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I've been studying convection and come across empirically-derived formulas for calculating the Nusselt number for various geometries.

For my particular use case, I'd like to measure the actual convective losses inside an enclosed box with air as the fluid, for an enclosure heated from below and losing heat above.

I'm considering the following experimental design. Is it accurate? Any flaws, small or fundamental, with it?

Experimental Set-up

  • Enclosure with styrofoam walls and floor
  • On the top, an aluminum plate with an aluminum container filled with water sitting on top of it. An immersion circulator is inside the water bath.
  • On the bottom, an aluminum plate, below which runs flat nichrome wire (0.25mm thick, 5mm wide) running up and down the back of the plate
  • The inside surfaces are all lined with aluminum foil (highly reflective, low emissivity).
  • The wire is connected to a circuit with a controllable power supply where the voltage&amperage can be precisely specified and wattage measured.
  • thermocouples on the top of the bottom plate, and the bottom of the top plate.

Procedure

To calculate the sum heat losses from bottom to top given a fixed $T_{bot}$ and $T_{top}$ is:

  • Set the immersion circulator to a temperature, $T_{top} + \epsilon$, such that the top thermocouple registers $T_{top}$ consistently
  • Experimentally vary the power output of the resistance-heated circuit until the bottom thermocouple registers $T_{bot}$
  • Continue until all parameters are stable and temperatures don't change for ~30 minutes
  • The resulting heat loss is then the power output of the circuit

Results

The heat loss I believe it will actually measure is the sum of the following:

  • convective loss from bottom to top
  • any conductive loss across the sides of the chamber and the bottom of the chamber (through the styrofoam)
  • any radiative loss, which should be extremely minimal due to the foil-lined insides

Further, the outside air temp can be varied to separate out any conductive losses through the walls.

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    $\begingroup$ Have you considered modeling this? $\endgroup$ Commented Mar 5 at 13:56
  • $\begingroup$ To the close voters: This isn’t a homework question or a do my work, it’s asking about the principles and experimental design of an experiment. $\endgroup$
    – Cloudyman
    Commented Mar 5 at 17:38
  • $\begingroup$ @ChetMiller: I believe I have a good model for it (see my other question), but I want to actually measure it to test the correctness of the model. That’s the scientific method isn’t it? $\endgroup$
    – Cloudyman
    Commented Mar 5 at 17:39
  • $\begingroup$ By my calculations, with 0.03 emissivity at the temp range I’m looking at there will be essentially no radiative heat loss. I just want to see if I’ve missed anything. $\endgroup$
    – Cloudyman
    Commented Mar 5 at 17:40

1 Answer 1

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IF I understand the function of the water is to act as a heat sink and to distribute the heat evenly on the top plate. Evaporation may present a problem for a long running a heating experiment -- if so , maybe an oil that is less prone to evaporation.

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  • $\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Mar 6 at 10:12

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