Trying to come up with a MATLAB code for calculation of heat transfer due to incident radiation on a building's walls, would the solution involve using the conduction equation only? What would be the boundary conditions used here?

  • $\begingroup$ Covered in Heat Transfer by Simonson amongst others. $\endgroup$ – Solar Mike Feb 3 '20 at 9:08
  • $\begingroup$ Why are you looking to use MATLAB here? Are you taking a time-step approach to account for how the temperature inside the building affects the transfer rate due to the change in $\Delta T$? I think I'd be more likely to use Excel, even so... $\endgroup$ – Jonathan R Swift Feb 3 '20 at 13:06
  • $\begingroup$ Well, because the solution involved PDEs, and I'd probably be overcomplicating things if I'd be doing it via excel. That said, I need values of Q at 1 hr intervals throughout the day. $\endgroup$ – afterburner77 Feb 3 '20 at 16:19
  • $\begingroup$ You're overcomplicating it if you're using PDE's, in my opinion. Take averaged historical data for your environment and model the energy iteratively as a constant flow in one second time steps. The error from this approximation with be orders of magnitude smaller than errors from unknown inputs such as heat transfer coefficients, wind speeds etc. $\endgroup$ – Jonathan R Swift Feb 3 '20 at 20:02
  • $\begingroup$ Not-withstanding that a good answer has been provided to lay the groundwork, I am downvoting this question. It provides only nebulous information about the problem (where is a picture and statements of the known system conditions), has no sense that some work has been done to solve it, and is all over the place in terms of explaining where help is needed. $\endgroup$ – Jeffrey J Weimer Feb 4 '20 at 14:18

How complex this is depends on your needs. Once you know the solar flux, you need to calculate how much of that energy is absorbed by the wall (a function of the surface - how much is reflected? This itself may be a function of the angle of incidence, which will vary through the day...). This will heat up the outside of the wall, and it will start to conduct through to the building... But... There will be heat lost from the external surface of the wall, which reduces the total energy that makes it to the inside of the building. This will be lost as Convection and Radiation. Convection depends on the surface and the wind, Radiation depends on the temperature difference between the wall and the black-body temperature of the sky. Both of these values will vary on a minute-to-minute basis throughout the day... And all of this is before you even think about the variable convection on the inside of the building, and how the temperature difference with the air there will also vary etc...

So, if you want to calculate a single point in time, then sure - it's not so bad. Just do an energy balance. But if you want to model how the building behaves over the course of a day? things get a bit more tricky.

  • $\begingroup$ 😅 good spot. I blame autocorrect/dictation? $\endgroup$ – Jonathan R Swift Feb 3 '20 at 18:54
  • $\begingroup$ I’ll agree - gets me often as well. Plus 1 as a good answer anyway. $\endgroup$ – Solar Mike Feb 3 '20 at 18:56

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