# Electronic – heat dissipation in watts of equipment in a box

heatpowertemperaturethermalwatts

Here is the situation, some electrical equipment will be in low ambient temperatures and I need to make it warmer so that there is no damage to it.
I want to calculate how much power in watts is needed to heat up equipment inside a box made of aluminum.

The box is 5 inches X 5 inches X 11.5 inches (surface area is then 1.727 ft^2) it is made of aluminum and it is .1 inches thick and insulated.

from previous tests I recorded that when the ambient temperature was at -20 Celsius for a long time (at least 1hr) the surface temperature of equipment was steady at -10 Celsius and the air between the box and equipment was -11 Celsius.

Two questions:
1) How much power in watts is being dissipated by the electronics?
2) How much power in watts is needed to bring the temperature of the surface of equipment to 0 degrees Celsius? to 10 C?

I did some research and found this: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatcond.html

heat conduction formula

Q/t = kA(Thot – Tcold)/d

where k = thermal conductivity,
A = surface area,
Thot – Tcold = 10,
d = thickness,

The issue with this is that when I plug in k for aluminum = 205 or .5 by adjusting the units in the formula I get a large value for Watts either way…
am I doing this completely wrong is there another formula that would better model this problem?