The temperature field problem described in the paper is analytically solved for the absorber of a new type solar collector. The absorber consists of two plates, one of them being flat and placed on top of the other plate made with a square profile. The temperature field is calculated for four areas using the Laplace equation under stationary conditions. For each area the boundary conditions are written and the Laplace equation solved. The resultant temperature fields are found for each area separately.

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-The paper is dedicated to the exploration of one of the methods of renewable energy research. A significance lies in the economically efficient facilities; therefore, it is important to establish distribution of temperatures in the parts of facilities.Considering a nonstationary process, the temperature field is described in the polar coordinate system by using Laplace's equation and corresponding mixed-type boundary data. The solution was obtained by the Laplace Transform Method, applying an integral function of complex variables. The inverse Laplace Transform and the original temperature are expressed as an integral. For the integration, a closed contour, which excludes branching and provides the integral of a function that is analytic, was employed. The Cauchy theorem was applied to the calculations. As a result, indefinite integrals were derived for the temperature estimate in the heat pipe cover and the surrounding environment, depending on the temperature of a fluid within the heat pipe.

In the work, the temperature field model is developed for the absorber of a round-pipe collector. As distinguished from previous models when the temperature of liquid was assumed to be constant over the entire pipe crosssection, the results obtained clearly show the temperature variations in the absorber’s cross-section. In the work, optimal values are found in the work for geometrical parameters of the collector (i.e. the plate thickness and the pipe diameter) that allow the highest possible temperature of liquid to be achieved.

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][2][3][4][5][6][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 nonstationary conditions might not be taken into account in longlasting 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.