This module calculates the radiative heat flow per unit surface between two plane surfaces, considering the case when these are separated by a number of absorptive thin shields.
On account of the Stefan-Boltzmann law, the unit radiative heat flow between the two surfaces separated by shields is given by
with , the emissivity factors of the first and second surface , the emissivity factor of the -th shield , the emissivity constant of the black body and , the corresponding absolute temperatures of the two plane surfaces.
The above expression of the unit heat flow can be further simplified to the following formula
In the diagram below is shown the radiative heat transfer between two plane surfaces, separated by shields , , , .
Example 1
The example below computes the unit radiative heat flow between an oxidated aluminium plane surface at 873.16 degrees Kelvin and an oxidated copper plane surface at 403.16 degrees Kelvin, separated by two thin shields. The first shield is made of zinc-covered iron at 297.16 degrees Kelvin, while the second is made of brass at 323.16 degrees Kelvin.
You may notice that in the presence of these two thin shields, the heat flow between the given plane surfaces decreases by a factor of 72% than in the case of a non-absorptive medium, as calculated in the Engineering/Heat_Transfer/Radiation/flow_noshield module.
#include <codecogs/engineering/heat_transfer/radiation/flow_shield.h>#include <stdio.h>int main(){// the temperature of the oxidated aluminium surfacedouble T1 = 873.16;
// the temperature of the oxidated copper surfacedouble T2 = 403.16;
// the emission factor of the aluminium surfacedouble e1 = 0.19;
// the emission factor of the copper surfacedouble e2 = 0.76;
// the number of shieldsint n = 2;
// the emission factors of the iron and brass shieldsdouble es[3] = {0.276, 0.22};
// display radiative heat flow between the two plane surfacesprintf("Radiative heat flow = %.5lf W per sq. meter\n",
Engineering::Heat_Transfer::Radiation::flow_shield(T1, T2, e1, e2, n, es));
return0;
}
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shields is given by
where
and
with 
, 
the emissivity factors of the first and second surface 
, 
the emissivity factor of the 
-th shield 
, 
the emissivity constant of the black body ![\displaystyle \left(C_0 \approx 5.669 \left[\frac{W}{m^2 K^4}\right]\right)](/images/eqns/67fc33bfe68b5caa3581d0d7912ffcd6.gif)
and 
, 
the corresponding absolute temperatures of the two plane surfaces.
The above expression of the unit heat flow can be further simplified to the following formula
In the diagram below is shown the radiative heat transfer between two plane surfaces, separated by 
, 
, 
, 
.
![q = e_{1, S_1, S_2, \ldots, S_n, 2} \,\, C_0 \left[\left(\frac{T_1}{100}\right)^4 - \left(\frac{T_2}{100}\right)^4\right] \qquad \left[\frac{W}{m^2}\right]](/images/eqns/fbf5d7b97a41f0570a5e9371ed382dc5.gif)
![q = C_0 \left[\left(\frac{T_1}{100}\right)^4 - \left(\frac{T_2}{100}\right)^4\right] \left[\frac{1}{e_1} + \frac{1}{e_2} - (n + 1) + 2 \sum_{i=1}^n \frac{1}{e_{S_i}} \right]^{-1} \qquad \left[\frac{W}{m^2}\right].](/images/eqns/22931ce0fdd0890b8e7523bdea086e45.gif)
