Radiative Shield Temperature

M.M. Yovanovich

RADSHIELD2.MWS

Temperature of a radiative shield placed between two large gray, isothermal surfaces.

The system consists of two large surfaces separated by a single radiation shield.

The temperatures of the isothemal gray surfaces are denoted with , their

radiative properties are denoted and and their surface areas are denoted .

The radiation shield is assumed to be very thin and its thermal conductivity is

high. Therefore the temperature drop across the shield is negligible and it's temperature is where

and . Assume that all surface areas are equal.

> restart:

Surface temperatures.

> temps:= (T1=350, T2=290);

System parameter values.

> syspar:= (sigma=5.67e-8, epsilon1=0.8, epsilon2=0.9, epsilon31=0.1, epsilon32=0.1,
F13=1, F32=1, A1=A, A2=A, A3=A, A=1);

Realtion between radiative exchange between surfaces and the shield.

> heatbalance:= Q13-Q32=0;

> Q13:= (Eb1-Eb3)/Rtotal13;

> Q32:= (Eb3-Eb2)/Rtotal32;

Obtain relation for .

> Eb3:= solve(heatbalance, Eb3);

> Eb1:= sigma*T1^4; Eb2:= sigma*T2^4;

Since , we can solve for . We require the positive real root.

> T3:= (simplify(Eb3/sigma))^(1/4);

>

> Rtotal13:= Rs1+R13+Rs31;

> Rtotal32:= Rs32+R32+Rs2;

Radiative resistances: surface and spatial.

> resists:= (Rs1= (1-epsilon1)/(A1*epsilon1), Rs2= (1-epsilon2)/(A2*epsilon2), Rs31= (1-epsilon31)/(A3*epsilon31), Rs32= (1-epsilon32)/(A3*epsilon32), R13= 1/(A1*F13), R32= 1/(A3*F32));

Calculation of the shield temperature.

> T3:= evalf(subs(resists, syspar, temps, T3),5);

> temps;

>