphite foam exhibits unique thermal physical properties and geometric characteristics in heat transfer applications. It has the advantages of low density, high specific surface area, high porosity and high bulk thermal conductivity, which can be used as the core component of small, lightweight, compact and efficient heat sinks. Effective thermal conductivity serves one of the key thermophysical properties for foam-cored heat sinks. The complex three-dimensional topology and interstitial fluids significantly affect the heat conduction through such kind of porous structures, reflecting a topologically based effective thermal conductivity. This paper presents a novel geometric model for representing the microstructure of graphite foams, with simplifications and modifications made on the actual pore structure of graphite foam. For calculation simplicity, we convert the realized geometry consisting of complex surfaces and tortuous ligaments into a simplified geometry with circular ligaments joined at cuboid nodes, on the basis of the volume equivalency rule. The multiple-layer method is used to divide the proposed geometry into solvable areas and the series-parallel relations are used to derive the analytical model for effective thermal conductivity. To physically explore the heat conduction mechanisms at pore scale, direction numerical simulations were conducted on the reconstructed geometric model. Achieving good agreement with experimental data, the present analytical model (based on the simplified geometry) is validated. Further, the numerically simulated conductivities follow the model prediction, favoring thermally that the two geometries are equal. The present geometry model is more realized and capable of reflecting the internal microstructure of graphite foam, which will benefit the understandings for the thermo-physical mechanisms of pore-scaled heat conduction and micro structures of graphite foam.

An Analytical Unit Cell Model for the Effective Thermal Conductivity of High Porosity Open-Cell Metal Foams

2014 ◽  
Vol 102 (3) ◽  
pp. 403-426 ◽  
Author(s):  
Xiao Hu Yang ◽  
Jia Xi Bai ◽  
Hong Bin Yan ◽  
Jiu Jie Kuang ◽  
Tian Jian Lu ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Cell Model ◽  
Metal Foams ◽  
Unit Cell ◽  
High Porosity ◽  
Unit Cell Model ◽  
Open Cell

Effective Thermal Conductivity of Fully-Saturated High Porosity Metal Foam

Volume 1 ◽  
2004 ◽  
Author(s):  
Eric N. Schmierer ◽  
Jason Paquette ◽  
Arsalan Razani ◽  
Kwang J. Kim
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Metal Foam ◽  
Three Dimensional ◽  
Element Calculation ◽  
One Dimensional ◽  
Cubic Lattice ◽  
Surface Areas ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Geometric models are used to simplify the complex, three-dimensional geometry of metal foams for calculations of effective thermal conductivity. The first is based on a conventional three-dimensional cubic lattice and the second is a tetrakaidecahedronal model. The models consist of interconnecting ligaments with a spherical node at their intersections. The geometry of the foam is determined based on two dimensionless parameters: 1) the porosity and 2) the product of the specific surface area of the foam and the length of the interconnecting ligaments. A free parameter represents the size of the lumps at the ligament interconnections. It is shown that the remaining unknown geometric parameters of the models can be obtained as a solution of a cubic equation that has only one acceptable solution. From the cubic lattice model, a one-dimensional heat conduction analytical model is used to find the effective thermal conductivity of fully saturated metal foam. A three-dimensional finite element calculation of the effective thermal conductivity for the cubic lattice is then compared to the one-dimensional model. In the case of the tetrakaidecahedronal model, a similar three-dimensional finite element calculation is performed to find the effective thermal conductivity. Anisotropy of the models is explored. The results of the models are compared with experimental results from this study and the literature to substantiate their accuracy. The experimental results are reported for fully saturated aluminum metal foam in air, water, and oil. Results show that both the cubic lattice model, which is less complex, and the tetrakaidecahedronal model can both be used to represent one-dimensional effective thermal conductivity. Finally, the dimensionless surface areas for each geometric model are compared. The models produce significantly different surface areas, and therefore do not both represent the density and specific surface area of foam accurately.

Thermal Conductivity Prediction Model for Composite Thermal Interface Materials Using Copper Metal Foam

2021 ◽  
Author(s):  
Shinya Kawakita ◽  
Yuki Ishizaka ◽  
Kazuyoshi Fushinobu
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Metal Foam ◽  
Three Dimensional ◽  
Calculation Model ◽  
Silicone Resin ◽  
Thermal Interface Materials ◽  
Copper Foam ◽  
Steady State Method ◽  
Thermal Conductivity Calculation

Abstract In the previous research, we prototyped the TIC in which a conventional TIM composed of silicone resin and filler was filled in pores of copper foam, and measured its thermal conductivity by a steady-state method. In addition, the effective thermal conductivity of TIC was predicted by Bhattacharya’s equation and Boomsma’s equation. As a result, it was reported that the experimental value and the predicted value match within 0.7 W/(m·K) by modifying the thermal conductivity of copper to 120 W/(m·K) in the Boomsma’s equation. The issue of that was to investigate the cause of the decrease in thermal conductivity of copper to 120 W/(m·K). In this paper, the effective thermal conductivity of TIC was predicted using the WP structure instead of the Kelvin structure, which is the basis of the Bhattacharya’s equation and Boomsma’s equation. As the result, it was clarified that the effective thermal conductivity predicted by the three-dimensional thermal conductivity calculation model based on the WP structure is more accurate than that predicted by the Kelvin model. And it was found that the experimental value and the predicted value match in the range of 0.4 W/(m·K) by considering the TIC surface structure without modifying the thermal conductivity of copper.

scholarly journals A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
X. Bai ◽  
C. Hasan ◽  
M. Mobedi ◽  
A. Nakayama
Keyword(s):  
Thermal Conductivity ◽  
General Expression ◽  
Metal Foam ◽  
Solid Angle ◽  
Periodic Structures ◽  
Three Dimensional ◽  
High Thermal Conductivity ◽  
Numerical Calculations ◽  
The One ◽  
Good Agreement

A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures.

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