How Long Should My Double Pipe Heat Exchanger Be for a 22kW Capacity?

[thestudent101]

I'm trying to design a double pipe heat exchanger for two different water lines. One line is chilled water of approximately 7degC and the other is chilled water return from an air handling unit, of around 12degC. I want to design this heat exchange for a capacity of approximately 22kW. The part I'm having trouble with is the heat transfer coefficients of the water. I'm planning to have a counter-current flow, with the 12degC on the inside copper pipe, with the chilled water running the opposite direction surrounding the other copper pipe. I've assumed there is sufficient insulation around the outside of the system so the overall system is adiabatic. I've tried a few different methods of finding the heat transfer coefficients. One way is simply looking them up, and another calculating them from the Reynold's number and Nusselt number. Both have given me very different answers. My objective is to calculate how long this heat exchanger needs to be for it to have an overall capacity of 22kW. The flow rate can be up to 8L/s and the pipe sizes have no real constraints.

Here's some pictures of what I've calculated and assumed
https://ibb.co/mxz0T5
https://ibb.co/f1GQvk

When looking up the heat transfer coefficients, on the engineering toolbox it listed the coefficients for water-copper-water as 340-455W/m^2K http://www.engineeringtoolbox.com/overall-heat-transfer-coefficients-d_284.html

From my calculations though I've found the coefficients to be 1189 and 823W/m^2K, which changes the length required from 104m to 41m with the calculated coefficients. The engineering toolbox coefficients assume a "practically still fluid", but my velocities are only 0.33m/s and 0.11m/s. This just seems like a very big difference in length required for such low velocities, so just wondering if I went wrong somewhere in my calculations.

One other question, when calculating h1 & h2, I've used the thermal conductivity of water rather than the copper pipe. Is this correct?

 

[thestudent101]

Also if I wanted to increase the capacity of the heat exchanger, is there anything wrong with assuming the LMTD can be far smaller. If I have the air handling unit return water at 12degC and the chill water inlet at 7degC, is it practically possible to have the 12degC cooled to 7.5degC, and the 7degC chill water heated to 11.5degC?

 

[Chestermiller]

I looked over your calculations, and they looked OK. I got a little lower values for the liquid side Nussult numbers, but not drastically lower. I got about 165 for the tube side using the Seider Tate equation. See what you get.

Using the thermal conductivity of water was the correct thing to do.