Two square plates, with the sides a and b (and b > a), are coaxial and parallel to each other, as shown in Fig. P21€“133, and they are separated by a center-to-center distance of L. The radiation view factor from the smaller to the larger plate, Fab, is given by

where, A = a/L and B = b/L.

(a) Calculate the view factors F_ab and F_ba for a = 20 cm, b = 60 cm, and L = 40 cm.

(b) Calculate the net rate of radiation heat exchange between the two plates described above if T_a = 800°C, T_b = 200°C, ε_a = 0.8, and ε_b = 0.4.

(c) A large square plate (with the side c = 2.0 m, ε_c = 0.1, and negligible thickness) is inserted symmetrically between the two plates such that it is parallel to and equidistant from them. For the data given above, calculate the temperature of this third plate when steady operating conditions are established.

[(B + A)? + 4]0.5 - [(B A) + F. ab 2A b.