The temperature distribution (Equation 9) in the paper "CONSTRICTION/SPREADING RESISTANCE
MODEL FOR ELECTRONICS PACKAGING" seems to be faulty. There appears to be a "1" between the "coth" and the "+" sign in the denominator, which doesn't make any sense. I tried to look for the original document but without any luck. Nor I could find another reference to the same equation. Does anybody have a pointer?
I believe something must have gone wrong when the original document was scanned because there are many other "typos" in the document.
http://www.aavid.com/sites/default/files/technical/papers/constriction-resistance-electronics-packaging.pdf
I have found a solution to a more generalized problem: Equation 6 in "Thermal Resistances of Circular Source on Finite Circular Cylinder with Side and End Cooling".
Anyhow, it would be nice to know what is wrong with Lee's solution.
Perhaps in the numerator the "tanh(.) + lambda/Bi" should be enclosed with parentheses, and same goes to the "1+lambda/bi * tanh(.)" in the denominator.
Not sure if I am correct.
Yes, that seems indeed the most probable case. I implemented the function and played around with the symbols and parenthesis. I couldn't obtained, however, any meaningful output... So I guess there is more wrong with the equation then just those parenthesis. Solving the partial differential equation analytically will solve the problem for sure. (on my TODO list)
On the bright side, I have implemented Yovanovich's solution (Equation 6 from "Thermal Resistances of Circular Source on Finite Circular Cylinder with Side and End Cooling") as well. This equation works like a charm! There is however an error in Table 1; for \mu=0, the epsilon in the denominator should not be there. This is a direct result from Equation 11.
As Yovanovich's solution is more general than Lee's, I am satisfied.
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