Oil cooler math
Transmission cooler math:
We need to adjust our assumptions when dealing with the transmission (versus the engine oil) because many of the parameters are different; the density of ATF fluid is 52.66 lbs/cu.ft, the oil flow rate is closer to 4 gpm and the gearbox operating temperature is closer to 240degF.
Using the previous formulae, we get oil mass flow rate (W) = 4 x 231 x 1/1728 x 52.66 =28.19 lb/min.
Solving the heat transfer equation, we have:
Q = 0.5205 x 28.19 x (240-185) = 807 BTU/min
assuming the specific heat capacity of ATF fluid is comparable to motor oil (which it is) and the inlet and outlet temps are 240 and 185 deg F respectively.
Using an ITD ref of 100degF, the heat loss Q/ITD = 807 x 100/(240-80) = 504.375 BTU/min @ 100 degF.
This equates to 30,262 BTU/hr. This suggests that the trans oil cooler is correctly sized for the heat load at 31,000 BTU/hr.