Heat Flow Rate through Thin Metallic Plates: Air vs. Vacuum

[salsero]

Two parallel thin metallic plates with a gap between them are used as a heat insulator. How does the heat flow rate through this device depend on the temperatures on its two sides in the following two cases?

Case 1: The gap is filled with air.
Case 2: There is a vacuum in the gap.

 

[Integral]

Energy transfer will be by blackbody radiation.

E= σ(ΔT)⁴

σ=5.67e-8 (Wm^-2C^-4)
(ΔT)= Temperature difference between the plates.

Air or vacuum will have little effect as long as the gap is small. If the gap is large enough to allow air convection then all bets are off. It is a very different and difficult problem.

 

[salsero]

1. Should it be (dT)^4 or d(T^4)?
2. What would be the answer if the gap were filled with wood?

 

[Integral]

That is

(ΔT)= Temperature difference between the plates.

The energy transfer is proportional to the fourth power of the temperature difference


If the gap were wood heat transfer would be by conduction.

E= kAΔT/L

k = Thermal conductivity of Wood (will depend upon the type of wood)
A = Area
L= Length

 

[Integral]

That should be

E = σΔ(T⁴)

Sorry I missed that the first time!