Error in a simplified calculation of the average temperature of the heat-transfer agent at the heating pipeline section

The problem of error estimation for the calculation of the average temperature of the heat-transfer agent on a heating pipeline section as a half-sum of two temperatures of its boundary points is considered. It is established that in accordance with the physics of the process, the temperature of the heat transfer agent along the length of the pipe is distributed by an exponential curve. Precise formulas are obtained both for the mean length of the heat transfer agent temperature region and for the error in estimating the average temperature from the simplified formula. It is shown that the simplified formula gives the exact value of the average temperature only if the distribution of the temperature of the heat transfer agent along the heat pipeline is linear, which is approximately observed under real conditions. The cases are presented where the error in estimating a simplified formula is a sufficiently small quantity. It is established that the estimation error depends on the linear thermal resistance to heat transfer, consumption of a heat transfer agent, its specific thermal capacity and the length of the heat-pipe section. With the increase in real ranges of the linear thermal resistance of the heat transfer, the consumption of a heat transfer agent, its specific thermal capacity, the estimation error decreases, and the temperature distribution along the length of the section approximates the linear one to a greater extent. On the contrary, with an increase in the length of the section, the estimation error increases. For selected specific conditions, the dependence of the estimation error on the consumption of a heat transfer agent and the length of the section has been investigated. The results of the work can be used in performing thermal and technical calculations of heating and heat supply systems, as well as pipeline systems.