Development of Generalized Nusselt Number Correlations for Laminar Flow in Curved and Helically Coiled Micro-Tubes

Curved and helically coiled microtubes have shown to be particularly effective designs for improving heat transfer in microscale thermal systems. Their intrinsic geometric curvature produces centrifugal forces that create robust secondary flows, even under laminar flow conditions when standard straight micro-channels generally exhibit restricted mixing. These secondary flow structures consistently disrupt the thermal barrier layer, enhancing fluid mixing and markedly improving convective heat transfer efficiency. Owing to these benefits, curved micro-tubes possess significant potential for compact and high-performance applications, including micro-heat exchangers, micro-reactors, and sophisticated cooling systems utilized in microelectronics and biomedical devices. The intricate flow and heat transfer dynamics caused by curvature effects provide significant obstacles in precisely forecasting the Nusselt number, which is crucial for dependable thermal design. This paper formulates generalized Nusselt number correlations for laminar flow in curved and helically coiled micro-tubes to bridge this gap. The correlations are derived from an extensive examination of existing experimental data combined with validated computational fluid dynamics (CFD) simulations, ensuring practical relevance and numerical precision. The suggested correlations encapsulate the impact of essential non-dimensional parameters, such as Reynolds number, Prandtl number, Dean Number, curvature ratio, and coil pitch, all of which are pivotal in defining heat transfer characteristics at the microscale. The performance evaluation demonstrates a high correlation between the projected Nusselt values and the reported data, with discrepancies remaining within acceptable engineering tolerance thresholds. The presented models provide a cohesive, resilient, and dependable method for estimating convective heat flow in curved micro-scale channels. These insights are anticipated to substantially assist thermal designers in optimizing device geometry, enhancing energy efficiency, and progressing next-generation thermal management systems.