0
Research Papers: Conduction

# Fractal Model for Thermal Contact Conductance

[+] Author and Article Information
Mingqing Zou, Jianchao Cai, Peng Xu

Department of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074 Hubei, P.R.C.

Boming Yu1

Department of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074 Hubei, P.R.C.yuboming2003@yahoo.com.cn

1

Corresponding author.

J. Heat Transfer 130(10), 101301 (Aug 08, 2008) (9 pages) doi:10.1115/1.2953304 History: Received August 12, 2007; Revised March 05, 2008; Published August 08, 2008

## Abstract

A random number model based on fractal geometry theory is developed to calculate the thermal contact conductance (TCC) of two rough surfaces in contact. This study is carried out by geometrical and mechanical investigations. The present study reveals that the fractal parameters $D$ and $G$ have important effects on TCC. The predictions by the proposed model are compared with existing experimental data, and good agreement is observed by fitting parameters $D$ and $G$. The results show that the effect of the bulk resistance on TCC, which is often neglected in existing models, should not be neglected for the relatively larger $G$ and $D$. The main advantage of this model is the randomization of roughness distributions on rough surfaces. The present results also show a better agreement with the practical situation than the results of other models. The proposed technique may have the potential in prediction of other phenomena such as friction, radiation, wear and lubrication on rough surfaces.

<>

## Figures

Figure 1

Constriction of heat flow lines through contacting spots

Figure 6

The asperity diameters simulated by the present method at lmin=1nm

Figure 7

(a) A typical three-dimensional surface as D=1.44, G=9.46×10−13m, and lmin=0.1nm, and (b) the cutaway view of (a)

Figure 8

Dimensionless conductance across the contacting solid spots versus dimensionless pressure

Figure 9

Variation of dimensionless conductance with dimensionless pressure at various values of G when D=1.6

Figure 10

The separation d versus dimensionless pressure at different values of G (as D=1.6)

Figure 11

Effect of G on contact resistance (D=1.6): (a) G=1×10−13m, (b) G=1×10−11m, and (c) G=1×10−9m

Figure 2

Contact between a rough surface and a flat producing isolated contact spots

Figure 3

The thermal resistance network of two contacting rough surfaces

Figure 4

Geometry model in this work: (a) model for stacked asperities, (b) geometry of an asperity with deformation, and (c) schematic for the determination of m1

Figure 5

Elemental flow channel (2)

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections