Radiation Shield

M.M. Yovanovich

RADSHIELD1.MWS

Effect of radiation 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.

The radiative network consists of 7 radiative nodes denoted as .

The nodes are connected by 6 radiative resistances which are in series. The total radiative resistance

for one shield is .

The neat radiative exchange is given by the relation .

> 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);

Net radiative exchange with one shield.

> Q12:= (Eb1-Eb2)/Rtotal;

Stefan-Boltzmann Law of Black-Body Radiation.

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

Total radiative resistance of system.

> Rtotal:= Rs1+R13+Rs31+Rs32+R32+Rs2;

> 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);

Net radiative heat exchange without shield.

> Q12wo:= (Eb1-Eb2)/(Rs1+R12+Rs2); R12:= 1/(A1*F12); F12:= 1:

Calculations of net radiative exchange per unit area.

> Q12wo1:= evalf(subs(syspar, temps, Q12wo), 5);

> Q121:= evalf(subs(syspar, temps, Q12), 5);

The effect of the radiation shield is large.