I've been racking my head around calculating the amount of heat loss still water will experience through a run of insulated piping. The water in the tank is maintained at roughly 550°F saturated, and a standpipe measures the water level some distance away. However, most of the example problems and literature I can find assume some movement of water through the piping, and here, we know the water will be still. I'm assuming this needs to be setup in a way that we can equate the Qin to be equal to Qout, with Qout being losses due to radiation and convection, and we should be able to find the temperature at the end of the pipe if we know all of the other parammeters, but I'm not sure how to setup my Qin. Any ideas? Thank you in advance.enter image description here

  • $\begingroup$ I don't think there is any somple way to do this; it's well beyond undergrad heat transfer. I think what you will find is that steam will condense in the leg and create a cold convection loop down and back to the tank. You will need actual measurements to get it right. I would start at zero flow, and once you have an idea of the flux rate figure out what that would do in terms of steam condensation and use that for flow rate. $\endgroup$ – Tiger Guy Feb 25 '20 at 20:31

Have a look at heatsink calculations used in power electronics. The thermal loss calculation is quite analogous to an electrical circuit. This will all be much simpler in SI units rather than your quaint °F but I've left the numbers there for now.

  • Voltage ⇆ Temperature above ambient (°C or K)
  • Current ⇆ Heat flow (W)
  • Resistance ⇆ Thermal resistance (°C/W or KW-1)
  • Ground ⇆ Ambient temperature (°C or K)

enter image description here

Figure 1. A thermal model built using CircuitLab1.

With the values I've chosen the simulator shows that the junction of pipe X and Y should be at 358°F and a heat throughput of almost 6 W.

I suggest that you make up a resistor model as complicated as you require, measure the temperatures at each junction and calculate the heatloss on some section that you know the ratings for and play with the resistor numbers until the model agrees with your readings. Ultimately you're interested in the current through Rx.

1 CircuitLab is not free but if you head over to SE's Electrical Engineering you can play with it for free. There's a button on the question editor toolbar.


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