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 (A_j) for radiation heat transfer calculations. As shown in Fig. P21€“131, the tube-bank (A_j) is placed opposite a large flat wall (A_i) such that the tube-bank is parallel to the wall.

(a) Calculate the view factors F_ij and F_ji for s = 3.0 cmand D = 1.5 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°C, T_j = 60°C, ε_i = 0.8, and ε_j = 0.9.

(c) A fluid flows through the tubes at an average temperature of 40°C, resulting in a heat transfer coefficient of 2.0 kW/m²·K. Assuming T_i = 900°C, ε_i = 0.8, and ε_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.

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