A large number of long tubes, each of diameter \(D\), are placed parallel to
each other and at a center-to-center distance of s. Since all of the tubes are
geometrically similar and at the same temperature, these could be treated
collectively as one surface \(\left(A_{j}\right)\) for radiation heat transfer
calculations. As shown in Fig. P13-140, the tube bank \(\left(A_{j}\right)\) is
placed opposite a large flat wall \(\left(A_{j}\right)\) such that the tube bank
is parallel to the wall.
(a) Calculate the view factors \(F_{i j}\) and \(F_{j i}\) for $s=3.0
\mathrm{~cm}\( and \)D=1.5 \mathrm{~cm}$.
(b) Calculate the net rate of radiation heat transfer between the wall and the
tube bank per unit area of the wall when $T_{i}=900^{\circ} \mathrm{C},
T_{j}=60^{\circ} \mathrm{C}, \varepsilon_{i}=0.8\(, and \)\varepsilon_{j}=0.9$.
(c) A fluid flows through the tubes at an average temperature of $40^{\circ}
\mathrm{C}\(, resulting in a heat transfer coefficient of \)2.0 \mathrm{~kW} /
\mathrm{m}^{2} \cdot \mathrm{K}\(. Assuming \)T_{i}=900^{\circ} \mathrm{C},
\varepsilon_{i}=0.8\( and \)\varepsilon_{j}=0.9$ (as above) and neglecting the
tube wall thickness and convection from the outer surface, calculate the
temperature of the tube surface in steady operation.
