One of my experiments has a water-cooled apparatus. I plan on building a heat exchanger to keep the apparatus cool. However, I am not very good at thermodynamics and could use a hand. Also, from a didactic perspective, this gives me an excellent opportunity to learn more about heat exchangers.
From what I remember / could learn via Google and other posts (cough thank you Alan Rominger):
(Qdot) = (UA)*(ΔTm)
UA = (heat transfer coefficient of system) * (area)
ΔTm = (log mean temperature difference)
(UA) = (2*Pi*n)/((1/(h1*ri))+(1/(R*L))+ln(ro/ri)+(1/(h2/ro)))
n = number of pipes
h1 = convective heat transfer coefficient of fluid 1
h2 = convective heat transfer coefficient of fluid 2
ro = outer radius of pipe
ri = inner radius of pipe
R = heat transfer coefficient of pipe material
L = length of pipe
ΔTm = (ΔT1-ΔT2)/ln(ΔT1/ΔT2)
n (number of pipes)
ro (outer radius of pipe)
ri (inner radius of pipe)
R (heat transfer coefficient of pipe material)
T1in (temperature of fluid 1 entering exchanger)
T2in (temperature of fluid 2 entering exchanger)
Qdot (the energy I need to pull out of the system with the exchanger)
- T1out (temperature of fluid 1 leaving heat exchanger)
- T2out (temperature of fluid 2 leaving heat exchanger)
- L (length of pipe, I'm trying to calculate this)
- h1 (convective heat transfer coefficient of fluid 1)
- h2 (convective heat transfer coefficient of fluid 2)
Other information (that may or may not be helpful):
- Are h1 and h2 material properties of the respective fluids?
- Heat exchanger type: counterflow
- Also known is the volumetric flow rate of both fluids
Calculate L (length of the pipe needed to achieve Qdot given input conditions)
- Are the equations I have going down the right track?
- What other equations or assumptions do I need to calculate L?
- I have not yet used the fact that this is a counterflow exchanger, will this change any of my equations?