Efficiency parameters conversion

In the equations representing the performance of the solar collectors presented so far, the inlet fluid temperature is used. In some European standards, however (e.g. EN 12975-2: 2006), the average temperature is used, T_m, defined as the arithmetic average of the inlet and outlet temperatures [(T_i + T_o)/2] and the efficiency is plotted against (T_m − T_a)/G_t. In this case the collector instantaneous efficiency is given by:

(4.35)

where  is the mean temperature collector efficiency factor.

If the temperature rise through the collector is linear with distance, which is correct for most applications  and the collector efficiency factor given by Eq. (3.48).

Therefore, in the case where T_m is used for the collector performance, Eq. (4.35) plots as a straight line and the intercept  and slope  of the curve are related to F_R(τα)_n and F_RU_L, respectively, by eliminating η and T_o from Eq. (4.2) and (4.4) and using the equation for T_m:

(4.36a)

(4.36b)

And

(4.36c)

(4.36d)

To apply these equations the fluid flow rate through the collector must be known.

Similarly in the case where T_o is used for the collector performance and the efficiency is plotted against (T_o − T_a)/G_t, sometimes applied in the case of air collectors, the collector instantaneous efficiency is given by:

(4.37)

Equation (4.37) also plots as a straight line and as above, the intercept  and slope  of the curve are related to F_R(τα)_n and F_RU_L, respectively, from:

(4.38a)

(4.38b)

And

(4.38c)