The maximum possible useful energy gain can be achieved when the collector is at the same temperature as the inlet fluid. In this case, the heat losses are minimized. However, in an actual operation setting, this is not always the case. To describe the effective (actual) useful energy gain via heat exchange, we should introduce the *heat removal factor* - **F _{R}**

This coefficient shows how much energy remains after heat losses to the surrounding due to collector and inlet temperature difference. Therefore, the energy balance equation for the actual system can be written as follows

\[{Q_u} = {A_c}{F_R}[S - {U_L}({T_i} - {T_a})]\]

This equation reminds us the energy balance equation discussed in the previous page of this lesson, only with the *F _{R}* factor. This flow factor depends on the mass flow rate of the fluid and heat capacity, and you can learn more details about the flow factor and practical application of the above equation from the following reading.

#### Reading Assignment

Duffie, J.A., and Beckman, W.A., Solar Engineering of Thermal Processes, Wiley and Sons, 2013, Chapter 6, Sections 6.7 (4 pages).

The theoretical models and calculations described in the D&B textbook can be checked in practice by performing collector tests. As new materials and new collector designs appear on market, there is a need for standardized testing procedure, and metrics, which would allow clear comparison and assessment if a collector performance is good or not so good.

The basic method of assessment of collector performance is to expose the system to solar radiation, run the fluid through it, and measure the inlet and outlet temperature along with the flow rate. Then the useful energy gain can be calculated from the experimental data as follows

\[{Q_u} = m{C_p}({T_o} - {T_i})\] In addition the incident radiation on the collector (*G*_{T}) and ambient temperature (*T*_{a}) can be recorded, so we can express the useful gain in terms of incident radiation:

\[{Q_u} = {A_c}{F_R}[{G_T}{(\tau \alpha )_{average}} - {U_L}({T_o} - {T_i})]\]

and further the experimental efficiency of the system at each instant of operation can be obtained:

\[\eta {}_i = \frac{{{Q_u}}}{{{A_c}{G_T}}}\]

To see how the collector test data and efficiencly look like in practice, please refer to the following reading:

#### Reading Assignment

Duffie, J.A., and Beckman, W.A., Solar Engineering of Thermal Processes, Wiley and Sons, 2013, Chapter 6, Sections 6.15-6.18 and 6.23 (16 pages).

Make sure to complete all the assigned reading in this lesson and take the reading quiz.