# Equations developed for total thermal efficiency of the collector system

The FPC or CPC collector module available in the market has an effective area of approximately 2.0 m2 . Its thermal efficiency can be expressed by the following equation:

П = П -|(T – T“) –B(T – Ta)2 (7)

Solar thermal electric generation system may demand tens or hundreds of collectors in series, and the temperature differences between neighboring collectors will be small. Thus, it is reasonable to assume the following: 1) the average operating temperature of the collector changes continuously from one module to anther module; and 2) the function of the simulated area of the collector system is integrable.

With inlet temperature T and outlet temperature To, the required solar collection area is obtained by the following : L°mCv (T)

: f P dT T n(T)G

Temperature of conduction oil in the CPC changes within a small range. This is discussed further in Section 5.2. Heat capacity can be well approximated by the following : Cp (T) = Cp,0 +a(T – T0)

In the case of FPCs, organic fluid is preheated in low temperature ranges and the first-order approximation of heat capacity can be used as well.      With c1 = A / G, c2 = B / G, the collection area according to Eqs. 8 and 9 is integrated by the following:

where в, and в2 are the arithmetical solutions of the following equations (в, < 0, в2 > 0 ).

По – с, в – ев = 0. (11)

Cp, a = CV,0 + a(Ta – T0) (12)

Subsequently, total thermal efficiency of the collector system is calculated using the following:

T m г  Пс = GS J Cp (T )dT

Effect of c1 is expressed by Eq.11 There are two inlet temperatures, as well as two outlet temperatures in the two-stage collectors. Total collector efficiency is calculated by the following: = Q = AH 1 + AH 2 Пс = GS ~ AH 1 + ah2

Hfpc Hcpc

where nFPC or nCPC is the first – or second-stage collector efficiency, and AH1 or AH2 is the enthalpy increment of working fluid in the first – or second-stage collectors. The value of Cp 0 or a or collector heat loss coefficient varies when the fluid or the collector is different.

Updated: August 23, 2015 — 6:27 am