So, yes I’m sucking you all back in. The OP turned me onto this thread from my own thread about towing and my tranny temp by kindly calling me "irrational" and “incompetent.” So I did my due diligence and read all 15 pages and thought I saw the horse twitch and decided to kick it one more time.
I brought you all back to hopefully put an end to this (IMHO). Though if the last 15 pages are any indication I'm sure the OP will refute me anyway. It required my getting my old physics book out and doing some research on thermodynamics so for those of you who want “facts” this is the best I personally can come up with. This may seem ridiculous but so was most of the last 15 pages. If you aren’t interested in the details, feel free to skip to the bottom.
Lets start with the equation for heat conduction:
Q= (k·A·ΔT)t/L
Q= heat conducted
A= surface area
ΔT = change in temp
t = time
L = length of conduction (this is negligible in this case as you’ll see below)
k = thermal conductivity of a given substance
Now the OP was absolutely correct about the fact liquid conducts much better than air. As seen here.
k of air = 0.0256
k of water = 0.60 (I don’t have the k value of tranny fluid or coolant but it is likely the same)
To prove this point I will leave all other variables constant between both groups. For this first example we are also going to assume that ambient air temp is the same as engine temp (180°F) and transmission temp is 230°F. Therefore ΔT will be 50°F. And time will be 60 seconds. L will be 1 given the fact the distance heat is traveling is millimeters.
Q Air = (0.0256 · 1 · 50°F) · 60s/1 = 76.8
Q Water = (0.60 · 1 · 50°F) · 60s/1 = 1,800
As you can see if the thermal conductivity is the only variable then the OP is certainly correct and the external cooler is far inferior to the radiator. Water is essentially 23 times better at conducting heat. BUT there are a few other variables to consider.
First lets consider the ΔT, since nowhere on this planet are people driving around in 180°F heat. Conduction is highly variable based on the temperature gradient, the higher the gradient the faster heat will move. So on this next step I’ll change the ambient temp to 100°F. Now ΔT for the external cooler is 130°F.
Q Air = (0.0256 · 1 ·130°F) · 60s/1 = 199.68 which I’ll round to 200
Given this the rad cooler is still 9 times more efficient than the external cooler.
Now I’m going to factor one last variable and that’s surface area. I have no concrete data as to how large the internal tube is that the rad runs the tranny fluid through. My measuring the distance between the inlet/outlet is roughly 14” long, and for this I’ll say it’s 1” diameter which is probably an overestimate. That makes the surface area of this around 44 square inches (2 · π ·r · h). I recently purchased a Derale 13403 stacked plate cooler for my towing needs (see my thread), which is the largest they make. Based on the online specs I’ll say the plates are 10” across, 2” inches deep and there are 19 of them. Keeping in mind each plate has 2 sides the surface area 760 square inches. Now lets compare:
Q Air = (0.0256 · 760” · 130°F) · 60s/L = 151,756
Q Water = (0.60 · 44” · 50°F) · 60s/L = 79,200
Lo and behold! The external cooler wins! Now of course not everyone has the same cooler I bought, and I’ll still admit the surface areas are rough estimates.
There is also one more variable to consider but I should really go do something productive (after wasting FAR too much time reading this thread) and that’s how much faster air conducts when moving (AKA wind chill), which also vary based on ambient temp and speed but I think we can all agree that the internal rad cooler will have zero.
Class adjourned (insert smiley that drops the mic and walks away).
