Analyzing the thermodynamics of a hot tub

[olafurjt13]

Hi everyone,

I'm working on a project at my university and I'm having trouble figuring out how much heat escapes a hot tub when it's at 42°C and outside temperature is at around 7°C (I live in Iceland).
I'm considering the hot tub closed with a styrofoam cover about 10cm thick and walls of the same material.
Any advice on how to calculate the heat transfer from the tub?
The size of the tub is 2,35 x 2,35 x 0,98 m

 

[mfb]

If the styrofoam cover would be perfect, with the regular heat conduction equation. You might need some approximations for the edges and corners (like "just ignore them") if you want to avoid numerical simulations.
In reality, you also have to consider losses between the cover and the wall. This could be a significant part of the total loss.

 

[russ_watters]

So start by looking-up the insulation value for styrofoam and making sure you understand how to use it.