# Derive equation (7.21) for a planar filter TPV system from equation (7.13) using the following approximations

1) for 0 < X < X& pC « 0 and pfFE, CFCE, ^ 1

2) for Xg < X < да, г2 « pf pj

7.2 Derive equation (7.34) for a cylindrical filter TPV system with a blackbody emitter from equation (7.33) using the following approximations.

1) for 0 < X < Хг, pC « 0 and pf [F22 + FE, CFCE, ] ^ 1

2) for Хъ < X < то, і;2 « pfpj

Show that equation (7.33) reduces to the planar filter TPV system result [equation (7.21)] if pfF22 ^ 1.

7.3 Derive equation (7.45) using the radiation transfer theory results of section 6.2 [equations (6.5), (6.7), (6.30), (6.31)].

7.4 Derive equation (7.78) for the radiation flux leaving the PV cells, qoC, when only the emitter emissive power terms are retained in the source terms SE and SC in equation (7.75).

7.5 Use equation (7.77) in (6.85) to obtain QE [denominator of equation (7.79)].

7.6 Using the view-factor result AjFjj = AjFj;, show that AEfE, C = ACfCE, where fE, C and fCE, are given by equations (7.71) and (7.72) and AE = AW, AC = Af.

7.7 For a planar TPV system with perfect end reflectors (pb = 1) where the emitter and window are together and the filter and PV array are together the cavity efficiency, qc, is directly proportional to the effective view-factor,

array. For a system without end reflectors qc ~ FE, C . Calculate the ratio

F

aE’C

for a planar system with circular emitter and PV array of radii 5cm (RE = RC = 5cm) when the distance between the emitter and PV array is h = 0.5cm and h = 1cm. What can be said about the benefit of perfect end reflectors for the two cases?