RSM optimization of wire-coil insert parameters for enhancement of thermal performance factor of a shell and tube heat exchanger

The enhancement of heat transfer plays a crucial role in various engineering applications, particularly in shell and tube heat exchangers (STHEs). Among the available passive enhancement techniques, wire-coil inserts mechanically fitted inside the tubes are considered effective and economically attractive methods for improving the thermal performance of STHEs. Compared with in-tube meshes and twisted tapes, wire-coil inserts reduce clogging problems and significantly decrease periodic maintenance requirements. The present study aims to optimize the geometrical parameters of wire-coil inserts, including wire-coil pitch, coil diameter, and wire diameter, using Response Surface Methodology (RSM) in order to maximize the thermal performance factor (TPF) of an STHE operating under laminar flow conditions. The experiments were conducted using a laboratory-scale STHE consisting of 30 stainless-steel tubes with a length of 550 mm and inner and outer diameters of 4 mm and 6 mm, respectively. The hot-water flow rates were set at 1, 3, and 6 L/min, while the cold-water flow rate was maintained constant at 3 L/min throughout all experiments. In addition, the inlet temperatures of the hot fluid were adjusted to 30, 40, and 50 °C. Four Pt100 temperature sensors (temperature range: −50 to 400 °C, accuracy: ±1%) were used to measure the inlet and outlet temperatures of both hot and cold streams. Furthermore, a differential manometer was employed to determine the pressure drop across the STHE. To enhance the thermal performance factor, wire-coil inserts were installed inside the tube side of the heat exchanger. Moreover, to comprehensively investigate the effects of wire-coil geometrical parameters on TPF and determine the optimum operating conditions, Response Surface Methodology (RSM) was employed. The results demonstrated that the use of wire-coil inserts significantly enhanced the overall heat transfer coefficient (U) at different hot-fluid flow rates under both co-current and counter-current flow configurations. In addition, the effect of wire-coil inserts on the enhancement of U became more pronounced with increasing Reynolds number. At low flow rates, variations in flow temperature had only a minor influence on the enhancement of U. However, at higher flow rates, increasing the inlet temperature of the fluid passing through the coil insert substantially improved the overall heat transfer coefficient. The RSM optimization results further revealed that, for all coil diameters, decreasing the wire-coil pitch initially increased the TPF to a maximum value, after which it decreased. The interaction between wire-coil pitch and wire diameter also indicated the existence of an optimum pitch corresponding to the maximum TPF. However, for all wire-coil pitches, increasing the wire diameter led to a reduction in TPF. In contrast, the effects of coil diameter and wire diameter on TPF were opposite; increasing the coil diameter enhanced the TPF, whereas increasing the wire diameter reduced it. Finally, the optimum operating conditions were determined as follows: wire-coil pitch = 11.5521 mm, coil diameter = 3.89805 mm, and wire diameter = 0.300855 mm, which resulted in a maximum thermal performance factor of 1.71833.