A rigorous proof for the uniformity principle of temperature difference field in heat exchanger with deductive method

In this paper, the uniformity principle of temperature difference field (TDF) in heat exchanger has been proved with deductive reasoning. A new parameter which is used to measure the uniformity of TDF in heat exchangers is defined as the universal uniformity factor instead of the two-dimensional factor. An infinitesimal change of flow arrangement is studied, and the corresponding variations of the uniformity factor and the total thermal conductance are calculated. By analyzing the relation between the variations, it is proved that the more uniform the distribution of TDF, the smaller the total thermal conductance of heat exchanger for given heat transfer rate and inlet parameters of fluid. The deduction proves that the uniformity principle of TDF is strictly true in heat exchangers. An optimization problem is analyzed to show the better applicability of the universal uniformity factor compared with the spacial uniformity factor, and it illustrates that the uniformity principle of TDF applies to the heat exchangers with variable thermal conductivity.