Equation (8.41) shows that the temperature will continue to increase with time, which can be a problem, especially when the water does not flow to put some heat load on the collector. At this condition, when water is not flowing, the device will increase in temperature and reach a steady-state temperature called the stagnation temperature. This can be a challenge to the materials used and could warp or otherwise damage the device, as well as either boiling the water or chemically degrading the heat transfer fluid if water is not used. The stagnation temperature, Tstag, is found by balancing the various heat flows which can be written
jar || Pd (в) = flop + qbot
Consider qtop = qpc = qca first, the two components are
qpc = hpc[Tstag – Tc] + gS|Tstag Tc ] (8.31a)
— +——- 1
qca = hca[Tc – Ta] + asec[T4 – T^ky] (8.31b)
The bottom heat transfer rate is
qbot = – [Tstag – Ta] (8.32)
One assumes that when solving the above equations Tp = Tstag, which is a reasonable approximation since the absorber plate will be at the highest temperature and, at equilibrium, all parts of the device will achieve the same temperature. The method of solution is given below.
(1) Know: All the parameters in Table 8.1
(2) Determine: jar|PD(в) using eqn (8.29)
(3) Assume: Tstag value
(4) Iterate: change Tc until qpc = qca (eqns (8.31a) and (8.31b)) which will involve calculating the heat transfer coefficients that will depend on temperature. Use the equations in Appendix B to find the effect of temperature on the properties of air, which should be evaluated at the mean temperature at each position (i. e. Tm =
1 [Tstag + Tc] for heat transfer from the plate to cover and Tm =
2 [Tc + Ta ] for heat transfer from the cover to air)10
(5) Calculate: qbot from eqn (8.32)
(6) Validate: if eqn (8.42) is satisfied
(7) Check: if validation is not obtained then go to item 3 and assume another Tstag until validation occurs; otherwise the solution is found
The stagnation temperature can be quite high and approach 200 °C! The next example shows this is, in fact, true.
Find the stagnation temperature using the standard conditions given in Table 8.1 Assume there is a cover.
We follow the method of solution given above to find the stagnation temperature. First the insolation absorbed by the system is jar ЦРп(в) = 764.2 W. If we define qout = q_in+qbot we can iterate until qout = jar jPD (в), with the results shown in Table 8.8
First an absorber plate temperature of 170°C was assumed and qout was too low so the plate temperature was increased to 190°C, which was found to be too high as qout was now too large. An intermediate temperature was assumed which was much closer and after one more iteration a temperature of 181°C represents a fairly accurate solution. The stagnation temperature is very high and materials selection should be made to ensure that they can withstand such temperatures.
In this chapter the operation of a flat plate solar energy collector has been considered. A considerable deviation from the previous literature has been made to incorporate engineering heat transfer calculations, rather than correlative techniques which have been presented in the past. The reason for this was given in the introduction. The previous technique has its roots in the pioneering work of Hottel from the 1940s and 1950s which has served well for over 60 years. As new materials and designs are developed a more flexible technique may have to be used which has served as motivation for this chapter.
The efficiency of these devices is impressive: greater than 50%. If any other energy generating device could work at this efficiency level, this would be a major technological breakthrough. Of course, turbines at the bottom of dams are extremely efficient, approximately 90%, however, there is only a limited amount of hydroelectric power available. The energy developed from flat plate collectors is relatively low quality as it makes low temperature water and not high pressure steam. If it could be developed to boil water at high pressure then this would represent a major breakthrough. Of course this is the subject of the next chapter where the insolation is concentrated to do just that and a solar-thermal power plant is discussed. Regardless, a flat plate solar energy collector is a very useful device and has great utility.