Application of dimensional analysis in determining the heat loss in district heating systems

Abstract

Existing procedures for determining the heat loss in heat distribution use balance relations, or rather they are based on the theory of heat and mass transfer. Dimensional analysis enables a new point of view that demonstrated the functionality of heat loss from selected physical quantities that contribute to heat loss. The solution provides one complex criterion and four simplex criteria of similarity. Transforming these criteria of similarity leads to the formulation of the functional dependence of only two criteria, on the basis of which the amount of heat loss can be determined. The resulting criterial dependency is simple, and is calculated in this paper for a pipe one meter in longth. The mathematic model for demonstrating the heat loss is of universal validity, and applies to a wide range of piping used for hot water distribution. However, for each nominal diameter of piping it is necessary to take into account the mutual dependency of the dimensionless arguments pi(5) on pi(1), the form of which is always different. In the paper, this dependency is demonstrated for two nominal diameters DN65 and DN125.