I know this is a complicated question, and depends on a lot of factors. So, I will do my best in explaining the situations. I am trying to regulate the temperature of a pool of circulating water. I have 8' of stainless 304, 1" OD, 14 awg, pipe, positioned against the flow of water (to provide as much thermal transfer as possible in this pool). The average maintained temperature of the pool is 70F. Hot water is heated in a boiler system to a temperature of 170F. This heated water will be pumped at a rate of 15 gallons per minute, through the 1" stainless steel heat exchanging pipe, mentioned above (8' length). In this water to water heat exchanging application, can someone tell me how many Btu's I will get? If I left an important factor out of the equation, please let me know. Thanks :)
Welcome to PF! You're right that this is a bit of a complicated problem. You said you have the pipe position so pool water is flowing against it. Do you know how fast? Otherwise it would just be natural convection carrying the heat away. Do you have the ability to put radiator-type fins on the outside of the pipe? 15gpm is pretty fast and capable of transferring a lot of heat, but what's going on on the outside of the pipe would be your limiting factor. If you can get effective heat transfer you might be able to pull 75,000 BTU out of it, but I'm guessing with what you have it'll be around a tenth of that. There is an easy equation with a dirty assumption for convective heat transfer coefficient here: http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html Basically, you take the surface area of the pipe times the delta-T times the coefficient to get heat transfer rate. If you need help with it after playing with it a bit, let me know.
Russ, thanks for the info. To clarify, I am not needing to better my btu transfer. I already have the stainless steel pipe in place and am satisfied with the amount of heat transfer, for the application. I just need to try to figure out what kind btu's are being transferred. Yes, hot water goes in to the pipe, and slightly less hot water comes out of the pipe. So, I know there is not much heat transfer happening. I have found one piece of the puzzle. The thermal conductivity of 304 stainless steel is around 14 W/m-K (at 293 K...whatever that means). And, natural convection would be fine to assume. From there, I am still not savvy to put the rest of the puzzle together, even with the link to the "easy equation". I wish I was better with formulas. If you could help, even with a dirty assumption, I would be grateful. Thanks, Jim