I have a box outside that I want to insulate such that the temperature inside the box doesn't drop below 10°C given outside temperatures of (in the most extreme case - at night) -10°C. Inside the box I have a "heater" of 5 W. The box is in direct sunlight during the day (only if the sun shines, though).
I want to simulate the temperature in the box in order to help me decide on isolation material / thickness. I'm unsure which factors I need to account for. So far I have:
- heat loss due to heat transfer through box walls
- heat "gain" due to the 5 W "heater".
- heat "gain" due to the sun shining on the box at day.
- heat capacity due to the box (isolation material as well as air volume)
Are there other things to consider? Any thing which I'm modelling too simple?
Heat loss due to heat transfer through box walls:
lambda = (Q * l) / (A * deltaT) thus => Q = A * lambda * deltaT * (1/l) where Q = heat transfer lambda = thermal conductivity of material deltaT = temperature difference l = thickness of isolating material A = surface area of box
Heat capacity of box:
Once for the air and once for the isolation material.
E = c_v * V * T where E = "heat energy" in box c_v = (volume) specific heat capacity V = volume T = temperature (in K)
Heat gain due to the sun:
The most tricky I guess. Assuming (https://en.wikipedia.org/wiki/Sunlight) I probably get about
120 W / m^2 due to sunlight and just (for simplicity) the top side of the box (
A_top) I guess I still need a "efficiency" factor? This is on the outside, though, so I guess the maximal heat transfer to the box (heating) is limited by the isolating material?
I'd start with the box (air and isolation material) being at outside temperature. Then adding all heat gains (heater and due to sunlight during day) and (using the now higher temperature in the box and thus a temperature difference) subtract the heat lost due to heat transfer through the walls. And all that for each second.
1. E' = E_n + (P_heater + P_sun) * 1s 2. use E' to calculate T_box and thus delta_T 3. use delta_T to calculate Q 4. E_(n+1) = E' - Q