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.