A unified approach to the analysis of unidirectional and bi-directional parallel flow heat exchangers

Virtually all sources devoted to heat exchanger theory, (in particular the heat transfer textbooks), start the analyses of the main thermal features of various heat exchangers by emphasizing the differences between the two basic flow arrangements: (i) the unidirectional parallel flow (in the literature often called parallel flow or co-current flow), and (ii) bidirectional flow (in the literature often called counterflow or counter-current flow). This is justified by a convincing argument that the two arrangements correspond to the two theoretical limits of performance. Namely, among all possible flow arrangements, the unidirectional flow is characterized with the smallest and the bi-directional with the largest effectiveness. Modeling of the two arrangements is, as a rule, performed simultaneously but separately. More importantly, the concept of heat exchanger effectiveness is usually introduced as the ratio of the heat transfer rate, exchanged in a given heat exchanger, and the maximum possible heat transfer rate that could be exchanged in a hypothetical bidirectional flow (counterflow) heat exchanger of an infinitely large thermal (and physical!) size.In contrast, this paper promotes a unified approach to both flow arrangements and advocates the use of the effectiveness definition based on a notion of the dimensionless outlet temperature of fluid stream. It is argued that this approach evades pedagogical drawbacks of formal integration of two mathematical models and, more importantly, eliminates the need for an introduction of a vague concept of 'infinitely large counter-current heat exchanger'. Instead, a unified analysis of a single model should be performed and the effectiveness should be introduced as a figure of merit that takes into account performance only of the actual heat exchanger. This approach leads to the same final results as the conventional one, but it follows methodologically a simpler path, without a need for an early introduction of vague (although plausible) thermodynamic concepts.