*Article* **Numerical Study of Heat Transfer Intensification in a Circular Tube U Radiation-Absorbing Insert. Part 1: Thermo-Hydraulic Characteristic**

**Piotr Bogusław Jasi ´nski**

Institute of Turbomachinery, Lodz University of Technology, 90-924 Lodz, Poland; piotr.jasinski@p.lodz.pl; Tel.: +48-42-631-23-49

**Abstract:** The presented paper, which is the first of two parts, shows the results of numerical investigations of a heat exchanger channel in the form of a cylindrical tube with a thin insert. The insert, placed concentrically in the pipe, uses the phenomenon of thermal radiation absorption to intensify the heat transfer between the pipe wall and the gas. Eight geometric configurations of the insert size were numerically investigated using CFD software, varying its diameter from 20% to 90% of the pipe diameter and obtaining the thermal-flow characteristics for each case. The tests were conducted for a range of numbers *Re* = 5000–100,000 and a constant temperature difference between the channel wall and the average gas temperature of Δ*T* = 100 ◦C. The results show that the highest increase in the Nu number was observed for the inserts with diameters of 0.3 and 0.4 of the channel diameter, while the highest flow resistance was noted for the inserts with diameters of 0.6–0.7 of the channel diameter. The *f*/*f* s(*Re*) and *Nu*/*Nu*s(*Re*) ratios are shown on graphs indicating how much the flow resistance and heat transfer increased compared to the pipe without an insert. Two methods of calculating the *Nu* number are also presented and analysed. In the first one, the average fluid temperature of the entire pipe volume was used to calculate the *Nu* number, and in the second, only the average fluid temperature of the annular portion formed by the insert was used. The second one gives much larger *Nu*/*Nu*s ratio values, reaching up to 8–9 for small *Re* numbers.

**Keywords:** heat transfer enhancement; radiation insert; numerical simulations; friction factor; *Nu* number
