Cross-sectional temperature field of a solar collector’s absorber in the case of annular pipe

Abstract

In households, solar collectors are finding ever increasing use for hot water preparation. Although the design of solar collectors is relatively simple, the authors over many years concentrate attention on modelling the cross-sectional temperature field of the solar collector’s absorber [1-7]. In solving the cross-sectional temperature field for an annular pipe [1], the periodical cross-sectional domain is divided into three sub-domains where the first sub-domain is the plate between pipes, the second – a pipe’s wall, and the third – the liquid; as a result, the temperature field expressions have been obtained for all the three sub-domains. In works [2, 3] the temperature fields obtained were simplified. To define its variations in time, the temperature field was found by solving the Laplace equation under non-stationary time-dependent conditions [4]. The obtained results evidence that the non stationary conditions might not be taken into account in long- lasting sunny weather, while such non-stationarity changes considerably the temperature field when it is short-term (e.g. in cloudy weather). The temperature has also been found for a square-pipe absorber [7] as more technological in design. In the present work, the final temperature field model is proposed for the absorber of a round-pipe collector. As distinguished from [1], in this work the temperature of liquid is assumed to be constant over the entire pipe cross-section. Such an assumption significantly simplifies the calculation while not changing the physical essence.