# The effect of mass flow rate and device area

In order to understand the effect of mass flow rate and device area on the operating point of a flat plate solar energy collector, eqn (8.20) is modified slightly by writing it in a more general form to include trans­mittance through the cover,

This equation, which neglects heat losses, will be used to understand how m and Ad affect the operating point. Since heat losses are not included, the design equation is not required and A Tmax represents the operating temperature rise in the device.

Now one can guess that as the mass flow rate increases, the tempera­ture rise will decrease while if the area is increased the temperature rise will increase. This is certainly what will be observed, however, direct proportionality to either variable is not found. Interestingly, eqn (8.38) is a reasonable approximation to the temperature rise found in a device having a cover since heat losses are minimized in the operating device.

First consider the effect of mass flow rate on device performance, par­ticularly for the devices having a cover. Consider the data given in Table 8.7 and the effect of increasing the mass flow rate from 0.06 kg/s (approximately 1 gal/min) to 0.12 kg/s, given in the upper half of the

 table (Ad = 6 m2). As expected AT decreases when m is increased, however, it does not halve when m is doubled. Heat transfer consid­erations prohibit this. This is due to an increase in hw from more efficient heat transfer and from the absorber plate temperature being lower, which reduces radiant energy losses when m is larger. Glancing at other trends in the data for the larger area systems reveals similar observations. Also, there is a slight increase in Qu due to favorable heat transfer conditions at the larger water flow rate. For reference, the de­sign and operating lines are shown in Fig. 8.12 when m is doubled from the standard condition. Values of ATmax are also given in the table. As long as the system has a cover and the operating temperature is not too high then ATmax is a good first approximation to the temperature rise one may expect in a solar hot water heater. This is because the low operating temperature, that approaches the air temperature and cover reduces heat losses, which forces the operating point to move closer to ATmax. So, one can estimate the temperature rise and useful heat to within 20% by knowing a minimal number of parameters for the system, allowing a good first design to be made. Does an increase in the mass flow rate raise the operating cost for the system since the pump used to force water through riser tubes must consume more energy? The mechanical work or rate of energy required to drive the pump Wm can be found from the FLOT in an intermediate form, as given in eqn (3.11), by assuming that the riser pipes are hori­zontal, there is no velocity change and there is no temperature change (so the internal energy change for a liquid is essentially zero as they are basically incompressible) to be Wm = mVw AP = [m/pw ]AP, VW is the specific volume of water. Assuming laminar flow, which is a good assumption for a residential system, one can use the definition of the friction factor (eqn (8.14)) and the friction factor-Reynolds number cor­relation for laminar flow (eqn (8.15a)) to find the pressure drop and ultimately Wm,

 m2 2 4 mkg-s

 (8.39)

 if all other flow loss terms, other than those in the riser pipes, are ne­glected. The approximation represents an equation for the standard conditions where physical parameter and dimensional values have been inserted in the equation. Since m is of order 0.1 kg/s the power is ex­tremely small, less than 1 W. Even accounting for other pressure losses in the system, like flow through valves and the header, and using a heat transfer fluid other than water, which can have a viscosity 10-100 times that of water, the power required to drive the pump is minimal. So, using a higher water mass flow rate is not economically or energetically limiting. However, if there is an electrical power outage the system will not work!

The effect of mass flow rate on AT, Tp and the efficiency n is shown in Fig. 8.13. Several observations can immediately be made. As al­ready discussed AT falls in value upon an increase in m, as does Tp. Since the overall system temperature decreases, the efficiency improves due to a reduction in heat losses from the system. Ultimately, at infi­nite mass flow rate, the efficiency would achieve the theoretical value, Qu/PD(в)Ad, which is equal to |ат||. For the standard conditions with a cover this ultimate efficiency is 0.813.

Should the area be doubled, two things occur (see Table 8.7). Firstly, the overall area is increased to allow more insolation for the devices to use and this immediately increases AT. Secondly, the number of riser pipes operating in parallel increases from 16 to 32 which reduces the velocity of water in the risers. The temperature rise does not double though nor does the useful heat.

The reason is twofold. The lower velocity in the larger area system re­duces the heat transfer coefficient from the riser pipe wall to the flowing water which reduces AT and Qu. Furthermore, the lower velocity forces the system to operate at a higher absorber plate temperature which increases radiative heat transfer. Both these effects inhibit a direct dou­bling of AT and Qu, as can be seen in the data in Table 8.7.

The result obtained from calculating the operating and design lines for the system having doubled the device area and mass flow rate from the standard conditions is given in Fig. 8.14. Firstly, the thin lines in the figure are the same as those in Fig. 8.12, where the only change from the standard conditions is that the mass flow rate of water was increased to 0.12 kg/s. Clearly, doubling the area increases AT as well as Tp, as discussed above. The slope of the operating line also increases, which is the result of increased radiative heat transfer for the elevated system temperature.

Updated: August 19, 2015 — 3:43 pm