**Chapter 1: Introduction**

**1.5.1 Flat-Plate Collectors**

A typical flat-plate collector consists of an absorber, transparent cover sheets and an insulated box, as shown in Figure 4. The absorber is usually a sheet of high-thermal conductivity metal with tubes or ducts either integral or attached. Its surface is painted or coated to maximise radiant energy absorption and in some cases to minimise radiant emission. The insulated box provides structure and sealing and reduces heat loss from the back or sides of the collector (Kalogirou, 2004).

**Figure 4: Configuration of a typical flat-plate collector (adapted from, Kalogirou, 2004). **

The most widely used method of evaluating the performance of flat plate collectors has been the thermal energy analysis. This performance evaluation relies on the energy balance of the collector in steady state, which indicates the distribution of incident solar energy into useful energy gain, thermal losses and optical losses.

If G is the intensity of the solar radiation, in W/m^{2}, incident on the aperture plane
of the solar collector with a collector surface area of *A, in m*^{2}, then the amount of
solar radiation received by the collector can be expressed using Equation 1 (Cox
and Raghuraman, 1985).

*Q**i *= GA (1)

Where, Q* _{i}* is collector heat input in W.

However, this equation doesn’t account for the losses caused by the reflection of radiation back to the atmosphere. If glazing is used, this absorbs another component and is transferred through it to the absorber plate as short wave radiation. Therefore, the percentage of the solar radiation, which penetrates the transparent cover of the collector and the percentage of radiation being absorbed, is indicated by a conversion factor. Basically, it is the product of the rate of transmission of the cover and the absorption rate of the absorber, Equation 1 is then modified to account for this and shown in Equation 2.

*Q**i** = G (τα) A * (2)

Where, τα is the transmission and absorption coefficient of the glazing and plate

As the collector absorbs heat, its temperature becomes higher than that of the
surrounding and thermal energy is transmitted to the atmosphere through
convection and radiation. The rate of heat loss, Q*o* is dependent on the overall heat
transfer coefficient, U_{L}*, of the collector and its temperature. The rate of heat loss, *
*Q**o*, can be expressed by Equation 3.

*Q**o** = U**L** A (T**c**−T**a**) * (3)

Where, *Q** _{o}* is heat loss, W,

*U*

*is the collector overall heat loss coefficient in W/m*

_{L}^{2},

*T*

*c*and T

*a*is the collector average temperature and ambient temperature in

°C, respectively.

Thus, the rate of useful energy extracted by the collector *Qu, expressed as a rate *
of extraction under steady state conditions, is proportional to the rate of useful
energy absorbed by the collector, less the amount lost by the collector to its
surroundings (Smyth et al., 2006). This is expressed in Equation 4 (da Silva and
Fernandes, 2010).

*Q**u** = Q**i**−Q**o** = G τα A−U**L** A (T**c**−T**a**) * (4)

Where, *Qu is useful energy gain in W. The rate of heat extraction from the *
collector can be measured by means of the amount of heat carried away by the
fluid passing through it and is expressed in Equation 5.

*Q**u** = m C**p** (T**o**−T**i**) * (5)

Where, m is the mass flow rate of the fluid through the collector in kg/s.

In most cases Equation 4 is modified because of the difficulty in defining the
collector average temperature. It is easy to define a quantity, which relates to the
actual useful energy gain of a collector surface, such as the fluid inlet temperature,
*T**i*. This quantity is known as the collector heat removal factor, *F**R* (there are
actually three types of heat removal factors) for a collector and is shown by
Equation 6.

*F*_{R}* = m C*_{p}* (T*_{o}*−T*_{i}*) / A [G τα −U*_{L }*(T*_{i}*−T*_{a}*)] * (6)

When the whole collector is at the inlet fluid temperature the maximum possible
useful energy gain in a solar collector is achieved. The product of the collector
heat removal factor, *F**R* and the maximum possible useful energy gain gives the
actual useful energy gain, Q*u*, allowing the rewriting of Equation 4. This equation
is commonly known as the Hottel–Whillier–Bliss equation, shown in Equation 7
(Duffie and Beckman, 2006).

*Q**u**=A F**R** [G (τα) −U**L** (T**i**−T**a**)] * (7)

The most useful indicator of a collector’s performance is the collector efficiency,
*η, *which can be calculated from Equation 7 as it is defined by the ratio of the
useful energy gain, *Q** _{u}*, to the incident solar energy over a particular time period,
expressed in Equation 8.

*η =∫Q**u** dt / A∫G dt * (8)

The following equations can be used to define the instantaneous efficiency of the collector.

*η = F**R** (τα) −F**R** U**L** (T**i**−T**a**) / G * (9)

*η = m C**p** (T*_{o}*-T*_{i}*) / AG * (10)

These equations form the basis of test standards such as AS/NZS 2535, ISO 9806,
ASHRAE 93 and EN 12975. By plotting the collectors efficiency against *(T*_{i}* − *
*T**a**)/G, useful information can be obtained. Such as, the slop (−F**R**U**L*) which
represents the rate of heat loss from the collector and the Y-intercept (η*0*) being
the optical efficiency (though it is actually a combination of the optical
absorptance and collector fin efficiency). The parameters acquired from these
standardised tests also form the basis for simulation modelling of the performance
of SWH systems that use these collectors.

Similar to SWH systems, research on flat-plate collectors has been vast and innumerable. The flat plate collector was initially investigated by Hottel and Woertz (1942), and Bliss (1959), who developed equations which describe the performance of flat plate collectors in terms of its efficiency, as described above.

The performance of the collector in terms of design parameters relating to, types of absorber plates were investigated by Mathur et al. (1959) and Patil (1975);

number and type of glass covers was studied by Whillier (1963); thickness and type of insulation was studied by Whillier and Saluja (1965); anti-reflective coating on glass cover was studied by Hsieh and Coldewey (1974); heat mirror coating on inner glass as an alternative for selective absorber was investigated by Winegarner (1976); spacing between absorber and inner glass and successive glazings were studied by Nahar and Garg (1980); studies on coatings on absorber plates were taken up by Nahar and Garg (1981).

In summary the majority of works on flat plate collectors have focused on improving heat transfer characteristics through the optimisation of different components, reducing heat losses within different designs and development of new and innovative designs which go hand in hand with the development of technology in the area of solar heating.