Nusselt number correlation for compact heat exchangers in transition regimes

Highlights: • A theoretical and experimental thermal analysis is performed. • Study laminar and transition flow regimes in compact heat exchanger. • Critical Reynolds number is estimated to start at 1800. • A Nusselt number correlation for transition regimes is proposed. -- Abstract: A compact heat exchanger is characterized by high heat transfer rates in small volumes. Basically it can be considered as a solid metal block where hot and cold fluid streams flow through mini or micro channels. The fluids usually flow in laminar regime, but the equipment can also operate in transition and in turbulent regimes. However, no model for the transition flow regimes, applied to compact heat exchangers, is available in the literature, as the few papers in this subject are usually focused in the classical correlations. The present work performed a theoretical and experimental thermal analysis of the laminar and transition flows in a diffusion bonded cross flow compact heat exchanger and proposed a new Nusselt number correlation for the transition regime. The theoretical model and the main correlations for laminar, turbulent and transition regime are presented. To validate the model, a stainless steel cut plate heat exchanger, with 450 square channels of 3 mm edge, was manufactured. The test facility was designed to operate with hot water and air at ambient temperature. The tests were performed with different mass flow rates, operating with Reynolds numbers between 360 and 2500. The theoretical and experimental results compared well, with theoretical data located within the range of the experimental uncertainty. However, for high Reynolds numbers, greater than 1650, the difference between the results tended to increase. Due to limitations of existing correlations, a Nusselt number correlation for air flow in the transition region and the liquid under constant temperature conditions, based on the asymptotic correlation method, is proposed for compact heat exchangers. The new model provides a smooth transition from the developing laminar flow to the turbulent. To validate the equation, a new test set was performed, and the proposed correlation presented a good accuracy in the transition regime.