 In the last segment we talked about thermal resistances and we solved an example problem of conduction through a wall. There is another thing that can occur when you have two dissimilar materials that are in contact with one another. That brings up the idea of a thermal contact resistance. That's what we're going to talk about now. We will give the idea of the thermal contact resistance a quantified value of being RTC to stand for a thermal resistance and it's due to contact. This occurs when you have two different materials that are in contact with one another. If you have two different materials in contact with one another, the temperature drop across that interface can be quite significant. What I'm going to do now is draw a schematic of the two materials that are in contact with one another. We'll take a look at the exaggerated version of what the contact might look like and then what the temperature profile may be for that particular scenario. Here we have two materials, material A and material B. They are in contact with one another. What I've done is I've exaggerated the surface finish but any material is going to have surface roughness. What happens is where we have physical contact we will have conduction due to that contact. In an area like that we'll have contact and conduction. Then you'll notice there are gaps. That would be what we would call an air gap or whatever the gas might be. Other areas you're going to have a gap and the conduction is going to be different where you have a gap and consequently this will inhibit the amount of conduction that is going from one material to another when they're in contact with one another. This would then lead to an overall heat conduction that is going to occur across that gap. Sometimes what we'll do is we put in thermal grease and that's basically a high thermal conductivity grease material that goes in and it helps fill in those gaps. Sometimes electronics for cooling fins they'll put thermal grease on the fins when they put it onto the silicon chip that they're trying to cool. If we look at the temperature profile I'll plot that out now and then we'll take a look at what the temperature profile looks like. Here we have a plot showing the temperature distribution and we can go from a temperature up here in material A then we go down to a temperature in material B but the thing that is notable is the fact that we have this big jump that occurs across the gap. That discontinuity reduces the amount of conductive heat transfer that is occurring across that gap and so it's actually a bad thing that we don't want to have and the way that we quantify that gap is we use a thing called the thermal contact resistance and so the contact resistance itself is related to the pressure between the two materials. So if we were to exert pressure on the interface between the two materials so we were to push them together that would have an impact on the amount of thermal conductivity that is occurring or the amount of conduction I should say and if we also vary the gas pressure so the pressure of the gas that would have an influence upon the thermal conductivity of the gas and that would then influence the gap heat transfer so we can either by increasing pressure have an impact on the physical contact or by changing the pressure we can have an impact on the heat transfer across the gap so with those two things we can write so those two things can have an influence on the contact resistance remember we said a low resistance low thermal resistance means that it is a good conductor of heat and consequently either pressure of the joint or increasing the gas pressure will lower the resistance and increase the conduction of heat now this contact resistance is very difficult to estimate and so we typically use empirical data so it are things that are measured through experimentation and that is how we quantify it and then the contact resistance itself is going to be T2A minus T2B divided by whatever the heat flux is going to be through that system so looking back at our schematic T2A was the temperature before the gap T2B is the temperature after and then Q is the total heat transfer going across that gap so that's an equation that you can use again like I said you can put thermal grease into the contact or the gap and then put your two materials together and that will enhance heat transfer but this is just something that you should be aware of if you're ever involved with problems where you have dissimilar metals or materials in contact this is an issue that you have to be aware of