Heat balance equation of air solar collector with heat accumulator

Abstract

The aim of the paper is to find the mathematical dependence of temperature of heat-receiving surface of heat accumulator of a solar collector on its operating time under conditions of variable external factors. In this case, variable solar activity throughout the day is considered as the key external factor. Air solar collector with heat accumulator is a basic element of solar power plants intended, for example, for grain drying, water heating, natural ventilation systems of livestock houses etc. By the example of operation of a drum solar grain dryer with water heat accumulator, the differential equation of heat balance of solar collector is obtained. The equation takes into account the following components of heat balance: amount of heat coming into solar collector with atmospheric air; amount of heat coming from solar energy and absorbed by heat-receiving surface of water accumulator; amount of heat taken away by drying agent (warmed-up atmospheric air) after heat exchange with heat-receiving surface; amount of heat for heating of accumulator walls; amount of heat for heating of water in accumulator; external heat loss. On the basis of available experimental data, it is assumed that water temperature in accumulator is directly proportional to the temperature of its walls, and the enthalpy of atmospheric air is proportional to the flow density of solar energy. Required dependence of temperature of heat-receiving surface of a heat accumulator is found by solving the Cauchy problem for differential equation of heat balance of solar collector. The obtained exponential expression connects the parameters of variable external factors with design and technological parameters of a solar collector. This allows to model the output thermal performance of solar power plants used in agriculture depending on various external conditions.