# What causes the temperature to drop at the interface when two slabs are brought in contact?

Consider two slabs made up of different materials which are brought in contact with each other as shown. Thermal energy is supplied from the left, and it flows through the two slabs towards right.

The surfaces are rough and there are asperities. As a result of this, there will be some points of contact between the two slabs at the interface and the voids will be filled by, say, air.

The sources that I'm referring to say that at the steady state, because of surface roughness there will be a temperature drop at the interface and we can associate a resistance to this temperature drop called the contact resistance.

What is the reason that there is a temperature drop at the interface because of the presence of asperities?

Also, why there is not temperature drop when there is an ideal contact between the surfaces (perfect contact with no roughness)?

• What sources are these? Please specify and preferrably link. Nov 13, 2021 at 13:31
• hyominsite.files.wordpress.com/2015/03/… Section - 3.1.4 - Contact resistance Nov 13, 2021 at 14:00
• draw the thermal circuit. Two paths in parallel - one thru the solid contact, very low area. Other path thru voids, much larger area. Despite very low conductivity etc of air, the big area of that thermal path makes it significant in the overall equivalent $R_{th}$ Nov 13, 2021 at 15:10

You're interpreting things that aren't there. I did not see anywhere in the source materials where it says the temperature at the interface is lower because of air gaps. The temperature is going to be lower at the interface with or without air gaps if the "interfacial fluid" in the gaps is a lower thermal conductivity than the two materials.

The source material is characterizing the behaviour of the temperature of drop across the interface due to air gaps. It is not saying that the drop across the interface is because of the air gaps.

In a perfect interface, the temperature at the interface of both materials is the same (since they are the same location). But there is still a temperature drop as you track through the bulk material from the hot-side to the cold-side. In a imperfect interface with airgaps, the interface of both materials is different so there is just a third section where the temperature drops with different behaviour, but it still drops.

The reason the temperature drop behaviour changes at a rough interface as you track from hot-side to cold-side is because the interfacial fluid filling the gaps has a different thermal conductivity and also because the contact area between adjacent matter at the interface is different than that in the bulk material (which I guess you can assume is perfect except for voids and bubbles).

(But now it makes me wonder what would determine the thermal resistance in a situtation with perfect contact between two materials...it could only be a result of the thermal resistance of the two materials themselves...an average?)

• The temperature Of both the slabs (say A and B) is the same at the interface when there is perfect contact (no roughness). However, when there is roughness, the temperature of slab A and B at the interface will be different (this is the temp drop I'm referring to). The book has assumed, same temperatur at the interface for both slabs before section 3.1.4 but then introduces that temperatures will not be the same when surfaces are rough. Nov 13, 2021 at 17:12
• @HarshitRajput Ah, yes. I see what you mean. You are distinguishing the interface between both materials. Material A has its own interface and Material B has its own interface both of which may not necessarily be the same. Still, even with a perfect interface there is a temperature gradient across the bulk of the material itself as it approaches the interface. The only thing perfect and imperfect contact changes is how the temperature drops as you track it from the hot side to cold side, but it still drops. Nov 13, 2021 at 17:19
• Yes I agree with that. I was actually looking for an answer which can explain why temperature drop happens. Because the explanation flow in most books I referred is like - There is some temperature drop because of roughness => we can associate a resistnace to this temperature drop => that resistance is contact resistance. The 'why' to the starting argument of this explanation flow (tempr drop at interface) is not explained Nov 13, 2021 at 17:26
• So you're asking for why the temperature drop behaviour changes at a rough interface? The surface area contact between adjacent matter is different at the interface between adjacent matter in the bulk material, and also the fluid filling the interface has different thermal conductivity. Is that what you're looking for? Nov 13, 2021 at 17:26
• Yes this is what I'm looking for. So is it like, if I take a layer at the interface in slab A, this layer in any given time gains more energy but gives off lesser energy because of low conductivity of air and lesser contact area, because of which this layer (in A, at interface) experinces a higher temperature rise than a layer in B at interface. Does that make sense? Or else I ll add a figure to explain. Nov 13, 2021 at 17:35