# Contact Resistance Heat Transfer Explained

Heat transfer occurs in multiple ways. One of these such ways is through conduction, the heat transfer between two materials that are touching. Resistance to heat transfer within this contact is a measure of how much the flow of heat is blocked.

## How Does Contact Resistance Affect Heat Transfer?

Heat transfer occurs in three ways: conduction, convection, and radiation. Conduction is the ability to transfer heat between two bodies that are touching. Heat will travel from the warmer body to the colder one in order to reach a thermal equilibrium, and there are many material and external conditions and properties that will dictate the rate and effectiveness of said heat transfer.

Thermal contact resistance is the inverse measurement of conduction. It’s how unwilling heat is to transfer between two touching bodies, because of both material properties and improper contact and irregularities between the bodies.

What does “improper contact” mean exactly? Well, while it is nice to idealize conduction occurring smoothly between two bodies at a point of contact, the reality is not as clean. With any two surfaces touching, it is unlikely that along the perceived length of contact the two bodies are perfectly touching the whole way.

Why is this the case? It’s just that nearly every surface is not going to be perfectly smooth or straight. There will be surface imperfections and some amount of roughness the prevents perfect contact between the two bodies undergoing heat transfer through conduction.

These “gaps” in the contact add to the contact resistance of heat transfer. If the two surfaces are not truly touching in spots, then there is little or no conduction occurring there. Because air has such low thermal conductivity and little heat transfer occurs within the gaps, these gaps in the contact can be thought of as insulating the bodies with the air.

While the general principals of conduction, as well as hypothetical example problems in a learning setting, typically do not take into account contact resistance in the form of air gaps, it is very much a real world problem. Engineers designing all sorts of parts and systems need to take contact resistance into account.

## How To Calculate Contact Resistance

There are a few formulas and constant which dictate how to calculate contact resistance:

where:

• Rc = contact resistance (°K/W or °C/W)
• Ri = internal conductive resistance (K/W)
• hc = interfacial conductance (W/m2-K)
• L = length of material (m)
• A = cross sectional area (m2)
• K = thermal conductivity (W/m-K)
• Q = rate of heat transfer or heat flux (W/m2)
• ΔT = difference in temperature (°K)

The biggest variable here is interfacial thermal conductance (hc). This is like a coefficient that defines the rate of heat transfer at the contact point. It changes between various materials and their finishes, as well as the pressure of the contact and the external air. There are tables that have predefined values for common material interfaces.

To calculate heat transfer in a system of two distinct material bodies, it’s convenient to think of the transfer happening in a series. Heat moves from one end to the other internally of the first body (temperature difference and heat transfer between sides dependent on internal resistance/material conductivity), then at the point of contact where there are no gaps (this time dependent interfacial conductance), and then moving from the contact surface to the opposite side of the second body (again through internal heat transfer via conduction).

Having a lower contact resistance will obviously increase the rate of heat transfer through conduction. So will a greater temperature difference, either internally between opposing surfaces or between the two bodies at the point of contact. There are a number of other factors that can contribute to the effectiveness of conduction and amount of contact between two materials, as we will discuss below.

## What Does Contact Resistance Depend On?

Besides the factors discussed above, there are numerous others that can play an even bigger role in conduction and help to reduce contact resistance. Here are a few of the most important:

### Contact Pressure

The force at which two bodies are pushed together plays a huge role in how much contact resistance is present. In fact it plays the largest role in reducing contact resistance between touching bodies.

The logic in why this might be true follows pretty easily. If two surfaces are being forced together more, then in theory they should be touching more as gaps in points of contact are reduced. As the area of contact increases when the bodies press together, then conductance will also increase.

### Surface Finish

Polishing the surfaces of two bodies in contact will help in a similar manner to increasing the contact pressure. By smoothing out the touching surfaces, you are reducing the irregularities and bumps that create gaps in the contact.

Additionally, the construction of the material on a fractal (ie microscopic) dimension, ensuring that it is more smooth across a very small scale, and more smooth over all. This is an aspect of surface finish that can be controlled during the machining and creation process.

### Surface Cleanliness and Deformations

Another way to reduce the contact resistance is to ensure that there is minimize the amount of dust, debris, and other particles between the bodies in contact. These small particles act as obstructions that reduce contact the same way a gap caused by irregularities would.

Deformations, on the other hand, happen either over time or directly as a result from contacting forces. Plastic deformations are permanent changes to the shape of the material, which may change how much the bodies come into contact. It’s possible for these deformations to occur as the two bodies get pressed into one another.

### Ambient Pressure and Temperature

If the two materials undergoing conduction are in a controllable environment, increasing both pressure and temperature of the air in between the gaps will help to reduce contact resistance. While air still acts as an insulator, heat transfer is more effective with air that has higher temperatures or higher pressures, or both.

### Intercontact Materials

The last big way to reduce contact resistance (besides carefully choosing which materials will act as conductors) is to change the material that fills the gaps in contact. As discussed above, raising the temperature and pressure of the air in between is one way of changing the material, but there are more effective ways to do this.

There are multiple greases or other fluids with high thermal conductivites that can be applied to both surfaces before contact. This grease will fill the interstitial contact gaps, and because of its high thermal conductivity will promote heat transfer at a far greater level. The grease being technically a fluid, it is more malleable and able to actually fill the gaps and shape with the materials.

Conduction in a vacuum is actually the worst environment for conduction, as the lack of a fluid between the contact gaps will have no conduction, and therefore there is higher contact resistance.

Finally, some materials are better than others at conducting heat, and so contact resistance due to contact gaps will be less of a factor regardless of the methods use to fix it. Iron and aluminum have an extremely high conductance coefficient with each other, where as ceramic on ceramic conductance is much lower.

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