A figure of merit for selective absorbers in flat plate solar water heaters

•We express the relative efficiency of a flat plate heater as ηR=α−Aε−B.•We then derive a figure of merit for the heater, FM=α−Aε.•We show that A can be expressed as a simple function of inlet water temperature, A=0.0073Tin.•For a fixed water temperature, e.g. 60°C, FM is extremely simple: FM=α−0.44ε. 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-0.44ε