We derive from first principles an analytical expression for a figure of merit (FM) for a selective solar absorber in a single glazed flat plate water heater. We first show that the efficiency of a collector with an absorber with absorptance α and emittance ε, relative to the maximum efficiency for an ideal absorber, can be expressed as ηR=α−Aε−B. The effectiveness of the absorber can then be written as a figure of merit, FM=α−Aε. The larger the value of FM, the better the solar absorber performs in the collector. This is shown to give quite different results from the coating selectivity, α/ε. A is a function of many heater parameters as well as the orientation and geographical location of the heater but, to a good degree of approximation, can be simplified sufficiently to be expressed as a linear function of the inlet water temperature only: Aav=0.0073Tin. For typical average water temperatures between 30°C and 60°C, Aav ranges from 0.22 to 0.44 so the emittance is relatively less important than the absorbtance. In the latter case, for example, the figure of merit is a very simple expression which can be used by developers of solar absorbers without any knowledge of the parameters or location of the HWH: FM=α-0.44εFM=α-0.44ε.
Reference:
RobertS, DE. 2013. A figure of merit for selective absorbers in flat plate solar water heaters. Solar Energy, vol. 98(C), pp 503-510
Roberts, D. (2013). A figure of merit for selective absorbers in flat plate solar water heaters. http://hdl.handle.net/10204/8142
Roberts, DE "A figure of merit for selective absorbers in flat plate solar water heaters." (2013) http://hdl.handle.net/10204/8142
Roberts D. A figure of merit for selective absorbers in flat plate solar water heaters. 2013; http://hdl.handle.net/10204/8142.