# FEA-Based Numerical Simulation and Theoretical Modeling for Predicting Thermal Contact Conductance

Sachin Rana (ABES Institute of Technology Ghaziabad, India)
DOI: 10.4018/978-1-5225-3722-9.ch007

## Abstract

The chapter states the problem of thermal contact conductance between surfaces. Rough surface generation and thermal contact conductance has been simulated using Finite Element Method (FEM) based Ansys. The resulting geometry is meshed by different meshing method to convert the solid model into FEM model. The main aim of meshing is to create fine and coarse mesh at the contact to reduce the computational time. To create a fine mesh at contact free meshing with refinement and mapped mesh has been used. The analysis has been performed on the FEM model with varying loading condition of different surface roughness and different materials to get the real contact area and thus thermal contact conductance. The variation of thermal contact conductance and real contact area with pressure of different surface roughness and with surface roughness of different loading condition of the specimen made of aluminum and mild steel has been plotted and compared.
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## Introduction

All engineering surfaces exhibit some level of microscopic roughness. The resistance to heat flow through a contact interface occurs because only a small portion (usually 1-2%) of the nominal surface area is actually in contact. Heat may pass through the interface via three paths: conduction through the contact spots, conduction through the gas present in the gap between the surfaces, and radiation across the gap. Convection may be neglected due to the small length scales involved. Also, radiation does not play a significant role at temperatures below 500°C.

Since the conductivity of the gas is much smaller than that of the substrate, most of the heat is constrained to flow through the contact spots. This constriction and subsequent spreading of heat flow lines in the two materials in contact manifests as a thermal resistance at the interface. The total resistance of the surface is found by summing, in parallel, the constriction resistances of all of the contact spots. This thermal resistance impedes the heat flow across the interface, when two solid bodies at different temperatures are brought into mechanical contact, and results in a temperature drop as shown in Fig. This resistance, commonly known as thermal contact resistance, is well-explained by the fact that the real contact area is exceedingly small as compared to the apparent contact area due to the presence of roughness and waviness of the engaging surfaces. As the interstitial material, such as air, is a poor heat conductor and the radiative heat transfer is often insignificant, a large portion of the heat flow converges to the discrete solid-solid contact spots as illustrated in Figure 1. Hence, the increase in the heat-flow path length causes the thermal contact resistance. Its reciprocal is called thermal contact conductance, defined as:

(1) where q is the heat flow rate, A is the apparent contact area, and △T is the temperature drop at the interface.

Figure 1.

Illustration of thermal contact conductance

Thermal contact conductance plays an important role in all thermal systems where a mechanical contact is involved. Recently, such conductance has received special interest and attention in small-scale heat removal systems such as microelectronics and in heat transfer between superconductor films. More recent attempts at predicting thermal contact conductance at an interface, especially focusing on the low contact pressures allowable in electronics cooling, have taken advantage of the speed and processing power of modern computers to track the number of asperities in contact at a surface by directly using surface profile data. Inputs to the model include the surface profiles, mechanical and thermal material properties, nominal contact area, and specified loads. The mode of deformation of each asperity is not assumed, but determined by guessing the mean plane separation between the surfaces, calculating the pressure and area of each microscopic asperity in contact, and summing the contribution to the total load from each asperity.

Surface roughness is a measure of the microscopic irregularity, whereas the macroscopic errors of form include flatness deviations, waviness and, for cylindrical surfaces, out of roundness. Two solid surfaces apparently in contact touch each other only at a few individual spots as shown in Figure 1. Even at relatively high contact pressure of the order of 10 Mpa, the real area of contact for most metallic surfaces is only about 1 to 2% of the nominal contact area Leung (1998).

Thermal contact conductance is an important factor in a variety of applications, largely because many physical systems contain a mechanical combination of two materials. Some of the fields where contact conductance has importance are Electronic packaging Luo (2010) Microelectronics Yovanovich (1984), Biomedicine Singhal (2005), Nuclear reactor Mochizuki (1994), advanced materials, space applications Peterson (1990), I.C. Engine Marotta (1999), Heat exchanger Jeng (2006) Metal-Forming Rosochowska (2003) and Super Conductor Mantelli (1980) etc.

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