P. Shipkovs1*, M. Vanags1, KXebedeva1, G. Kashkarova1, J. Shipkovs1, V. Barkans2

institute of Physical Energetics, Aizkraukles Street 21, Riga LV-1006, Latvia
2 Latvian Maritime Academy, Kronvalda Boulevard 6, Riga, LV-1206, Latvia
* Corresponding Author, shipkovs@edi. lv

Abstract

The paper gives the stationary heat conduction process is studied theoretically for flat plate surfaces of the absorber of a solar collector. Based on the mathematical model of a stationary heat conduction process in flat surfaces of a solar collector’s absorber described by the authors in previous works, the geometry of such an absorber is analysed from the viewpoint of the most optimal temperature field in it. Special attention is given to simplification of the mathematical model and to creation of a computer model that would reflect the two-dimensional temperature field in the collector’s absorber. Introducing into the computer model the solar radiation density received from an external data source/storage medium the authors obtain the temperature field in the absorber and show that it is possible to define its optimal geometry if the maximum heat power is found from the cross-sections area, since the main parameters in the mathematically described heat conduction process are geometrical sizes of the absorber. The developed computer model will form a basis for creation of new software intended for this particular new innovative idea relating to the design and making technology of flat plate solar collectors without application of expensive experimental materials. The main conclusion is that the carried out mathematical description can help to find the optimal sizes for the absorber, which, taken for the whole collector, would provide its maximum efficiency.

Keywords: heat flow, solar collector’s absorber, mathematical modeling

1. Introduction

The heat flow in the absorber of a solar collector, which occupies there a definite space and in which this heat spreads by conduction, is now being studied intensively [1-3]. The process can be considered mathematically if we know the temperature at any time and any point of this space. There are cases when it is sufficient to measure the temperature at separate points and to tabulate the data obtained. However for a solar collector it is advantageous to preliminarily analyze the heat conduction thus considering the problem theoretically. Besides, the temperature not always can be measured at all points. The challenge is therefore to obtain the temperature function theoretically, depending on the time and spatial coordinates. Having obtained such a function we can use it further for mathematical modeling. This function will definitely contain some solar collector’s parameters, such as, e. g., the thickness of the absorber’s plate and the distance between the tubes (which are ideally connected by soldering to the absorber), the tube diameter, etc.; by varying these parameters in our mathematical model we can calculate the most optimal temperature condition in the absorber, making it possible to abandon a huge time-consuming and expensive experimental work for determination of the heat transfer from the absorber’s plate to the heat carrier flowing through the tube [1].

The paper presents the mathematical description for the heat conduction on the plane surface of a solar collector’s absorber (further in the text absorber). The collector plate’s cross-section is considered that is perpendicular to the axis of a tube with liquid. The cross-section is conditionally divided into three parts. Having chosen one of them, we will attach to it a corresponding coordinate system.

The temperature [K] on the plate (the OiABC section) is designated with T(x, z), the
temperature in the cylindrical coating — with Т2(г, ф), and the temperature of the liquid — with T3(r,

,ф).