Radiation across an annular gap
Input(s)
\(T_{1}\): Temperature at Cylinder \(1(\mathrm{~K})\)
\(T_{2}\): Temperature at Cylinder \(2(\mathrm{~K})\)
\(e_{1}\): Emissivity at Cylinder 1 (fraction)
\(e_{2}\): Emissivity at Cylinder 2 (fraction)
\(A_{1}\): Area at Cylinder \(1(\mathrm{ft})\)
\(A_{2}\): Area at Cylinder \(2(\mathrm{ft})\)
\(\mathrm{k}\): Stefan-Boltzmann Constant \(\left(\mathrm{BTU} / \mathrm{h} \mathrm{ft}^{2}{ }^{\circ} \mathrm{R}^{4}\right)\)
Output(s)
Q: Heat Transfer Rate \((B T U / h)\)
Formula(s)
\[
\mathrm{Q}=\frac{\mathrm{k} *\left(\left(\mathrm{~T}_{1}^{4}\right)-\left(\mathrm{T}_{2}^{4}\right)\right)}{\left(\frac{1}{\mathrm{~A}_{1} * \mathrm{e}_{1}}\right)+\left(\frac{1}{\mathrm{~A}_{2}}\right) *\left(\left(\frac{1}{\mathrm{e}_{2}}\right)-1\right)}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 16, Page: 494.