Analysis of Heat Transfer Mechanisms in Multi-Helical Tube and Shell Heat Exchangers Using Computational Fluid Dynamics

2.1 Four helical coils and shell modeling

A three-dimensional flow domain is used in this investigation to estimate input velocity effects in four helical tubes and a shell. The simulation geometry designed by ANSYS CFD 2024 R1 is a modular design with four helical tubes used as a hot fluid domain and an outer shell, which was designed by the same design software, used as a cold fluid domain. The input and outlet points for both cold and hot fluids are designed to flow in opposite directions inside the heat exchanger. After that, the designed geometry was exported to ANSYS CFD 2024 R1 to complete the mesh process and solve the governing CFD simulation equation, and finally, the simulation was run. The four helical tubes, shell geometry dimensions, and physical properties are illustrated in Table 2. Figure 1 demonstrates the modeling of four helically coiled tube heat exchangers used in this CFD analysis.

Table 2. Helically coiled tube and outer shell dimensional parameters

Figure 1. ANSYS modeler geometry design (A) helical coils design, (B) shell design, (C) helical coils and shell assembly

2.2 Re calculations

Re is a critical factor in fluid dynamics because it establishes the flow pattern of fluids in systems. The behavior of fluids and the operational performance of heat exchange processes depend on the Re. The computational process of CFD simulations demands calculating Re for multiple fundamental reasons. The flow condition classification occurs through Re computation because it distinguishes between three types of flow: laminar, transitional, and turbulent. The smooth flow pattern of laminar behavior occurs at Re below 2000, but turbulent flow with its disordered patterns appears when Re exceeds 4000 [17]. The transitional flow regime occurs between 2000 and 4000 Re because the flow maintains an uncertain status between laminar and turbulent conditions. CFD model selection for turbulence simulation depends on determining the Re value. Using laminar flow modeling requires simple models for systems experiencing laminar flow conditions, yet requires advanced models such as k-ε or k-ω modeling in turbulent systems. The precise anticipation of turbulence patterns determines heat transfer outcomes, pressure loss values, and system performance levels. The pressure drop observed in a system depends on the Re as one of its main variables. The knowledge of Re before simulation helps generate better predictions for energy usage and system operational effectiveness [18]. Re evaluation within the helical coil requires understanding the following information update. Outer tube diameter (Do) will be 5 mm (0.005 m), and the Inner tube diameter (Di) will be 4 mm (0.004 m). Inlet hot water temperature will be 77℃, and cold water inside the outer shell inlet temperature will be 10℃. Inlet velocities of 0.2, 0.6, and 1 m/s will be used to compute Re for each case. The Re is calculated using the following formula:

$R e=\frac{\rho u D_h}{\mu}$      (1)

where, $\rho$ is water density at 77℃, approximately 975 kg/m³, $u$ is the inlet velocity at m/sec, $\mu$ is water dynamic viscosity at 77℃, approximately 0.355 × 10⁻³ kg/m·s, and finally $D_h$ is the tube hydraulic diameter calculated by the following formula:

$D_h=\frac{D_{0 \text { tube }}-D_{\text {in tube }}}{2}$      (2)

All inlet flow patterns in the system yield Re under 2000 with initial velocities at 0.2 m/s corresponding to Re = 275. The Re at 0.6 m/s equals 824, corresponding to Laminar flow due to Re < 2000. With a speed of 1 m/s, the Re is established at 1374, which indicates Laminar flow (Re < 2000). The helical coil demonstrates laminar flow because all three inlet velocities measure less than 2000. In straight pipes, switch-ins in the flow usually happen at Re = 2300, where the laminar to turbulence switch takes place. Nevertheless, geometrical curvature and centrifugal effect may move the critical Re of helical or coiled tubes. These cause secondary flows (Dean vortices), and these can, under some circumstances, stabilize the flow and delay transition, or can, instead, introduce instabilities at lower Re, speeding transition. Since the research focuses on inlet rates that lead to Re resembling 1300 to 1400, the system will run in laminar-turbulent. It will not manifest the transition point of curved structures. A small perturbation, like flow pulsations, inlet turbulence, or buoyancy forces driven by temperature, might make the system lose stability and enter transitional flow.

2.3 Boundary conditions and simulation assumptions

The hot water domain utilized different inlet speeds of 0.2 m/s, 0.6 m/s, and 1 m/s at the Four Helical Coils. At the inlet point, hot water entered with a temperature of 77℃. Laminar flow occurs throughout the entire structure of the coils. Every case setup requires an explicit application of external heat fluxes. The Shell Inlet Conditions accept the parameter that determines the Cold-Water Domain's initial movement speed. The analysis uses identical water velocity for hot water, yet reversed. The temperature of cold water entering the system has been established at 10℃. An area of laminar flow exists in the domain where cold water flows. The tube surfaces receiving hot water require a zero-velocity condition, which represents the no-slip boundary. The heat transfer dynamics between hot water and tube wall surfaces depend on the thermal conductivity value of copper at 401 W/m·K that appears in the data table. The outer shell surface (cold water side) also receives the boundary condition of no slip. The imperfect thermal junction between the coils and shell needs special consideration through thermal contact resistance [19]. The Laminar Flow Solver serves both domains (hot water and cold water) because their fluid movement operates under laminar conditions. The simulation operates with steady-state behavior since fluid characteristics and velocities maintain constant rates at every point in time. The mathematical simplifications become possible due to this valid assumption, which applies to systems that maintain fixed flow rate conditions while operating at consistent temperatures. The simulation considers two incompressible fluids that enter as a hot water inlet fluid and cold water in the outer shell. The assumption holds because water density shows minimal variation during typical heat exchanger-operating temperatures. During the simulation, we maintain the belief that fluid density remains consistent. During simulation, all thermophysical water properties, including viscosity, density, and specific heat, remain constant within the simulation domain. Hot and cold water temperature properties are estimated at an average system temperature value, which usually originates from inlet and outlet measurements [20]. The pure convective heat transfer between hot and cold fluids can be calculated using helical coil correlations to evaluate the convective heat transfer coefficient. The fluid displays perfect behavior since we won't estimate any chemical or phase transformation. The model stays simple because the heat exchanger design assumes no boiling or condensation takes place, thus bypassing the requirement for phase-change calculations. Standard correlations help us calculate pressure drops that occur throughout the helical tube system. The Darcy-Weisbach equation, with comparable empirical formulas, serves as the method for determining friction forces and pressure drops in helical coil structures. The performance modeling of the heat exchanger requires this information to forecast both fluid pumping energy needs and system performance accuracy. The heat transfer coefficient inside helical coils remains constant because existing equations for helical fluid flow determine it according to either Dittus-Boelter theory for fast-moving fluids or Sieder-Tate theory for slow-moving ones. The heat exchange between hot and cold water depends significantly on the heat transfer coefficient value. The helical coils show an ideal heat exchange between fluids and coil walls, not including fouling or scaling. The thermal resistance stays fixed between the fluid material and the coil surface, which ensures continuous heat transfer performance regardless of socioeconomic contamination.

The simulation model does not impose a slip boundary condition at the bounds of the helical tube (one that the hot water flows), in addition to the outer shell (one that the cold water flows). This supposition holds both in hot and cold fluid areas. The study does not mention the application of any more sophisticated wall functions (such as increased wall treatment models under turbulent flow), as the analysis is done under laminar flow. The boundary condition of no-slip is used at the tube walls without any treatment of the walls regarding turbulence.

The current study modeled the coils with a constant wall-temperature boundary condition instead of a continuous heat-flux boundary condition. The temperature of the tube-wall was thus held at a constant value of 368.15 K (95℃), which is close to an idealized condition whereby the heating medium, e.g., steam or thermal fluid, is used to provide a uniform wall temperature across the surface of the complete coil. This design allows for the analysis of the convective heat transfer between the wall and the cold fluid within the shell to be done with rigor. In the case of the flow boundaries, the inlet conditions were laid down as that of velocity, whereby the inlets of the shell and tube sides were set as inlet velocity conditions of the fluid, with its cold side inlet having a range of 0.2 to 1.0 m/s, and the fluid was maintained as an inlet temperature condition of 300.15 K (27℃). The pressure outlets on the left and right were characterized as 0 Pa gauge pressure, allowing the fluid to leave freely. No-slip walls were given to all wall surfaces, including the coil and the shell, i.e., the fluid velocity at the wall surface was zero. All these boundary conditions create an ideal heat transfer process model, which is laminar, single phase, steady state, that was sufficiently controlled to obtain equivalent behavior of a multi-helical coil and shell heat exchanger.

2.4 Simulation mesh parameters and testing

The foundation provided by meshes plays a crucial role in obtaining accurate physical phenomenon solutions when using CFD. Simulation accuracy directly correlates to the degree of mesh development accuracy. The physical domain mesh divides its territory into numerous cells, which approximate solutions for fluid motion, heat transfer, and system variables. Precise resolution of velocity, temperature, and pressure gradients depends on a mesh made with proper design. The accuracy of mesh functions is essential because it generates the simulation results. Simulation accuracy in predicting behavioral patterns of real-world systems becomes superior for complex heat exchangers that use proper mesh quality and density standards. One must establish the best possible connection between mesh resolution and computational performance to achieve reliable results. Mesh independence tests serve as standard procedures to identify the most suitable element size because these tests demonstrate minimal result changes while keeping computation costs affordable [21]. Mesh elements require precise definition to enable accurate heat exchanger analysis because they determine both thermal understanding and system optimization capabilities.

Figures 2(A) and (B) illustrate the mesh of the hot water coils and the cold-water outer shell. According to the images in Figure 2, the mesh structure uses unstructured tetrahedral and hexahedral elements with a mesh element size of 1 mm.

Figure 2. Simulation model mesh (A) four coil design mesh, (B) the complete simulation model design

Table 3. Mesh statistics and methods

The mesh area targets the internal and outer aspects of Figure 2(A) before presenting the four helical coils alone. Figure 2(B) shows the entire outer shell area, while the mesh tracks the coils to see how fluid interacts with the edges, coil surfaces, and nearby regions. The mesh statistics and methods are illustrated in Table 3.

2.5 Independent mesh test

In ANSYS CFD simulations, it's essential to perform mesh independence tests to check how accurate the simulation results are with different mesh sizes. The main goal is to identify the best mesh density that leads to precise results at a cost-effective computational level. To ensure high-quality mesh independence, we need to run several simulations with various mesh sizes, from rough to very detailed, and check for significant changes in the results. When results stabilize during mesh refinement, mesh independence is indicated because it demonstrates minimal changes. The mesh independence test was simulated with 10 different element sizes, ranging between 1 mm and 10 mm. The element size is the main component determining mesh resolution in this testing process. The analysis produces more mesh elements for small-sized elements and fewer elements when elements are bigger [22]. The test analysis allowed observation of the outlet temperature of the cold water as its primary measurement point. Table 4 below demonstrates the test results graphically represented in Figure 3.

Table 4. Independent mesh test results

Figure 3. Mesh independent test results graphical chart

Table 4, together with Figure 3, demonstrates that the cold water outlet temperature decreases steadily with increased element diameter (from 1 mm to 10 mm). By increasing the element size from 1 mm to 10 mm, the cold water outlet temperature decreases from 24.5 to about 20℃. Increased accuracy in outcome measurement occurs through a substantial temperature variation at the cold water outlet, which results from changing the element size from 1 mm to slightly coarse (2 mm). Beyond this stage, the element increases, causing the temperature to become more stable and produce less fluctuation. The slight difference between 3 mm and 10 mm element size implies that the simulation endpoint has started to converge. Further mesh refinement will yield minimal changes in the results since the mesh has developed approximate independence.

The accuracy level will remain satisfactory when using 3 mm or 4 mm size elements; however, the calculations will execute faster compared to 1 mm or 2 mm elements. These element sizes manage to find an appropriate equilibrium between computational execution speed and solution precision through their reduced heat flow pattern resolution compared to 1 mm mesh elements. Element sizes of 3 mm or 4 mm offer suitable options for receiving quick results alongside reasonable accuracy in preliminary design studies when high precision is not critical or across model regions where accuracy requirements are lower. The mesh product explains information with reduced detail in flow property change zones (boundary layers and turbulent regions) if element sizes rise above 4 mm. The larger elements in your simulation model reduce accuracy whenever flow separation, vortex shedding, or thermal gradients become significant. These simulations achieve high computational speeds but cause such accuracy to decrease substantially, affecting heat exchanger performance prediction [23].

4.1 Velocity profile effects

Flow in a helical cone coil heat exchanger is significantly disrupted all the way along its length due to centrifugal force generated by the coil's curvature. Before the area was fully established, this flow disturbance became dominant, causing irregular flow and challenges in forecasting. Therefore, the authors had to find a fully formed region to analyze the thermal characteristics of helical cone coil heat exchangers. The heat exchanger's coil contours of velocity flow profiles over the hot water outlet tube cross section are shown in Figures 4(A), (B), and (C) at three different inlet velocities.

We need to understand laminar flow basics before examining its velocity profiles because laminar flow produces organized fluid motion, which maintains separate layers of water throughout its path. At lower speed levels, laminar flow occurs, which results in thermal boundary layers creating themselves along the tube walls. The established boundary layer creates thermal resistance, reducing the heat transfer between the hot tub and external cold water. The fluid structure in laminar flow creates two distinct motions between the bulk flow and fluid neighboring the tube wall.

Heat exchange in laminar flow exists mainly through conduction inside the thermal boundary layer rather than the more inefficient convection. In Figure 4(A), a smooth parabolic shape is visible in the velocity profile, which reaches 0.2 m/s. Among the three profiles, this velocity represents the slowest condition, as fluid motion reaches its highest speed at the tube's central area, as compared to the fluid adjacent to the walls. The tube walls receive thick thermal boundary layers because the inlet velocity remains at a low level. The dense thermal boundary layer opposes efficient heat transfer from hot water to the cool water located in the shell at this slow water velocity. Most heat transfer occurs through conductive processes in the boundary layer, but such conductive transfer proves much less efficient than convective heat extraction [24].

Figure 4. Hot water coil velocity outlet profile (A) 0.2 m/s inlet velocity, (B) 0.6 m/s inlet velocity, and (C) 1 m/s inlet velocity

Between the tube walls, the flow maintains zero movement because this leads to weak convective heat transfer processes, which slow down total thermal exchange. The thermal energy from hot water does not dissipate effectively from tube surfaces because the tube wall fluid moves at a slower pace, thereby creating major temperature variations between the wall and flow area. The velocity profile develops a steeper slope when increasing the velocity to 0.6 m/s in Figure 4(B). A greater velocity exists within this system as the slope between the tube center and wall rises. At this elevated flow speed of 0.6 m/s, the thermal boundary layer grows thinner as a result of the increased velocity when compared to the 0.2 m/s flow. A velocity gradient exists in the system, which demonstrates faster flow motion at the tube center when compared to the wall areas while maintaining laminar flow characteristics. Rising flow speed leads to reduced thickness in the thermal boundary layer. The heat transfer efficiency from hot water to cold water surpasses that of 0.2 m/s because of the implementation of a lower boundary layer resistance. The raised velocity provides heat transfer efficiency that exceeds the values obtained during a velocity of 0.2 m/s. Despite these small advantages, the heat transfer remains limited in laminar flow since it does not produce enough turbulent mixing to achieve maximum convection heat transfer. The velocity profile in Figure 4(C) becomes exceptionally steep at 1 m/s while producing an increased distinction in velocity between the tube's center and walls. An established laminar flow exists, although the velocity gradient becomes more visible. As the boundary layer becomes thinner, the central velocity reaches much higher values than either of the other boundary conditions [25]. The acceleration in velocity does not affect the laminar characteristics of the flow regime. The velocity variation between the central flow region and the external areas of the flow process becomes progressively greater. The velocity's increased speed produces an even more slender thermal boundary layer, which optimizes heat transfer from hot fluid to the surrounding cold fluid. Heat transfer gets better with this improvement, although the flow continues to stay laminar. The decreased thickness of the boundary layer enhances heat conduction performance better than lower flow rates. The increased velocity of flow does not overcome the limiting effects that laminar flow has on heat transfer performance. The fluid velocity next to the wall is exceptionally low, which leads to temperature differences forming between the wall material and the fluid flow region distances. The heat transfer process depends heavily on the geometrical characteristics of the helical tube coil. The coil shape produces secondary flow in laminar streams, generating centrifugal forces that might somewhat destabilize thermal boundary layers. The geometrical properties of the helical tube coil help decrease the boundary layer thickness near walls, thus boosting heat transfer above a plain tube's performance. At turbulent flow conditions, the geometric structure has its most significant influence.

Helical coil creates secondary flow motion during laminar conditions where the resulting turbulence falls below the levels observed in turbulent flow, so its heat transfer contribution remains minimal [26]. Fluid dynamics and heat transfer expertise depend on recognizing the fluid velocity-related effects on thermal exchange to optimize heat exchangers and similar systems. Research and engineering professionals can use comparative velocity measurements to find essential understandings regarding how flow features control heat exchange efficiency. Compiling data in Table 5 enables simultaneous review of multiple analytical scenarios. Design and operational assessments become more feasible through this method because it depicts distinct patterns as well as design deficits for improvement. Table 5 presents data about the helical tube coil system, where three velocities (0.2 m/s, 0.6 m/s, and 1 m/s) demonstrate their impact on flow characteristics and boundary layer thickness, and heat transfer effectiveness.

Table 5. Velocity profile results comparison

4.2 Hot coil outlet temperature profile analyses

During laminar flow, the fluid displays smooth movement because fluid layers transfer parallel to adjacent layers. The main heat transfer mechanism in laminar flow consists of fluid conduction and heat transfer through the wall boundary layer adjacent to the tube structure. Laminar flow creates a wide temperature contrast between fluid that contacts the wall and fluid in the center because the wall cools quickly while the core remains heated. In cases of laminar flow, the helical tube coil creates secondary flow that minimally disrupts the fluid movement, yet the effect remains weaker than it would in turbulent flow conditions. Figures 5(A), (B), and (C) illustrate the helical tube outlet temperature profile for the three testing speeds. In Figure 5(A), the temperature gradient is very steep and runs through the entire tube cross-section when the flow velocity remains at 0.2 m/s. Positioned at the center of the pipe flow, the hottest temperature exists, while the surrounding fluid near the walls has become cooler because it has exchanged heat with the surrounding fluid shell. In this situation, conduction leads heat transfer operations while creating a wide thermal boundary layer that encircles the tube. The thick boundary layer hinders efficient heat exchange by creating insulation between hot and cold water substances. The temperature difference between hot water near the tube wall and the center of the coil is substantial because the wall temperature remains significantly cooler. The section directly adjacent to the cold fluid contacts hot water becomes the coldest point inside the tube wall. The low speed of flow results in diminished heat transfer capabilities because the tube wall fluid stays segregated from the flow center thermal energy. The laminar flow compounds this problem since it fails to adequately mix fluid, while the heat transfer mainly depends on conduction within the thin wall region [27].

In Figure 5(B), a velocity change to 0.6 m/s diminished the temperature difference across the cross-section. By increasing the velocity, the thermal boundary layer becomes thinner, which results in improved heat transfer between the hot fluid and the cold fluid adjacent to the shell. At 0.6 m/s flow speed, the fluid's central temperature stays warmer than before, yet the heat gradient between the core and the edges of the circulating fluid has decreased substantially in comparison to when the velocity was set at 0.2 m/s. The temperature distribution reveals reduced sharpness of the hot to cold fluid transition compared to 0.2 m/s due to the modified profile at 0.6 m/s. Near the tube wall temperature elevates while the outer areas maintain a cooler condition. An efficient heat transfer occurs because the thin thermal boundary layer enhances the rate at which heat moves from the hot water to the surrounding cold fluid. Because the fluid stays within laminar boundaries, the heat transfer remains compromised while conduction continues to be the primary heat transfer method. During the velocity level up 1 m/s in Figure 5(C), the heating system generates temperature uniformity throughout the cross-section better than previous velocity measurements. Heat loss from the central section throughout the tube length reduces because the central region of the flow remains cooler near the walls. Such velocities thin the thermal boundary layer, thus enabling better heat transfer efficiency. The fluid outlet's middle region dissipates heat quickly, creating an even temperature distribution throughout the cross-section. Compared to previous speeds, the temperature distribution throughout the flow is more uniform because the center maintains elevated temperatures at this velocity level. Better heat transfer performance appears in this visualization because the temperature difference is reduced between the boundary fluid and core fluid. The heat transfer efficiency improves because of the thinner boundary layer at increased velocity, yet the flow maintains laminar behavior. A better temperature spread exists, but the heat transfer primarily functions through conduction; therefore, performance achieves only moderate levels than turbulent operation. The authors note that temperature profiles show different patterns when entering at various velocities. The broader thermal boundary layer at lower velocities restricts the heat that escapes from the tube through its surface into the surrounding water [23]. Also, the boundary layer becomes thinner when velocities rise, yet this effect's heat transfer enhancement remains less dramatic than turbulent flow. Laminarity prevails throughout the flow process, thereby maintaining limited movement between different fluid sections. Due to higher temperature, the core fluid remains separate from the surrounding fluid near the tube walls. A significant temperature variation persists throughout the tube cross-section since the fluids fail to mix. The helical tube shape produces secondary flow patterns that contribute marginally to interferences in the boundary layer formation. These secondary flows show greater effects on heat transfer when the flow condition is turbulent because they increase mixing and improve transfer. The effects of these devices remain marginal under laminar flow conditions.

Figure 5. Helical coil tube outlet temperature profile (A) at 0.2 m/s inlet speed, (B) at 0.6 m/s inlet speed, and (C) at 1 m/s inlet speed

According to Figure 5(A), the evaluated temperature data spans between 43.99℃ and 45.64℃. The temperatures throughout the central cross-section of the tube probably approach the maximum values of this range, while wall-contacted fluid cools towards the minimum temperature measures. The core fluid temperature shows 45.64℃ because the flow has experienced limited heat loss. The hottest part of the profile resides in this segment. At the tube walls, the temperature reaches 44.17℃, which is much lower than the temperature elsewhere. The temperature of the tube wall-cooled fluid decreases because heat transfers between these layers to the surrounding cold fluid. The thermal boundary layer thickness is accomplished at this speed level, which produces an extensive temperature gradient between the internal core region and the external peripheral area. The temperature in Figure 5(B) ranges from 44.17℃ to 45.64℃. The dimensionless temperature gradient between the tube core and wall experiences reduced steepness compared to the 0.2 m/s flow condition. The heated fluid near the core maintains temperature levels at 45.64℃, which is slightly cooler than at 0.2 m/s because of enhanced heat transfer. The temperature near the tube walls has become slightly warmer since rising to 44.54℃ as compared to the 0.2 m/s flow condition. A better distribution of temperature appears because the boundary layer has become thinner. Higher velocities create thinner thermal boundary layers, which improves the exchange rate between the hot fluid and the surrounding fluid temperature. The temperature spread throughout the system achieves a better balance at higher velocities compared to reduced velocities. The temperature values in Figure 5(C) extend from 59.95℃ to 63.83℃. The hot water temperature across the center of the flow remains high because the boundary layer is slimmer compared to other conditions, but the temperature range from 59.95℃ to 63.83℃ is the highest among all three scenarios. Hot temperatures between 63.83℃ and 59.95℃ affect the core area of the fluid flow. Better heat transfer emerges from the reduced temperature separation between core and wall when examining 0.2 m/s against the other flow rate. The tube walls have exposed fluid at a temperature of 60.81℃ because of enhanced heat transfer compared to lower velocity scenarios. The improved thermal efficiency is notable at increased velocity since heat transfer from the tube reaches the surrounding cold fluid more efficiently. A remarkable trade-off occurs at this flow velocity because the boundary layer has narrowed to improve heat transfer, but the flow remains laminar. The temperature difference between water layers is minimal, while hot water dissipates heat to cold water at a greater rate than the 0.2 m/s condition. Table 6 below summarizes the temperature variation according to the velocity.

Table 6. Temperature ranges at each velocity comparison

4.3 Hot coil outer wall temperature profile analyses

The fluid layers in laminar flow avoid mixture among all layers. A temperature gradient extends from the central region toward the tube walls because the tube surface transfers heat toward the surrounding fluid. Fluid transport along the tube increases thermal boundary layers, establishing heat transfer insulation that decreases transfer speed. When the fluid speed rises, the boundary layer reduces in width, leading to more efficient heat transfer due to enhanced thermal gradient. Figures 6(A), (B), and (C) demonstrate the heat profile of the helical coil tube at the selected three velocities.

Figure 6. Helical coil tube outer wall temperature profile (A) at 0.2 m/s inlet speed, (B) at 0.6 m/s inlet speed, and (C) at 1 m/s inlet speed

In Figure 6(A), at 0.2 m/s, the outer wall of the hot water tube shows temperature variation between 39.72℃ and 77.03℃. Near the inlet of the coil exists the highest temperature range because hot water enters at a higher temperature. A proximity to the walls creates lower temperatures around 39.72℃ because heat escapes to the cool ambient fluid. Near the outer part of the coil, the temperatures fall mainly in the lower range because the thermal boundary layer extends generously, resulting in poor heat exchange efficiency. Insufficient heat transfer occurs at low velocities because of an extended thermal boundary layer. The temperature readings of the tube's exterior surface stay cool due to poor thermal conductivity between the hot and cold water. Heat escapes rapidly from the tube wall's outer surface, though the flow speed remains minimal, so convective heat transfer toward the shell water remains limited. The temperature variation measured along the hot water tube outer wall ranges from 36.54℃ to 71.94℃ when operating at 0.6 m/s in Figure 6(B). The velocity rise has increased the outer wall temperature of the tube to 41.60℃, exceeding the temperature recorded for 0.2 m/s velocity. An improved heat transfer efficiency occurs when the thermal boundary layer becomes thinner. The central fluid region remains hotter throughout, but the outer wall temperature drops gradually because effective heat transfer from the fluid contacts the surrounding cold water. The hot water tube exterior wall temperature spans from 39.72℃ to 77.03℃ when operating at 1 m/s, as illustrated in Figure 6(C). The highest velocity increases the outer wall temperature to 43.87℃ at this velocity since more heat moves from the hot water tube to the surrounding shell liquid. The hot fluid core temperature stays high at 72.89℃, while the outer wall temperature presents uniform distribution across the coil length. The outer wall temperature exceeds earlier readings at the 0.6 m/s and 0.2 m/s velocity settings, yet remains beneath the values of the central region temperature. The fluid velocity's elevated levels generate a reduced thermal boundary layer, making heat transfer more efficient. Improved heat transfer occurs between the hot and cold fluids because of the increased effectiveness of heat distribution. The outer wall temperature shows better performance than earlier velocities did. The continued laminar flow restricts the heat transfer efficiency because it fails to reach the maximal results achieved by turbulent flow regimes. Table 7 presents data about temperature changes and system heat transfer performance at the different inlet flow speeds ranging from 0.2 m/s to 0.6 m/s and 1 m/s. This table provides quick insights into flow velocity effects on heat transfer in laminar flow situations through helical tubes [28].

Table 7. Outer wall temperature and heat transfer efficiency in a laminar flow helical tube coil at different inlet velocities comparison

The entrance region can be considered as an important area of research in helical pipes because it is at this area that the first steps of the thermal and hydrodynamic boundary layer development occur. By gradually reducing the entrance length in increasing succession, the propagation of such layers towards the tube wall is enhanced, increasing the effective surface area of convective heat transfer through convection. At low Re found in low-velocity regimes, the boundary layer is relatively thick and slow to grow, lengthening the transition zone and decreasing the convective heat-transfer coefficient. Besides, the opposite is valid at greater velocities, wherein boundary-layer thinning enhances the transition and produces steeper velocity fluctuations at the boundary, consequently increasing the wall shear stress and the interfacial heat-transfer coefficient. At the same time, the increased field of velocities also performs the simultaneous job of reducing the thermal layer of the boundary adjacent to the wall and increasing the temperature difference, as it is closer to the wall and further away from the wall. The recurved geometry of helical tubes induces centrifugal forces that are not present in straight pipes and cause the Dean vortices. In this case, the fluid near the center flows fast, due to which vortices are formed. The produced centrifugal force gives the fluid inertia and drives it outward to generate two counter-rotating vortices within one pipe cross-section. Due to the thinner thermal boundary layers that come along with the elevated axial velocity, the reinforced Dean vortices produced by the elevated centrifugal force and the enhanced core-wall fluid mixing associated with high axial velocity, the thermal resistance at the wall-fluid interface is weaker; the heat-transfer performance of a helical tube with high axial velocity is better. Along with these makings, the Nusselt number also increases, yielding more heat efficiency. The trend, therefore, means that the cold-end temperature would have a significant rise when the inlet velocity is reduced to 0.2 m/s, when compared to the temperature with an inlet velocity of 1 m/s, at the same outlet velocity of 0.2 m/s; this variation would reflect greater absorption of heat by the hot fluid. The finding is associated with a rise in the convective heat-transfer coefficient related to secondary flows enhanced by the helical arrangement. Though the flow is laminar (Re < 2000), curvature-aroused Dean effects play the role of the acting entities as the sources of turbulence even in the laminar range of flows.

4.4 Outer shell inlet temperature profile analyses

The temperature patterns of a heat exchanger shell filled with cold water can be observed through Figures 7(A), (B), and (C), while showing different inlet temperature distributions with velocity conditions from 0.2 m/s to 0.6 m/s and 1 m/s. Research simulations based on ANSYS CFD software-generated profiles will be used to determine the thermal effects that water experiences while flowing inside the shell. The examination in this research investigates the thermal gradient that emerges because the shell wall transfers heat to the flowing cold fluid in laminar flow conditions. The temperature distribution in Figure 7(A) reveals heat accumulation at the outer boundary (shell wall) areas before declining toward the heat exchanger core. The laminar flow nature leads to this particular temperature distribution because the wall boundary layer becomes thicker while heat transfers mainly through conduction between the surface and fluid due to limited mixing. The shell wall's proximity to the fluid generates a thick heat resistance layer because the fluid near the wall moves at a slower speed during laminar flow motion. During laminar flow, heat transfer occurs mostly by conduction since fluid particles mix inefficiently, so convective heat transfer becomes less efficient. A velocity of 0.2 m/s at the inlet creates slow-flowing water, so enough time exists for wall-situated water to absorb heat. The material moves without mixing due to laminar flow, which leads to poor efficiency of heat transfer from the shell wall to its central area.

The distance from the center is the determining factor behind cooling temperatures in the contained area. The lack of mixing, together with poor convective heat transfer, lowers the heat exchanger's efficiency when operating in laminar flow. Water remains inside the shell for an extended period, but inadequate wall-to-center heat transfer decreases the total heat exchange efficiency. The central part of the fluid maintains a cool temperature, indicating inadequate fluid heating [29]. The shell temperature distribution shows improved uniformity under this velocity condition compared to 0.2 m/s, as shown in Figure 7(B). Heat transfers most efficiently from the shell perimeter, but the core area stays chilly. At this velocity, the laminar flow occurs with slightly less constraint than at 0.2 m/s.

Increased water movement at 0.6 m/s maintains laminar flow but reduces water exposure time to heating surfaces. Improved mixing performance happens because of faster velocity in laminar flow conditions. An improved convective heat transfer occurs since the slower speed boundary layer has reduced in intensity at this higher speed. The temperature spreads evenly around the perimeter due to the boosted convective heat transfer aspects achieved through velocity acceleration. The flowing fluid mixes better with increased velocity, improving how heat passes from the wall to the bulk of the liquid. The increase in velocity sustains laminar flow patterns; however, it results in superior convective heat transfer than at the 0.2 m/s velocity. Heat transfer efficiency receives better results near the shell wall through these enhancements. Overall performance of the heat exchanger shows improvement, even though the center shell temperature stays cooler than the surrounding areas.

According to Figure 7(C), the temperature profile at 1 m/s creates a smooth distribution of temperature throughout the shell wall. The shell undergoes a less significant temperature difference while obtaining distributed heat evenly. The central area reaches a higher temperature than 0.2 m/s and 0.6 m/s conditions, but shows minimal temperature variations. The improved convective heat transfer and better mixing occur because increased speed maintains laminar flow but delivers stronger fluid movement. The velocity increase causes the closest fluid layer to the wall to reduce thickness, which enhances heat transfer between the wall and the fluid. The lower thermal boundary layer created by a 1 m/s velocity allows more time for fluid particles to combine with nearby particles. The wall heat transfer to the center achieves better efficiency through a uniform temperature distribution. This increased velocity level can reach a hotter operation, which improves the heat exchanger performance. The shell surface benefits the most from the faster fluid movement because it improves transfer efficiency. Although the laminar flow maintains flow patterns, the heat exchanger has yet to achieve the maximum performance that would occur through turbulent flow conditions [30].

Figure 7. Cold water inside the shell inlet (A) at 0.2 m/s, (B) at 0.6 m/s, and (C) at 1 m/s

4.5 Outer shell outlet temperature profile analyses

Knowledge of how the inlet velocities at 0.2 m/s, 0.6 m/s, and 1 m/s affect heat transfer and temperature profiles in the cold water outlet of the heat exchanger under laminar flow conditions is required to analyze the temperature profile in Figures 8(A), (B), and (C). Laminar flow characterizes the conditions in all three cases. The fluid moves smoothly, meaning heat transfer mainly happens through conduction between the fluids, as weak convection has minimal effect compared to turbulent flow. Figure 8 shows the temperature distribution at the shell domain's cold water outlet section. Heat absorption from hot water within helical tubes causes a temperature increase of the fluid from 10℃ at its inlet to the outlet temperature [31]. Figure 8(A) shows substantial temperature variation resulting in an outlet temperature measurement of 31℃ while the inlet temperature was 10℃. The temperature drops extensively between the inlet and the terminating point at the outlet. The prolonged stay of cold water in the shell at 0.2 m/s velocity enables it to absorb significant heat from the tube's hot water, increasing the temperature. Due to the slow-moving fluid velocity, the thermal boundary layer near the shell wall becomes thicker, which impedes fluid mixing. The laminar flow restricts heat transfer through its thermal boundary layer because the fluid in proximity to walls flows poorly and does not exchange effectively with bulk fluid motion. The low efficiency of the heat exchanger appears because convective heat transfer occurs inadequately. The temperature gradient becomes too steep, thus diminishing the heat transfer effectiveness, allowing cold water near the wall to receive little heat. Temperature distribution in Figure 8(B) displays a less steep temperature gradient than 0.2 m/s conditions until reaching a final outlet value of 24.9℃. The temperature increase happens at a steady pace over the whole length of the path. A rise in flow velocity to 0.6 m/s creates a reduced thermal boundary layer that improves convective heat transfer. The laminar fluid flow becomes enhanced by higher velocity, which creates better fluid mixing that accelerates heat exchange between the tube-contained hot water and shell-contained cold water. When the velocity increases to 0.6 m/s, the mixing occurs more effectively than at lower speeds, even though the fluid remains near the wall surface. The heat exchanger displays better operational efficiency than at 0.2 m/s flow velocity. The smooth temperature gradient shows enhanced heat transfer, but steady flow retains insufficient turbulent characteristics for maximum heat exchange.

Figure 8. Shell cold water outlet profile (A) at 0.2 m/s, (B) at 0.6 m/s, and (C) at 1 m/s

The measured temperatures in Figure 8(℃) at the outlet indicate a uniform distribution that extends from 20.68℃ to 22.87℃. The temperature increase remains considerably lower than the lower velocity scenarios. At a velocity of 1 m/s, the cold water inside the shell sufficiently mixes throughout the entire area. The laminar flow pattern becomes thinner at these faster flow velocities, thereby improving thermal boundary layer heat exchange efficiency. The wall-connecting cold water mass more efficiently blends with the bulk fluid, producing less temperature variation and evenly distributing temperature throughout the domain. The observed heat exchange performance in this case reaches its peak rate. The thermal boundary layers generate reduced efficiency when the cold water absorbs heat evenly from the solution, according to the measurements. Under laminar flow conditions, convective heat transfer reaches its peak value, thus making it the most efficient of the three cases [32].

4.6 Key parameters affect heat transfer performance analysis

The current study utilizes copper (Cu) as a working substance, whereby the thermal conductivity value has been set at 401 W/m·K. Since the thermal conductivity is a very velocity-sensitive parameter, any difference can make a big difference in heat-transfer performance; hence, even small differences like that between pure Cu and the Cu alloys. To explicitly show this sensitivity, a set of numerical simulations was made by systematically changing the thermal conductivity of Cu in the domain of 300W/m·K–450W/m·K, resulting in a clear enhancement in the heat-transfer performance: the exiting temperatures were elevated, as well as a direct rise in thermal overall performance. The working fluid under implementation is water with a density of 975 kg/m³ and a dynamic viscosity of 0.355 × 10^-3 kg/m·s at the temperature of 77℃. Similar computations were carried out with glycerol-water mixtures, oils, and nanofluids based on similar densities and viscosities. An increase in viscosity thickens the boundary layer and reduces convective heat transfer, but additions of nanofluid, like water-based multi-walled carbon nanotubes (MWCNTs) or silicon dioxide (SiO₂) in the nanofluids can increase the limit of thermal properties and consequently increase the heat transfer. The helical coils with a diameter of 5 mm and a length of 145 mm were tested. Their ability in regards to promoting heat interchange was examined based on turn count. Extra turns increase thermal efficiency, but at the same time increase pressure drop. Besides, coil diameters that are varied on outer and inner surfaces were scrutinized in order to study the effect of the geometrical variation on the fluid flow and heat transfer. The smaller the diameter of the coil, the more it causes turbulent conditions to develop, which promotes the transfer by providing an additional heat source, but causes greater frictional losses. At last, the investigators adjusted the shell diameter and length to explain the individual impacts of it on the total heat-exchanger efficiency; increasing the shell also adds heat-transfer surface area, which, on the other hand, also spikes the corresponding frictional losses. Present studies have revealed that there is laminar flow in the studied channel when Re is in the range 275–1374. Of greater interest to understand the effects of high velocities on heat transfer would be further study of the transitional zone (2000 to 4000). Of particular interest are velocities of the range 1.2–1.5 m/s when the flow in the system should change to transitional or even turbulent flow. Determining this range of velocities would optimize the heat transfer with little pressure loss. This extension of the work would add a lot of strength to the knowledge of heat transfer in the baffled, inclined channels.

Table 8 below outlines how key parameters, thermal conductivity, fluid properties, geometrical configurations, and inlet velocities, impact the heat transfer performance of a multi-helical tube and shell heat exchanger under laminar flow conditions.

Table 8. A vital parameter sensitivity analysis that alters the heat transfer performance in multi-helical tube heat exchangers

The research under consideration makes it clear that the multi-helical tube designs have the potential to perform heat transfer in a compact heat exchanger exceptionally well, especially when the liquid-phase laminar flow is dominant. These configurations are particularly relevant to building and vehicle HVAC applications, pharmaceutical and food processing equipment, small chemical reactors, and preheating or economizing power station surfaces. The performance advantage observed at low Re also aligns well with its uses, where compact geometry and low pumping power are essential. To be applied practically, upgrading a bench-scale test to a full-scale industrial setting requires careful consideration of several points. Table 13 summarizes the impacts of these factors on the different heat exchanger parameters.

Table 13. Key scale-up factors to consider

In multi-coil configurations (heat exchanger systems), which are commonly used due to the high thermo-efficiency, the multiple fluid channels involve an internal cleaning and inspection, which may lead to complicated issues. As a result, extensive maintenance procedures should include adapting non-destructive testing procedures, including ultrasonic testing, and designing modular properties that allow disassembly. Although helical tubes can alleviate fouling through the generation of secondary flows, the accumulation of deposits caused by hard water, organic deposits, or particulate matter in the air can become an obstacle to a longer statistically expected service life, especially of the cold side of the fluid. Anti-fouling coatings, regular chemical clean-up, and pre-treatment of the water should be used to reduce the possibility of deteriorating the performance of the process in industrial practice. The stress levels are increased in thermal-cycled systems (e.g., start-up and shut-down), with high stress concentrations at the coil interface or bend. Hence, the CFD simulation model must be complemented with Finite Element Analysis (FEA) to compute the stress level under cyclic thermal loading. Temperature control, flow control, and temperature uniformity in large generation systems require sophisticated control architecture. Flow maldistribution between several helices may cause local overheating or underperformance. The results of CFD support the greater thermal efficiency of multi-helical tube exchangers with laminar flow., Still, the industry must allow geometric limitations during scaling, pressure drops, energy requirements, endurance of desired material compositions, and other long-run operational difficulties like fouling and repair. Another sensible step warranted in the future is to conduct pilot testing on a larger scale and to include multi-physics effects, namely fluid, thermal, and structural, to ensure robustness and durability of the systems.

The CFD simulation study on a multi-helical tube and shell heat exchanger shows that the speed of the fluid entering the system greatly affects how well heat is transferred, the thickness of the boundary layer, and the overall performance of the heat exchanger. The study also demonstrates how different fluid flow speeds affect temperature spread and heat transfer, highlighting the interplay between fluid movement and design features.

1. Based on CFD simulation results, the heat exchanger worked much better when the fluid speed at the entrance was increased from 0.2 m/s to 1 m/s. Heat transfer became restricted due to the thick thermal boundary layer, but wider velocity flow reduced this, improving convective heat transfer properties. Temperature patterns reached uniformity at 0.6 m/s, and the thermal gradient gap between inlet and outlet points declined. The system achieved maximum efficiency at 1 m/s due to enhanced mixing conditions and decreased temperature gradients.
2. In this study, it became clear that the boundary layer functions as the key factor in the heat transfer process during laminar flow. The shell experienced a significant temperature gradient at 0.2 m/s because the boundary layer was thick at this velocity. The prevailing heat transfer mode within this layer depended mainly on conduction and not convection, even though both conduct heat differently. The thinner boundary layer developed when velocity conditions increased, leading to greater convective heat transfer dominance. The hot fluid adjacent to the wall gained heat more efficiently because a higher fluid flow velocity existed. Heat exchanger theory explains this result because increased fluid motion produces faster heat transfer performance.
3. The temperature measurements at the cold water outlet depended strongly on the velocity at which water entered the tube. The system released the cold water at 31℃ at 0.2 m/s but dropped to 22℃ at 1 m/s. The system becomes more efficient at increased velocities because the temperature distribution becomes more equal. Increasing velocity enhanced cold water mixing inside the shell, creating better thermal contact between the cold fluid and the tube wall. A minimal rise in temperature difference occurred between the wall and core region fluid, which promoted an enhanced heat exchange process.
4. The form of the helical tubes proved vital for advancing thermal performance. The coil geometry affected heat transfer the most strongly under turbulent flow; however, studies revealed that secondary flow patterns provided marginal mixing benefits in laminar flow. Secondary flow patterns formed within the helical coils broke the boundary layer closest to the wall and enabled a small enhancement in heat transfer rate. The observed improvement in this case was less noticeable compared to turbulent flow conditions, where these secondary flows produce greater effects on convective heat transfer.
5. The simulations indicated that each case had smooth, steady flow (Re < 2000), with Re of 275, 824, and 1374 for the speeds of 0.2 m/s, 0.6 m/s, and 1 m/s. The heat exchanger presented a parabolic flow pattern, which is characteristic of laminar flow patterns. Re showed a direct impact that determined both the dimension of boundary layer formation and the heat transfer rate capabilities. The smooth flow continued while the inlet speed increased to raise the Re, causing the thermal boundary layer to become thinner, resulting in better heat transfer performance.