## 1 Introduction
Based on the heat transfer results, the flow inside the CFI sets augmented the \(N_{Nu}\) by 12-14%, relative to the flows in the STHE and PHE, and empirical correlations were obtained. [PERSON] and [PERSON] [24] evaluated the heat transfer performances of three CFI heat exchangers containing one, two, or four CFI sets. The geometric features of the prototypes were similar to those of the heat exchanger evaluated by [PERSON] et al. [22]. Experiments were conducted predominantly under turbulent flow, and in the setup with one CFI set. the \(U\) was up to 3.6 and 4.5 times higher, respectively, than that in the PHE and STHE obtained by [PERSON] et al. [23]. Numerical studies to investigate the transfer characteristics in CFI have also been conducted. [PERSON] and [PERSON] [25] characterized the hydrodynamics and forced convection in a CFI set, and compared them to those that occur in a straight coil configuration. Both scenarios were studied under laminar regime conditions, and the results revealed that the bent coil configuration (i.e., CFI set) showed a 20-30% enhancement in \(N_{Nu}\) when compared to that of the straight coil. [PERSON] and [PERSON] [26] analyzed a comparable scenario to the previously referred one, except for the additional use of the condition of uniform heat flux at the wall. The \(N_{Nu}\) values were 25-36% higher in coils with rather than without bends. [PERSON] and [PERSON] [27] studied the fluid flow and heat transfer characteristics in a CFI set under turbulent flow conditions. They numerically solved the three-dimensional differential governing equations of mass, momentum, and energy. The velocity and temperature profiles revealed that increasing the number of bends in the CFI set increased the uniformity of both secondary fields by radial mixing. In the simulation data, the heat transfer enhancement was 4-13% relative to a coiled tube without flow inversions. The literature review reveals that only a few numerical investigations in curved geometries have studied the process of simultaneously integrating both passive heat transfer enhancement techniques, NFs, and chaotic advection. [PERSON] et al. [28] numerically solved the governing equations of mass, momentum, and energy in straight tubes, straight helical coils, and a CFI set using Al\({}_{2}\)O\({}_{3}\)-W NFs at 1, 3, and 4 \(\
u\)/\(\
u\)% under laminar flow conditions. The computational \(N_{Nu}\) values were compared with the experimental values in water reported by [PERSON] et al. [22]. Relative to the base fluid (i.e., water), the NFs at 1, 3, and 4 \(\
u\)/\(\
u\)% augmented the \(N_{Nu}\) by 24%, 33%, and 42% in the CFI set and by 15%, 25%, and 35% in the straight helical coil, respectively. The superior heat transfer was attributed to chaotic mixing induced by flow inversion in the CFI set. Under the laminar regime, [PERSON] et al. [29] numerically analyzed the hydrodynamics and heat transfer characteristics of Al\({}_{2}\)O\({}_{3}\)-W and CuO-W NFs at 1, 2, and 3 \(\
u\)/\(\
u\)% in a particular chaotic geometry. The chaotic configuration was created by assembling consecutive sections of two regular helical segments with different pitches, and internal flow inversion was generated by the geometrical perturbation at the bend of each helical segment. The results of the chaotic configuration were compared to those in the straight helical coil. The \(h\) in the chaotic configuration was increased by 18%, 19%, and 21% for the Al\({}_{2}\)O\({}_{3}\)-W NFs at 1, 2, and 3 \(\
u\)/\(\
u\)% and by 18%, 21%, and 25% for the CuO-W NFs at the same concentrations, respectively. To the best of our knowledge, an experimental study of forced convective heat transfer in a coiled flow inverter using NFs as the working fluid is yet to be seen in literature. Furthermore, extensive heat transfer research has focused on Al\({}_{2}\)O\({}_{3}\)-W and CuO-W systems [30], while in comparison, there are limited studies on TiO\({}_{2}\)-W systems. This paper addresses those two aspects.