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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?
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closed as off-topic by CuriousOne, Gert, user36790, John Rennie, AccidentalFourierTransform Apr 23 '16 at 10:06

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  • $\begingroup$ 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. $\endgroup$ – Duncan Harris Apr 22 '16 at 23:55
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You are going down the right path. First decide upon the temperature change you want for your key stream. This will establish the heat load. For the counter flow, then calculate the temperature change, based on the flow rate you intend to use and the heat load. This will give you your four inlet and exit temperatures. After that, the rest is easy.

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    $\begingroup$ Thanks bro. It looks like I can use Q = (m, mass flow rate)*(Cp)*(deltaT) to find T1out and T2out. It looks like I can pull h1 and h2 from tables (turns out it is just a material property of the fluid). So that leaves me with four equations and four unknowns - that's where I like to be. I'll plug and chug and see what I end up with. $\endgroup$ – Tom Bombadil Apr 23 '16 at 20:37
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As far as I know in counter flow heat exchangers the temperature difference between hot and cold fluid remains roughly the same for any distance from either end.

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  • $\begingroup$ This is not correct. It depends on the flow rates and the heat capacities. $\endgroup$ – Chet Miller Apr 23 '16 at 12:00

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