Chapter 4, Problem 20P

The net heat exchange by radiation from plate 1 with radius b to plate 2 with radius athat are separated by a distance c is given by:

$q=\sigma \pi b^2{F}_{1-2}(T_1{}^4-T_2{}^4)$whereT₁and T₂are the absolute temperatures of the plates, $\sigma =5.669\times {10}^{-8}$ W/(m²-K⁴) is the Stefan-Boltzmann constant, and F_1-2is a shape factor which, for the arrangement in the figure, is given by:

$F_{1-2}=\frac{1}{2}\left[Z-\sqrt{Z^2-4X^2{Y}^2}\right]$

where $X=a/c,Y=c/b$. and $Z=\text{1}+\left(\text{1}+X^{\text{2}}\right)Y^{\text{2}}$ . Write a script file that calculates the beat exchange q. For input the program asks the user to enter values for T₁, T₂, a, b, and c. For output the program prints a summary of the geometry and temperatures and then prints the value of q. Use the script to calculate the results for $T_1=\text{4}00\text{K},T_2=\text{6}00\text{K}$ , a =1 m, b = 2 m, and $c=0.\text{1},\text{ 1}$ , and 10m.