Calculating Cooling Rate for a Black Body in a Vacuum with a Radiation Screen

[brainslush]

Homework Statement

A spherical black body with a radius r and a temperature T is placed in a spherical thin shell (radiation screen) with a radius R. The shell is also absolutely black on both sides. The space between the shell and the sphere and the space outer of the shell contain vacuum, i.e., no gas.
Find the cooling rate

Homework Equations

R = dQ / dT = h*A*dT

The Attempt at a Solution

The black body radiates heat with
h - some heat transfer constant
A - area of the radiating body

\frac{dQ}{dT}_{bb} = h_{vacuum} * 4 \Pi *r^{2} (T_{sphere} - T_{vacuum})

the same works for the radiation screen

\frac{dQ}{dT}_{rs} = h_{gas} * 4 \Pi *R^{2} (T_{vacuum} - T_{environment})

The point is that I'm not sure how to find the overall cooling rate of the system. Thanks.

 

[edgepflow]

In a vacuum, there will be no conduction or convection heat transfer (your equations are for convection). The only heat transfer mode will be black body radiation which is proportional to T^4.

 

[brainslush]

Upps, I mixed up radiation, conductivity...

So

dQ/dt = e*\sigma*4\Pi*r^{2}(T^{4}_{sphere}-T^{4}_{vacuum})

but what about the radiation screen? It is a thin shell. Can I neglect it?