*Article* **Investigation of Thermal-Flow Characteristics of Pipes with Helical Micro-Fins of Variable Height**

**Piotr Bogusław Jasi ´nski, Michał Jan Kowalczyk, Artur Romaniak, Bartosz Warwas \*, Damian Obidowski and Artur Gutkowski**

> Institute of Turbomachinery, Lodz University of Technology, 90-924 Lodz, Poland; piotr.jasinski@p.lodz.pl (P.B.J.); michal.kowalczyk.1@dokt.p.lodz.pl (M.J.K.); artur.romaniak@dokt.p.lodz.pl (A.R.); damian.obidowski@p.lodz.pl (D.O.); artur.gutkowski@p.lodz.pl (A.G.)

**\*** Correspondence: bartosz.warwas@dokt.p.lodz.pl; Tel.: +48-42-631-23-71

**Abstract:** The results of numerical investigations of heat transfer and pressure drops in a channel with 30◦ helical micro-fins are presented. The main aim of the analysis is to examine the influence of the height of the micro-fins on the heat-flow characteristics of the channel. For the tested pipe with a diameter of 12 mm, the micro-fin height varies within the range of 0.05–0.40 mm (with 0.05 mm steps), which is equal to 0.4–3.3% of its diameter. The analysis was performed for a turbulent flow, within the range of Reynolds numbers 10,000–100,000. The working fluid is water with an average temperature of 298 K. For each tested geometry, the characteristics of the friction factor *f*(*Re*) and the Nusselt number *Nu*(*Re*) are shown in the graphs. The highest values of Nusselt numbers and friction factors were obtained for pipes with the micro-fins *H* = 0.30 mm and *H* = 0.35 mm. A large discrepancy is observed in the friction factors *f*(*Re*) calculated from the theoretical relationships (for the irregular relative roughness values shown in the Moody diagram) and those obtained from the simulations (for pipes with regular roughness formed by micro-fins). The *PEC* (Performance Evaluation Criteria) heat transfer efficiency analysis of the geometries under study is also presented, taking into account the criterion of the same pumping power. The highest *PEC* values, reaching 1.25, are obtained for micro-fins with a height of 0.30 mm and 0.35 mm and with Reynolds numbers above 40,000. In general, for all tested geometries and for large Reynolds numbers (above 20,000), the *PEC* coefficient reaches values greater than 1, while for lower Reynolds numbers (less than 20,000), its values are less than 1.

**Keywords:** heat transfer coefficient; micro-fins; friction factor; numerical methods; CFD
