Thermal Contact Resistance
Apologies, it's my me time.
From Yungus and Cengel,
"In the analysis of heat conduction through multilayer solids, we assumed “perfect contact” at the interface of two layers, and thus no temperature drop at the interface. This would be the case when the surfaces are perfectly smooth and they produce a perfect contact at each point. In reality, however, even flat surfaces that appear smooth to the eye turn out to be rather rough when examined under a microscope, as shown in Fig. 3–14, with numerous peaks and valleys. That is, a surface is microscopically rough no matter how smooth it appears to be."
peaks...valleys... air gaps... act as insulation....
"and this resistance for a unit interface area is called the thermal contact resistance, R sub c." ...Determined experimentally...scatter of data...
A quantity of heat is given in joules (Q). Heat flow in watts is dot Q.
dot Q = dot Q sub contact + dot Q sub gap
dot Q = (h sub c)A(delta T sub interface)
"where A is the apparent interface area (which is the same as the cross-sectional area of the [thing]) and (delta T sub interface) is the effective temperature difference at the interface. "
(h sub c) is the "thermal contact conductance" is W/(m^2*K)
(R sub c) = 1/(h sub c) = (delta T sub interface)/(dot Q/A)
...That is, thermal contact resistance is the inverse of thermal contact conductance. ...
depends on...surface roughness... material properties... temperature... pressure... "type of fluid trapped at the interface"...
"Thermal contact resistance is observed to decrease with decreasing surface roughness and increasing interface pressure, as expected. "
is it significant?
" We can answer this question by comparing the magnitudes of the thermal resistances of the layers with typical values of thermal contact resistance. "
where h is usually convection (w/(m^2*k)) k is conduction (w*m/m^2*k)
consider 1cm of "insulation" [here]
R sub { c insulation} = L/k = 0.01m/0.04(w/m*k) = 0.25 m^2*k/W
and 1cm of "copper"
R sub { c copper} = L/k = 0.01m/386(w/m*k) = 0.000026 m^2*k/W
because dot Q = kA(delta T)/L a small L/k[A] means a big k[A]/L. coppers in their native uninterupted state are perfectly happy to conduct heat in whatever lattice structure copper happens to have.
gaps full of air disrupt... insulate...
"The thermal contact resistance can be minimized by applying a thermally conducting liquid called a thermal grease " ...commonly... electronic..." can also be reduced by replacing the air at the interface by a better conducting gas such as helium or hydrogen"
The point for this post however is the next revelation:
"Another way to minimize the contact resistance is to insert a soft metallic foil ... silver" ... "Experimental studies show that the thermal contact resistance can be reduced by a factor of up to 7 by a metallic foil at the interface. For maximum effectiveness, the foils must be very thin. The effect of metallic coatings on thermal contact conductance is shown in Fig. 3–16 for various metal surfaces. "
"There is considerable uncertainty in the contact conductance data reported in the literature"
Linus, if you're going to hacksaw a block of aluminum then do me a favor-- buy some silver leaf and coat a processor before you attach the heatsink; apply power, record the data, publish the results.
Further, is the community aware of the kinds of machine finishes that processor caps and heatsink connectors are worked to? How much would someone pay to silver leaf a processor? How much would it cost to minimize surface tolerances? What's the range of benefits we could expect to see by minimizing air gaps in surface contacts? Do thermal compounds compare to silver leaf? What about thermal compound AND silver leaf?!
Could a structurally sound chip support more pressure and more thermal contact?
ISBN 978-0-07-339818-1