I want to dissipate 3 kW of heat with an air conditioner. How big of an air conditioner do I need?

You probably don't need any airconditioner. if the temperature outside remains a constant $20-25[^oC]$ then the heat transfer through the walls should cool the room down under $60[^oC]$.

The only reason that might not be if you leave in a country with significant sunshine, and instead of having a good insulation at the roof you have something that heats up.

Instead of an airconditioner, (if you are not concerned about being at 40C, or humidity) I would just suggest that you do a half decent heat instulation at the root and leave it at that.

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If you insist on the airconditioner, you need to provide information about the wall heat conductivity coefficients and thicknesses.

Just go give you a very rough indication. Assuming that:

• all walls are exposed to $25^oC$,
• the thickness of the wall is 10 [cm]
• the wall is made out of fire brick (which does not propagate heat that much) with $k = 0.5 [J/mK]$

Then the overall temperature losses from all the side walls and the roof for a uniform temperature of 55[C] will be about 8.4kW.

For the 3[kW], you should expect a (uniform ) temperature difference of about $10 [K]$, i.e. the room temperature will be about $35[^oC]$.

IMHO, you could optionally (even that I think is an overkill):

• add louvres (top and bottom of the side walls) (As kamran suggested)
• add a fan inside the room pointed at the heat source (that will cool better and distribute the temperature in the room)

One simple and effective way is to install an intake window with adjustable louvers near the lower part of your heat sink and a hood (can be possibly a primitive cardboard one) on top leading to the window/ vent on top.

This way you create a self-sustaining circulation system that takes advantage of the rising tendency of the hot air coming off the heat sinks.

Air conditioning systems are a type of heat pump. Heat pumps are used to remove heat from a system at one temperature and transfer it to a system at a higher temperature. The heat pump lifts the energy from the lower temperature to the higher.

In your case the outside ambient temperature appears to be always much lower than the required operating temperature so there is no need for a heat pump (or air conditioning). You should be able to achieve adequate cooling by air circulation.

As a rough guide to the required airflow we can do a quick calculation. The specific heat capacity of air is approximately 1 kJ.kg^-1.K^-1. If you want to limit your air temperature rise to 10°C then we can calculate as follows:

$$ t = frac {Delta T cdot m cdot SHC} P $$ where $ t $ is the time, $ Delta T $ is the temperature change, $ m $ is the mass of air, $ SHC $ is the specific heat capacity and $ P $ is the power. Rearranging we get $$ frac m t = frac P {Delta T times SHC} $$ and for 3 kW of cooling with 10°C air temperature rise we get $$ frac m t = frac 3 {10 times 1} = 0.3 mathrm {kg/s} $$

Air has a density of 1.225 kg/m³ at sea level so your required airflow is $ frac {0.3 } {1.225} = 0.25 mathrm {m^3/s} $.

Bear in mind that even if you use air conditioning that you'll still have the problem of moving the air around the room to ensure elimination of local hotspots.

This simple fan solution should be much simpler, lower cost and environmentally friendly than an air conditioning system.