## Qu AcFr[GtTa UlT Ta

This is the same as Eq. (3.31), with the difference that the inlet fluid temperature (T) replaces the average plate temperature (Tp) with the use of the FR.

In Eq. (3.60), the temperature of the inlet fluid, T, depends on the characteristics of the complete solar heating system and the hot water demand or heat demand of the building. However, FR is affected only by the solar collector characteristics, the fluid type, and the fluid flow rate through the collector. FIGURE 3.29 Collector flow factor as a function of the dimensionless capacitance rate.

FIGURE 3.29 Collector flow factor as a function of the dimensionless capacitance rate.

From Eq. (3.60), the critical radiation level can also be defined. This is the radiation level where the absorbed solar radiation and loss term are equal. This is obtained by setting the term in the right-hand side of Eq. (3.60) equal to 0 (or Qu = 0). Therefore, the critical radiation level, Gtc, is given by

As in the collector performance tests, described in Chapter 4, the parameters obtained are the FRUL and Fr(to), it is preferable to keep FR in Eq. (3.61). The collector can provide useful output only when the available radiation is higher than the critical one.

Finally, the collector efficiency can be obtained by dividing Qu, Eq. (3.60), by (GAc). Therefore, n = FR (Ta) -

For incident angles below about 35°, the product t X o is essentially constant and Eqs. (3.60) and (3.62) are linear with respect to the parameter (T - Ta)/Gt, as long as UL remains constant.

To evaluate the collector tube inside heat transfer coefficient, hfi, the mean absorber temperature, Tp, is required. This can be found by solving Eq. (3.60) and (3.31) simultaneously, which gives

AcFrUl

Example 3.5

For the collector outlined in Example 3.4, calculate the useful energy and the efficiency if collector area is 4 m2, flow rate is 0.06 kg/s, (to) = 0.8, the global solar radiation for 1 h is 2.88 MJ/m2, and the collector operates at a temperature difference of 5°C.

Solution

The dimensionless collector capacitance rate is m c p _

0.06 X 4180

9.99

Therefore, the heat removal factor is

From Eq. (3.60) modified to use It instead of Gt,

= 4 X 0.866[2.88 X 103 X 0.8 - 6.9 X 5 X 3.6] = 7550kJ = 7.55MJ

and the collector efficiency is n = Qu/AcIt = 7.55/(4 X 2.88) = 0.655, or 65.5%

### 3.4 THERMAL ANALYSIS OF AiR COLLECTORS

A schematic diagram of a typical air-heating flat-plate solar collector is shown in Figure 3.30. The air passage is a narrow duct with the surface of the absorber

S Ut

S Ut plate serving as the top cover. The thermal analysis presented so far applies equally well here, except for the fin efficiency and the bond resistance. An energy balance on the absorber plate of area (1 X 6x) gives

S(6x) = Ut(bx)(Tp - Ta) + hCp_a(bx)(Tp - T) + hrp_b(fix)(Tp - Tb) (3.64) where hc,p-a = convection heat transfer coefficient from absorber plate to air (W/m2-K). hr, p-b = radiation heat transfer coefficient from absorber plate to back plate, which can be obtained from Eq. (2.67), (W/m2-K).

An energy balance of the air stream volume (s X 1 X8x) gives hc,p-a (§x)(Tp - T) + hcb-a(§x)(Tb - T) (3.65)

dTQ —ox dx where hCbb-a = convection heat transfer coefficient from the back plate to air (W/m2-K).

An energy balance on the back plate area (1 X 6x) gives hr,p_b (6x)(Tp - Ta) = hcb-a (6x)(Tb - T) + Ub (\$x)(Tb - Ta) (3.66)

As Ub is much smaller than Ut, UL~Ut. Therefore, neglecting Ub and solving Eq. (3.66) for Tb gives h T + h T

where F' = collector efficiency factor for air collectors, given by

The initial conditions of Eq. (3.71) are T = T at x = 0. Therefore, the complete solution of Eq. (3.71) is

This equation gives the temperature distribution of air in the duct. The temperature of the air at the outlet for the collector is obtained from Eq. (3.73), using x = L and considering Ac = WL. Therefore, 