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Mathematical Model of Temperature Changes in Heating Media

Climate conditions on the territory of Russia require heating of residential, public and industrial buildings. The regional variety of temperature modes distinguishes it from most countries of the world. Heat supply in terms of primary fuel and energy resources consumption is the largest segment in the country’s energy supply. Russia ranks first in the world in terms of the scale of heat supply: the volume of heat production, the development of heating, the length of heat networks, and fuel consumption for heat production. Development of modern, energy-efficient heat generating plants is required. Heat supply to agriculture in the Russian Federation lags behind the developed countries by 2-3 times. Various methods and equipment are being developed to reduce energy consumption in thermal processes. The most important task of developing and modernizing energy system and electrifying agriculture is to increase the energy efficiency of energy supply systems based on rational and reliable energy supply. A promising solution in the field of energy saving in agriculture is the use of heat pumps. (Research purpose) The research purpose is in creating a mathematical model of temperature changes in heat carriers. (Materials and methods) Authors used the Newton method for nonlinear systems of equations. The article presents the derivatives of the obtained functions of the system. (Results and discussion) The article presents the graph of the temperature distribution during heat transfer and a graph of changes in the temperature of heat carriers along the heat exchange surface. (Conclusions) The article presents a mathematical model suitable for studying the temperature distribution during heat transfer between two or more heat carriers, which can be recommended for engineering calculations. The convergence of the tangent method is achieved in no more than six iterations, regardless of the initial conditions; the accuracy of calculations is 0.1 percent. A static error is of 5-10 percent in mathematical modeling.