How can I calculate the necessary heating power for a 3D printer chamber?

[pingu_user]

Homework Statement: heating air in a chamber
Homework Equations: heating equations

Hi to everyone,
I want build a chamber for my 3d printer, the structure is a cube of 0.5m per side. Inside there will be the 3d printer that has a plate of 220mm x 220mm and 3mm thick that stays at a constant temperature of 90° celsius during the printing process, there is also the nozzle that reaches the 240°celsius but the dimension is really small. The box is made of plywood of 10mm. Now I would like to know if the plate is enough to increase the temperature of 15°Celsius, for sure I also need a controller to keep the temperature steady at 40°celsius. Now I've never studied anything that concern heat so sorry if I've formulated the problem in the wrong way.
Using the heating equation:
Q = c * m * ΔT
where
m ≈ 0.1613
c ~1.005kJ/kgK
T_room = 25° = 298.15K
T_desired = 40° = 313.15 K
Now the problem is that I don't know how relate the temperature of the plate with the Q in the formulation.
I should also consider an equilibrium between the heat provided by the plate and the heat dissipated through the box but I don't know how.
Maybe I should also consider the fact that inside the box there is no just air but also the 3d printer. I will also use a PI controller to keep the temperature as steady as possible but I would like to know if the only heating surface is sufficient, or i should insert something as hairdryer to pump heat inside the box. Sorry if the solution attempted is not thorough but I've no basis about this subject. Any help will be appreciated. Thanks to everyone

 

[Borek]

Your first problem is that you won't be able to easily determine amount of heat lost to the environment. Amount of heat required to heat the plate to the desired temperature is one thing, amount of heat per unit of time required to keep it there is a completely different thing.

In general such calculations are never trivial, as a lot depends on the thermal conductivity of the walls. Perhaps others will be able to suggest some viable approach.

 

[Dullard]

You picked a fairly complicated situation for your first foray into thermal problems.

Big (simple) picture:
The plywood box has a thermal resistance of (approximately) 0.1 C/W / m2. The units imply how to use the value - for a given temperature difference and surface area you can calculate the rate of energy xfer. If you know the room-temp power consumption of your printer, you can see if you're in the ballpark (printer power will be a bit lower 'in the box'). for your box (ignoring the table) and a 15C delta, I'd estimate about 180W.The power actually used to maintain the baseplate and nozzle will vary, and (absent stirring) the air temp will not be uniform. I would proceed as follows:

design the enclosure so that 50% of the temperature increase is theoretically produced by the heat from the printer (plywood thickness, dimensions...).
Add a 200W PI Heater (3x 60W incandescent bulbs would work) with (very low) continuous air flow (significant air flow will disturb baseplate/nozzle regulation and plastic cooling rate).