# Equations describing a counterflow heat exchanger [closed]

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):

## Eq1

(Qdot) = (UA)*(ΔTm)

where:

• UA = (heat transfer coefficient of system) * (area)

• ΔTm = (log mean temperature difference)

## Eq2

(UA) = (2*Pi*n)/((1/(h1*ri))+(1/(R*L))+ln(ro/ri)+(1/(h2/ro)))

where:

• 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

## Eq3

ΔTm = (ΔT1-ΔT2)/ln(ΔT1/ΔT2)

## Knowns:

• 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)

## Unknowns:

• 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

## Goal:

Calculate L (length of the pipe needed to achieve Qdot given input conditions)

## Questions:

• 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?

## closed as off-topic by CuriousOne, Gert, user36790, John Rennie, AccidentalFourierTransformApr 23 '16 at 10:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question appears to be about engineering, which is the application of scientific knowledge to construct a solution to solve a specific problem. As such, it is off topic for this site, which deals with the science, whether theoretical or experimental, of how the natural world works. For more information, see this meta post." – CuriousOne, Community, John Rennie
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• This is a pretty broad question. You are basically asking someone to write a textbook chapter on heat exchanger design. Perhaps someone will, but in the meantime you could probably get some simple, practical advice for your experimental setup by describing your experiment and its heat exchanger needs. – Duncan Harris Apr 22 '16 at 23:55