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I am trying to calculate the BTU/hr of cooling needed for an RV. I am willing to assume it is an 8'x16'x8' box with no windows with uniform insulation (lets say R15 if it matters) on all surfaces. Note that the cab of the box is separate from the living area so the no window assumption is not ridiculous. The outside surface is aluminum sheet metal with shiny white paint of unknown, but typical, absorption/reflectivity/emissivity. For simplicity I am willing to assume that the RV is parked in full sun at solar noon and exposed to 1000W/m2 of sun with am ambient outdoor temperature of 100F and a desired indoor temperature of 70F.

I can calculate the sources of heat inside the RV from people, heating elements, electrical inefficiencies, etc. For ventilation/infiltration I am using $0.018V\times\Delta T\times ACH$ where V is the volume of the RV, $\Delta T$ is the temperature difference between the outside temperature and the desired inside temperature and ACH is the number of air changes per hour. For conductive heat transfer I am using $\Sigma \Delta T\times A_i/R_i$ where A is the surface area of wall i, and R is the amount of insulation on wall i. For radiant heat transfer I am using $c1000\alpha A$ where $\alpha$ is the absorption coefficient of the roof material and c deals with the pesky units.

I have a number of related questions:

  1. Are my equations correct at least as a first approximation? I am particularly worried about the radiation equation.
  2. Is $\Delta T$ the difference between the ambient temperature and the inside temperature or the temperature of the surface? The temperature of the sheet metal surface can be significantly higher than the ambient temperature if it is in the sun, but maybe this is accounted for in the radiation part.
  3. For radiant heat transfer do I need to assume an orientation and account for the tilt angle of the walls?

Note that this question is similar to Simulation of temperature in insulated box but in that question radiation can be ignored while in my question radiation seems to be the crux.

StrongBad
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  • How hot does the inside of a car get on a sunny day? Location Phoenix Arizona or Barcelona Spain... – Solar Mike Apr 13 '23 at 15:46
  • In Phoenix the inside on a 100F day the inside of a car gets to 117F (https://www.tandfonline.com/doi/full/10.1080/23328940.2018.1468205), but cars have lots of windows and little insulation. The paper models what happens to a child left in the car and I want to know what happens to the "car". – StrongBad Apr 13 '23 at 15:55

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