Simplified number of transfer unit formulas for the thermal performance calculation of multi-pass fin-tube heat exchangers

Abstract

The known effectiveness–number of transfer units relationships of multi-pass fin-tube heat exchangers consist of a large number of terms in the series and are not expressed directly in terms of the number of transfer units; as a result, it is difficult to calculate the number of transfer units and the heat transfer coefficient of heat exchangers for a given effectiveness and thermal capacity ratio. To solve this problem, heat transfer models for multi-pass fin-tube heat exchangers based on the heat balance method were established in this article, and simplified number of transfer units formulas for thermal performance calculation were derived according to the flow arrangements of heat exchangers and the flow directions of two fluids. When the number of flow passes in a heat exchanger is greater than four, the relative errors between the calculated number of transfer units by these proposed formulas and those calculated by the effectiveness–number of transfer units relationships of the counter-flow or parallel-flow heat exchangers were all less than 2%. When the number of flow passes in a fin-tube heat exchanger is less than four, a two-pass counter-flow fin-tube heat exchanger was selected as the validation case due to the similar flow characteristics of heat exchangers. The results indicated that the relative errors between the calculated heat transfer coefficients of the heat exchanger according to these proposed number of transfer units formulas and those calculated using the LMTD factor were all less than 5% when the inlet water temperature was in the range of 45°C to 60°C and the water flow rate was in the range of 50 to 170 kg/h. These proposed number of transfer units formulas were determined to be valid and could be beneficial for the design of multi-pass fin-tube heat exchangers.