The radiation heat transfer from an inner cylindrical surface of radius r1 and emissivity ϵ1 at temperature T1 to concentric cylinder of radius r2, emissivity ϵ2 and at temperature T2 is proportional to

1
\(\frac{{T_1^4 - T_2^4}}{{\frac{1}{{{\epsilon_1}}} + \left( {\frac{1}{{{\epsilon_2}}} - 1} \right){{\left( {\frac{{{r_1}}}{{{r_2}}}} \right)}}}}\)
2
\(\frac{{T_1^4 - T_2^4}}{{\frac{1}{{{\epsilon_1}}} - \left( {\frac{1}{{{\epsilon_2}}} - 1} \right){{\left( {\frac{{{r_1}}}{{{r_2}}}} \right)}}}}\)
3
\(\frac{{T_1^4 - T_2^4}}{{\frac{1}{{{\epsilon_1}}} + \left( {\frac{1}{{{\epsilon_2}}} - 1} \right){{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)}}}}\)
4
\(\frac{{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)\left( {T_1^4 - T_2^4} \right)}}{{\frac{1}{{{\epsilon_1}}} + \left( {\frac{1}{{{\epsilon_2}}} - 1} \right)}}\)

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