New Analytical-Numerical Method for Modelling of Tube Cross-Flow Heat Exchangers with Complex Flow Systems

Abstract A new method for thermal calculations of cross-flow tube heat exchangers was proposed. The heat exchanger is divided into finite volumes, inside which the fluid temperatures are given by analytical formulas. The advantage of the semi-analytical method developed is that the temperature inside the finite volume can be determined at any point, unlike the finite difference method widely used in exchanger modelling. Even when dividing the entire tube in one heat exchanger pass into a few finite volumes, e.g. into three segments, satisfactory results are obtained. By dividing the whole heat exchanger into a small number of finite volumes, the computer calculation time of heat exchangers with complicated tube arrangement is very short. The proposed method can be used to calculate heat exchangers with a complicated flow system in which the physical properties of fluids depend on temperature. Analytical and numerical models were developed for one and two pass finned tube heat exchangers to assess the accuracy of the proposed method. A two-pass car radiator mathematical model with two rows of tubes using the proposed method was developed. The results of the car radiator and steam reheater calculations are in good agreement with the analytical or experimental results.