304 stainless steel coiled tubing chemical component ,Thermodynamic analysis of covalently and non-covalently functionalized graphene nanosheets in round tubes equipped with turbulators

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304 10*1mm Stainless steel coiled tubing in china

Size: 3/4 inch, 1/2 inch, 1 inch, 3 inch, 2 inch

Unit Pipe Length: 6 meter

Steel Grade: 201, 304 AND 316

Grade: 201, 202, 304, 316, 304L, 316 L,

Material: STAINLESS STEEL

Condition: New

Covalent and non-covalent nanofluids were tested in round tubes equipped with twisted tape inserts with helix angles of 45° and 90°. The Reynolds number was 7000 ≤ Re ≤ 17000, the thermophysical properties were evaluated at 308 K. The physical model is solved numerically using a two-parameter turbulent viscosity model (SST k-omega turbulence). The concentrations (0.025 wt.%, 0.05 wt.%, and 0.1 wt.%) of the nanofluids ZNP-SDBS@DV and ZNP-COOH@DV were considered in the work. The walls of the twisted tubes are heated at a constant temperature of 330 K. Six parameters were considered in the current study: outlet temperature, heat transfer coefficient, average Nusselt number, coefficient of friction, pressure loss, and performance evaluation criteria. In both cases (helix angle of 45° and 90°), the ZNP-SDBS@DV nanofluid showed higher thermal-hydraulic characteristics than ZNP-COOH@DV, and it increased with increasing mass fraction, for example, 0.025 wt. , and 0.05 wt. is 1.19. % and 1.26 – 0.1 wt.%. In both cases (helix angle 45° and 90°), the values ​​of thermodynamic characteristics when using GNP-COOH@DW are 1.02 for 0.025% wt., 1.05 for 0.05% wt. and 1.02 for 0.1% wt.
The heat exchanger is a thermodynamic device 1 used to transfer heat during cooling and heating operations. The thermal-hydraulic properties of the heat exchanger improve the heat transfer coefficient and reduce the resistance of the working fluid. Several methods have been developed to improve heat transfer, including turbulence enhancers2,3,4,5,6,7,8,9,10,11 and nanofluids12,13,14,15. Twisted tape insertion is one of the most successful methods for improving heat transfer in heat exchangers due to its ease of maintenance and low cost7,16.
In a series of experimental and computational studies, the hydrothermal properties of mixtures of nanofluids and heat exchangers with twisted tape inserts were studied. In an experimental work, the hydrothermal properties of three different metallic nanofluids (Ag@DW, Fe@DW and Cu@DW) were studied in a needle twisted tape (STT) heat exchanger17. Compared with the base pipe, the heat transfer coefficient of STT is improved by 11% and 67%. The SST layout is the best from an economic point of view in terms of efficiency with the parameter α = β = 0.33. In addition, an 18.2% increase in n was observed with Ag@DW, although the maximum increase in pressure loss was only 8.5%. The physical processes of heat transfer and pressure loss in concentric pipes with and without coiled turbulators were studied using turbulent flows of Al2O3@DW nanofluid with forced convection. The maximum average Nusselt number (Nuavg) and pressure loss are observed at Re = 20,000 when the coil pitch = 25 mm and Al2O3@DW nanofluid 1.6 vol.%. Laboratory studies have also been conducted to study the heat transfer and pressure loss characteristics of graphene oxide nanofluids (GO@DW) flowing through nearly circular tubes with WC inserts. The results showed that 0.12 vol%-GO@DW increased the convective heat transfer coefficient by about 77%. In another experimental study, nanofluids (TiO2@DW) were developed to study the thermal-hydraulic characteristics of dimpled tubes fitted with twisted tape inserts20. The maximum hydrothermal efficiency of 1.258 was achieved using 0.15 vol%-TiO2@DW embedded in 45° inclined shafts with a twist factor of 3.0. Single-phase and two-phase (hybrid) simulation models take into account the flow and heat transfer of CuO@DW nanofluids at various solids concentrations (1–4% vol.%)21. The maximum thermal efficiency of a tube inserted with one twisted tape is 2.18, and a tube inserted with two twisted tapes under the same conditions is 2.04 (two-phase model, Re = 36,000 and 4 vol.%). The non-Newtonian turbulent nanofluid flow of carboxymethyl cellulose (CMC) and copper oxide (CuO) in main pipes and pipes with twisted inserts has been studied. Nuavg shows an improvement of 16.1% (for the main pipeline) and 60% (for the coiled pipeline with a ratio of (H/D = 5)). Generally, a lower twist-to-ribbon ratio results in a higher coefficient of friction. In an experimental study, the effect of pipes with a twisted tape (TT) and coils (VC) on the properties of heat transfer and friction coefficient was studied using CuO@DW nanofluids. Using 0.3 vol. %-CuO@DW at Re = 20,000 makes it possible to increase the heat transfer in the VK-2 pipe to a maximum value of 44.45%. In addition, when using a twisted pair cable and a coil insert under the same boundary conditions, the coefficient of friction increases by factors of 1.17 and 1.19 compared to DW. In general, the thermal efficiency of nanofluids inserted into coils is better than that of nanofluids inserted into stranded wires. The volumetric characteristic of a turbulent (MWCNT@DW) nanofluid flow was studied inside a horizontal tube inserted into a spiral wire. The thermal performance parameters were > 1 for all cases, indicating that the combination of nanofluidics with the coil insert improves heat transfer without consuming pump power. Abstract—The hydrothermal characteristics of a two-pipe heat exchanger with various inserts made of a modified twisted-twisted V-shaped tape (VcTT) have been studied under conditions of a turbulent flow of the Al2O3 + TiO2@DW nanofluid. Compared to DW in base tubes, Nuavg has a significant improvement of 132% and a friction coefficient of up to 55%. In addition, the energy efficiency of the Al2O3+TiO2@DW nanocomposite in a two-pipe heat exchanger26 was discussed. In their study, they found that the use of Al2O3 + TiO2@DW and TT improved exergy efficiency compared to DW. In concentric tubular heat exchangers with VcTT turbulators, Singh and Sarkar27 used phase change materials (PCM), dispersed single/nanocomposite nanofluids (Al2O3@DW with PCM and Al2O3 + PCM). They reported that heat transfer and pressure loss increase as the twist coefficient decreases and the nanoparticle concentration increases. A larger V-notch depth factor or a smaller width factor can provide greater heat transfer and pressure loss. In addition, graphene-platinum (Gr-Pt) has been used to investigate heat, friction, and overall entropy generation rate in tubes with 2-TT28 inserts. Their study showed that a smaller percentage of (Gr-Pt) significantly reduced heat entropy generation compared to a relatively higher frictional entropy development. Mixed Al2O3@MgO nanofluids and conical WC can be considered as a good mixture, since an increased ratio (h/Δp) can improve the hydrothermal performance of a two-tube heat exchanger 29 . A numerical model is used to evaluate the energy-saving and environmental performance of heat exchangers with various three-part hybrid nanofluids (THNF) (Al2O3 + graphene + MWCNT) suspended in DW30. Due to its Performance Evaluation Criteria (PEC) in the range of 1.42–2.35, a combination of Depressed Twisted Turbulizer Insert (DTTI) and (Al2O3 + Graphene + MWCNT) is required.
Until now, little attention has been paid to the role of covalent and non-covalent functionalization in hydrodynamic flow in thermal fluids. The specific purpose of this study was to compare the thermal-hydraulic characteristics of nanofluids (ZNP-SDBS@DV) and (ZNP-COOH@DV) in twisted tape inserts with helix angles of 45° and 90°. The thermophysical properties were measured at Tin = 308 K. In this case, three mass fractions were taken into account in the comparison process, such as (0.025 wt.%, 0.05 wt.% and 0.1 wt.%). The shear stress transfer in the 3D turbulent flow model (SST k-ω) is used to solve the thermal-hydraulic characteristics. Thus, this study makes a significant contribution to the study of positive properties (heat transfer) and negative properties (pressure drop on friction), demonstrating the thermal-hydraulic characteristics and optimization of real working fluids in such engineering systems.
The basic configuration is a smooth pipe (L = 900 mm and Dh = 20 mm). Inserted twisted tape dimensions (length = 20 mm, thickness = 0.5 mm, profile = 30 mm). In this case, the length, width, and stroke of the spiral profile were 20 mm, 0.5 mm, and 30 mm, respectively. The twisted tapes are inclined at 45° and 90°. Various working fluids such as DW, non-covalent nanofluids (GNF-SDBS@DW) and covalent nanofluids (GNF-COOH@DW) at Tin = 308 K, three different mass concentrations and different Reynolds numbers. The tests were carried out inside the heat exchanger. The outer wall of the spiral tube was heated at a constant surface temperature of 330 K to test the parameters for improving heat transfer.
On fig. 1 schematically shows a twisted tape insertion tube with applicable boundary conditions and meshed area. As mentioned earlier, velocity and pressure boundary conditions apply to the inlet and outlet portions of the helix. At a constant surface temperature, a non-slip condition is imposed on the pipe wall. The current numerical simulation uses a pressure-based solution. At the same time, a program (ANSYS FLUENT 2020R1) is used to convert a partial differential equation (PDE) into a system of algebraic equations using the finite volume method (FMM). The second-order SIMPLE method (semi-implicit method for sequential pressure-dependent equations) is related to velocity-pressure. It should be emphasized that the convergence of residuals for the mass, momentum, and energy equations is less than 103 and 106, respectively.
p Diagram of physical and computational domains: (a) helix angle 90°, (b) helix angle 45°, (c) no helical blade.
A homogeneous model is used to explain the properties of nanofluids. By incorporating nanomaterials into the base fluid (DW), a continuous fluid with excellent thermal properties is formed. In this regard, the temperature and velocity of the base fluid and the nanomaterial have the same value. Due to the above theories and assumptions, efficient single-phase flow works in this study. Several studies have demonstrated the effectiveness and applicability of single-phase techniques for nanofluidic flow31,32.
The flow of nanofluids must be Newtonian turbulent, incompressible and stationary. Compression work and viscous heating are irrelevant in this study. In addition, the thickness of the inner and outer walls of the pipe is not taken into account. Therefore, the mass, momentum, and energy conservation equations that define the thermal model can be expressed as follows:
where \(\overrightarrow{V}\) is the mean velocity vector, Keff = K + Kt is the effective thermal conductivity of covalent and noncovalent nanofluids, and ε is the energy dissipation rate. The effective thermophysical properties of nanofluids, including density (ρ), viscosity (μ), specific heat capacity (Cp) and thermal conductivity (k), shown in the table, were measured during an experimental study at a temperature of 308 K1 when used in these simulators.
Numerical simulations of turbulent nanofluid flow in conventional and TT tubes were performed at Reynolds numbers 7000 ≤ Re ≤ 17000. These simulations and convective heat transfer coefficients were analyzed using Mentor’s κ-ω turbulence model of shear stress transfer (SST) averaged over the Reynolds turbulence model Navier-Stokes, commonly used in aerodynamic research. In addition, the model works without wall function and is accurate near walls 35,36. (SST) κ-ω governing equations of the turbulence model are as follows:
where \(S\) is the value of the strain rate, and \(y\) is the distance to the adjacent surface. Meanwhile, \({\alpha}_{1}\), \({\alpha}_{2}\), \({\beta}_{1}\), \({\beta}_{ 2 }\), \({\beta}^{*}\), \({\sigma}_{{k}_{1}}\), \({\sigma}_{{k}_{ 2 }}\), \({\sigma}_{{\omega}_{1}}\) and \({\sigma}_{{\omega}_{2}}\) denote all model constants. F1 and F2 are mixed functions. Note: F1 = 1 in the boundary layer, 0 in the oncoming flow.
Performance evaluation parameters are used to study turbulent convective heat transfer, covalent and non-covalent nanofluid flow, for example31:
In this context, (\(\rho\)), (\(v\)), (\({D}_{h}\)) and (\(\mu\)) are used for density, fluid velocity, hydraulic diameter and dynamic viscosity. (\({C}_{p}\, \mathrm{u}\, k\)) – specific heat capacity and thermal conductivity of the flowing fluid. Also, (\(\dot{m}\)) refers to mass flow, and (\({T}_{out}-{T}_{in}\)) refers to inlet and outlet temperature difference. (NFs) refers to covalent, non-covalent nanofluids, and (DW) refers to distilled water (base fluid). \({A}_{s} = \pi DL\), \({\overline{T}}_{f}=\frac{\left({T}_{out}-{T}_{in }\right)}{2}\) and \({\overline{T}}_{w}=\sum \frac{{T}_{w}}{n}\).
The thermophysical properties of the base fluid (DW), non-covalent nanofluid (GNF-SDBS@DW), and covalent nanofluid (GNF-COOH@DW) were taken from the published literature (experimental studies), Sn = 308 K, as shown in Table 134. In a typical In an experiment to obtain a non-covalent (GNP-SDBS@DW) nanofluid with known mass percentages, certain grams of primary GNPs were initially weighed on a digital balance. The weight ratio of SDBS/native GNP is (0.5:1) weighted in DW. In this case, covalent (COOH-GNP@DW) nanofluids were synthesized by adding carboxyl groups to the surface of GNP using a strongly acidic medium with a volume ratio (1:3) of HNO3 and H2SO4. Covalent and non-covalent nanofluids were suspended in DW at three different weight percentages such as 0.025 wt%, 0.05 wt%. and 0.1% of the mass.
Mesh independence tests were carried out in four different computational domains to ensure that the mesh size does not affect the simulation. In the case of 45° torsion pipe, the number of units with unit size 1.75 mm is 249,033, the number of units with unit size 2 mm is 307,969, the number of units with unit size 2.25 mm is 421,406, and the number of units with unit size 2 .5 mm 564 940 respectively. In addition, in the example of a 90° twisted pipe, the number of elements with a 1.75 mm element size is 245,531, the number of elements with a 2 mm element size is 311,584, the number of elements with a 2.25 mm element size is 422,708, and the number of elements with an element size of 2.5 mm is respectively 573,826. The accuracy of thermal property readings such as (Tout, htc, and Nuavg) increases as the number of elements decreases. At the same time, the accuracy of the values ​​of the friction coefficient and pressure drop showed a completely different behavior (Fig. 2). Grid (2) was used as the main grid area to evaluate the thermal-hydraulic characteristics in the simulated case.
Testing heat transfer and pressure drop performance independently of mesh using pairs of DW tubes twisted at 45° and 90°.
The present numerical results have been validated for heat transfer performance and friction coefficient using well known empirical correlations and equations such as Dittus-Belter, Petukhov, Gnelinsky, Notter-Rouse and Blasius. The comparison was carried out under the condition 7000≤Re≤17000. According to fig. 3, the average and maximum errors between the simulation results and the heat transfer equation are 4.050 and 5.490% (Dittus-Belter), 9.736 and 11.33% (Petukhov), 4.007 and 7.483% (Gnelinsky), and 3.883% and 4.937% (Nott-Belter). Rose). In this case, the average and maximum errors between the simulation results and the friction coefficient equation are 7.346% and 8.039% (Blasius) and 8.117% and 9.002% (Petukhov), respectively.
Heat transfer and hydrodynamic properties of DW at various Reynolds numbers using numerical calculations and empirical correlations.
This section discusses the thermal properties of non-covalent (LNP-SDBS) and covalent (LNP-COOH) aqueous nanofluids at three different mass fractions and Reynolds numbers as averages relative to the base fluid (DW). Two geometries of coiled belt heat exchangers (helix angle 45° and 90°) are discussed for 7000 ≤ Re ≤ 17000. In fig. 4 shows the average temperature at the exit of the nanofluid into the base fluid (DW) (\(\frac{{{T}_{out}}_{NFs}}{{{T}_{out}}_{DW } } \) ) at (0.025% wt., 0.05% wt. and 0.1% wt.). (\(\frac{{{T}_{out}}_{NFs}}{{{T}_{out}}_{DW}}\)) is always less than 1, which means that the outlet temperature is non-covalent (VNP-SDBS) and covalent (VNP-COOH) nanofluids are below the temperature at the outlet of the base liquid. The lowest and highest reductions were 0.1 wt%-COOH@GNPs and 0.1 wt%-SDBS@GNPs, respectively. This phenomenon is due to an increase in the Reynolds number at a constant mass fraction, which leads to a change in the properties of the nanofluid (that is, density and dynamic viscosity).
Figures 5 and 6 show the average heat transfer characteristics of nanofluid to base fluid (DW) at (0.025 wt.%, 0.05 wt.% and 0.1 wt.%). The average heat transfer properties are always greater than 1, which means that the heat transfer properties of non-covalent (LNP-SDBS) and covalent (LNP-COOH) nanofluids are enhanced compared to the base fluid. 0.1 wt%-COOH@GNPs and 0.1 wt%-SDBS@GNPs achieved the lowest and highest gain, respectively. When the Reynolds number increases due to greater fluid mixing and turbulence in the pipe 1, the heat transfer performance improves. Fluids through small gaps reach higher velocities, resulting in a thinner velocity/heat boundary layer, which increases the rate of heat transfer. Adding more nanoparticles to the base fluid can have both positive and negative results. Beneficial effects include increased nanoparticle collisions, favorable fluid thermal conductivity requirements, and enhanced heat transfer.
Heat transfer coefficient of nanofluid to base fluid depending on Reynolds number for 45° and 90° tubes.
At the same time, a negative effect is an increase in the dynamic viscosity of the nanofluid, which reduces the mobility of the nanofluid, thereby reducing the average Nusselt number (Nuavg). The increased thermal conductivity of nanofluids (ZNP-SDBS@DW) and (ZNP-COOH@DW) should be due to Brownian motion and microconvection of graphene nanoparticles suspended in DW37. The thermal conductivity of the nanofluid (ZNP-COOH@DV) is higher than that of the nanofluid (ZNP-SDBS@DV) and distilled water. Adding more nanomaterials to the base fluid increases their thermal conductivity (Table 1)38.
Figure 7 illustrates the average coefficient of friction of nanofluids with base fluid (DW) (f(NFs)/f(DW)) in mass percent (0.025%, 0.05% and 0.1%). The average friction coefficient is always ≈1, which means that non-covalent (GNF-SDBS@DW) and covalent (GNF-COOH@DW) nanofluids have the same friction coefficient as the base fluid. A heat exchanger with less space creates more flow obstruction and increases flow friction1. Basically, the coefficient of friction increases slightly with increasing mass fraction of the nanofluid. The higher frictional losses are caused by the increased dynamic viscosity of the nanofluid and the increased shear stress on the surface with a higher mass percentage of nanographene in the base fluid. Table (1) shows that the dynamic viscosity of the nanofluid (ZNP-SDBS@DV) is higher than that of the nanofluid (ZNP-COOH@DV) at the same weight percentage, which is associated with the addition of surface effects. active agents on a non-covalent nanofluid.
On fig. 8 shows nanofluid compared to base fluid (DW) (\(\frac{{\Delta P}_{NFs}}{{\Delta P}_{DW}}\)) at (0.025%, 0.05% and 0.1%). The non-covalent (GNPs-SDBS@DW) nanofluid showed a higher average pressure loss, and with an increase in mass percentage to 2.04% for 0.025% wt., 2.46% for 0.05% wt. and 3.44% for 0.1% wt. with case enlargement (helix angle 45° and 90°). Meanwhile, the nanofluid (GNPs-COOH@DW) showed a lower average pressure loss, increasing from 1.31% at 0.025% wt. up to 1.65% at 0.05% wt. The average pressure loss of 0.05 wt.%-COOH@NP and 0.1 wt.%-COOH@NP is 1.65%. As can be seen, the pressure drop increases with increasing Re number in all cases. An increased pressure drop at high Re values ​​is indicated by a direct dependence on the volume flow. Therefore, a higher Re number in the tube leads to a higher pressure drop, which requires an increase in pump power39,40. In addition, pressure losses are higher due to the higher intensity of eddies and turbulence generated by the larger surface area, which increases the interaction of pressure and inertia forces in the boundary layer1.
In general, performance evaluation criteria (PEC) for non-covalent (VNP-SDBS@DW) and covalent (VNP-COOH@DW) nanofluids are shown in Figs. 9. Nanofluid (ZNP-SDBS@DV) showed higher PEC values ​​than (ZNP-COOH@DV) in both cases (helix angle 45° and 90°) and it was improved by increasing the mass fraction, for example, 0.025 wt.%. is 1.17, 0.05 wt.% is 1.19 and 0.1 wt.% is 1.26. Meanwhile, the PEC values ​​using nanofluids (GNPs-COOH@DW) were 1.02 for 0.025 wt%, 1.05 for 0.05 wt%, 1.05 for 0.1 wt%. in both cases (helix angle 45° and 90°). 1.02. As a rule, with an increase in the Reynolds number, the thermal-hydraulic efficiency decreases significantly. As the Reynolds number increases, the decrease in the thermal-hydraulic efficiency coefficient is systematically associated with an increase in (NuNFs/NuDW) and a decrease in (fNFs/fDW).
Hydrothermal properties of nanofluids with respect to base fluids depending on Reynolds numbers for tubes with 45° and 90° angles.
This section discusses the thermal properties of water (DW), non-covalent (VNP-SDBS@DW), and covalent (VNP-COOH@DW) nanofluids at three different mass concentrations and Reynolds numbers. Two coiled belt heat exchanger geometries were considered in the range 7000 ≤ Re ≤ 17000 with respect to conventional pipes (helix angles 45° and 90°) to evaluate the average thermal-hydraulic performance. On fig. 10 shows the temperature of water and nanofluids at the outlet as an average using (helix angle 45° and 90°) for a common pipe (\(\frac{{{T}_{out}}_{Twisted}}{{ {T} _{out}}_{Regular}}\)). Non-covalent (GNP-SDBS@DW) and covalent (GNP-COOH@DW) nanofluids have three different weight fractions such as 0.025 wt%, 0.05 wt% and 0.1 wt%. As shown in fig. 11, the average value of the outlet temperature (\(\frac{{{T}_{out}}_{Twisted}}{{{T}_{out}}_{Plain}}\)) > 1, indicating that (45° and 90° helix angle) the temperature at the outlet of the heat exchanger is more significant than that of a conventional pipe, due to the greater intensity of turbulence and better mixing of the liquid. In addition, the temperature at the outlet of DW, non-covalent and covalent nanofluids decreased with increasing Reynolds number. The base fluid (DW) has the highest mean outlet temperature. Meanwhile, the lowest value refers to 0.1 wt%-SDBS@GNPs. Non-covalent (GNPs-SDBS@DW) nanofluids showed a lower average outlet temperature compared to covalent (GNPs-COOH@DW) nanofluids. Since the twisted tape makes the flow field more mixed, the near-wall heat flux can more easily pass through the liquid, increasing the overall temperature. A lower twist-to-tape ratio results in better penetration and hence better heat transfer. On the other hand, it can be seen that the rolled tape maintains a lower temperature against the wall, which in turn increases the Nuavg. For twisted tape inserts, a higher Nuavg value indicates improved convective heat transfer within the tube22. Due to the increased flow path and additional mixing and turbulence, the residence time increases, resulting in an increase in the temperature of the liquid at the outlet41.
Reynolds numbers of various nanofluids relative to the outlet temperature of conventional tubes (45° and 90° helix angles).
Heat transfer coefficients (45° and 90° helix angle) versus Reynolds numbers for various nanofluids compared to conventional tubes.
The main mechanism of enhanced coiled tape heat transfer is as follows: 1. Reducing the hydraulic diameter of the heat exchange tube leads to an increase in flow velocity and curvature, which in turn increases shear stress at the wall and promotes secondary movement. 2. Due to blockage of the winding tape, the speed at the pipe wall increases, and the thickness of the boundary layer decreases. 3. Spiral flow behind the twisted belt leads to an increase in speed. 4. Induced vortices improve fluid mixing between the central and near-wall regions of the flow42. On fig. 11 and fig. 12 shows the heat transfer properties of DW and nanofluids, for example (heat transfer coefficient and average Nusselt number) as averages using twisted tape insertion tubes compared to conventional tubes. Non-covalent (GNP-SDBS@DW) and covalent (GNP-COOH@DW) nanofluids have three different weight fractions such as 0.025 wt%, 0.05 wt% and 0.1 wt%. In both heat exchangers (45° and 90° helix angle) the average heat transfer performance is >1, indicating an improvement in heat transfer coefficient and average Nusselt number with coiled tubes compared to conventional tubes. Non-covalent (GNPs-SDBS@DW) nanofluids showed higher average heat transfer improvement than covalent (GNPs-COOH@DW) nanofluids. At Re = 900, the 0.1 wt% improvement in heat transfer performance -SDBS@GNPs for the two heat exchangers (45° and 90° helix angle) was the highest with a value of 1.90. This means that the uniform TP effect is more important at lower fluid velocities (Reynolds number)43 and increasing turbulence intensity. Due to the introduction of multiple vortices, the heat transfer coefficient and average Nusselt number of TT tubes are higher than conventional tubes, resulting in a thinner boundary layer. Does the presence of HP increase the intensity of turbulence, mixing of working fluid flows and enhanced heat transfer compared to base pipes (without inserting a twisted-twisted tape)21.
Average Nusselt number (helix angle 45° and 90°) versus Reynolds number for various nanofluids compared to conventional tubes.
Figures 13 and 14 show the average coefficient of friction (\(\frac{{f}_{Twisted}}{{f}_{Plain}}\)) and pressure loss (\(\frac{{\Delta P} _ {Twisted}}{{\Delta P}_{Plain}}\}} about 45° and 90° for conventional pipes using DW nanofluids, (GNPs-SDBS@DW) and (GNPs-COOH@DW) ion exchanger contains ( 0.025 wt %, 0.05 wt % and 0.1 wt %). { {f}_{Plain} }\)) and pressure loss (\(\frac{{ \Delta P}_{Twisted}}{{\Delta P}_{Plain}}\}) decrease. cases, the friction coefficient and pressure loss are higher at lower Reynolds numbers The average friction coefficient and pressure loss are between 3.78 and 3.12 The average friction coefficient and pressure loss show that (45° helix angle and 90°) heat exchanger cost three times higher than conventional pipes.In addition, when the working fluid flows at a higher speed, the coefficient of friction decreases. The problem arises because as the Reynolds number increases, the thickness of the boundary layer decreases, which leads to a decrease in the effect of dynamic viscosity on the affected area, a decrease in velocity gradients and shear stresses and, consequently, a decrease in the coefficient of friction21. The improved blocking effect due to the presence of TT and the increased swirl results in significantly higher pressure losses for heterogeneous TT pipes than for base pipes. In addition, for both the base pipe and the TT pipe, it can be seen that the pressure drop increases with the speed of the working fluid43.
Coefficient of friction (45° and 90° helix angle) versus Reynolds number for various nanofluids compared to conventional tubes.
Pressure loss (45° and 90° helix angle) as a function of Reynolds number for various nanofluids relative to a conventional tube.
In summary, Figure 15 shows performance evaluation criteria (PEC) for heat exchangers with 45° and 90° angles compared to plain tubes (\(\frac{{PEC}_{Twisted}}{{PEC}_{Plain}} \ ) ) in (0.025 wt.%, 0.05 wt.% and 0.1 wt.%) using DV, (VNP-SDBS@DV) and covalent (VNP-COOH@DV) nanofluids. The value (\(\frac{{PEC}_{Twisted}}{{PEC}_{Plain}}\)) > 1 in both cases (45° and 90° helix angle) in the heat exchanger. In addition, (\(\frac{{PEC}_{Twisted}}{{PEC}_{Plain}}\)) reaches its best value at Re = 11,000. The 90° heat exchanger shows a slight increase in (\ (\frac{{PEC}_{Twisted}}{{PEC}_{Plain}}\)) compared to a 45° heat exchanger. , At Re = 11,000 0.1 wt%-GNPs@SDBS represents higher (\(\frac{{PEC}_{Twisted}}{{PEC}_{Plain}}\)) values, e.g. 1.25 for 45° heat exchanger corner and 1.27 for 90° corner heat exchanger. It is greater than one at all percentages of mass fraction, which indicates that pipes with twisted tape inserts are superior to conventional pipes. Notably, the improved heat transfer provided by the tape inserts resulted in a significant increase in friction losses22.
Efficiency criteria for the Reynolds number of various nanofluids in relation to conventional tubes (45° and 90° helix angle).
Appendix A shows streamlines for 45° and 90° heat exchangers at Re = 7000 using DW, 0.1 wt%-GNP-SDBS@DW and 0.1 wt%-GNP-COOH@DW. The streamlines in the transverse plane are the most striking feature of the effect of twisted ribbon inserts on the main flow. The use of 45° and 90° heat exchangers shows that the velocity in the near-wall region is approximately the same. Meanwhile, Appendix B shows the velocity contours for 45° and 90° heat exchangers at Re = 7000 using DW, 0.1 wt%-GNP-SDBS@DW and 0.1 wt%-GNP-COOH@DW. The velocity loops are in three different locations (slices), for example, Plain-1 (P1 = −30mm), Plain-4 (P4 = 60mm) and Plain-7 (P7 = 150mm). The flow velocity near the pipe wall is lowest and the fluid velocity increases towards the center of the pipe. In addition, when passing through the air duct, the area of ​​low velocities near the wall increases. This is due to the growth of the hydrodynamic boundary layer, which increases the thickness of the low-velocity region near the wall. In addition, increasing the Reynolds number increases the overall velocity level in all cross sections, thereby reducing the thickness of the low velocity region in the channel39.
Covalently and non-covalently functionalized graphene nanosheets were evaluated in twisted tape inserts with helix angles of 45° and 90°. The heat exchanger is numerically solved using the SST k-omega turbulence model at 7000 ≤ Re ≤ 17000. The thermophysical properties are calculated at Tin = 308 K. Simultaneously heat the twisted tube wall at a constant temperature of 330 K. COOH@DV) was diluted in three mass amounts, for example (0.025 wt.%, 0.05 wt.% and 0.1 wt.%). The current study considered six main factors: outlet temperature, heat transfer coefficient, average Nusselt number, coefficient of friction, pressure loss, and performance evaluation criteria. Here are the main findings:
The average outlet temperature (\({{T}_{out}}_{Nanofluids}\)/\({{T}_{out}}_{Basefluid}\)) is always less than 1, which means that non-spread The outlet temperature of valence (ZNP-SDBS@DV) and covalent (ZNP-COOH@DV) nanofluids is lower than that of the base liquid. Meanwhile, the average outlet temperature (\({{T}_{out}}_{Twisted}\)/\({{T}_{out}}_{Plain}\)) value > 1, indicating to the fact that (45° and 90° helix angle) the outlet temperature is higher than with conventional tubes.
In both cases, the average values ​​of the heat transfer properties (nanofluid/base fluid) and (twisted tube/normal tube) always show >1. Non-covalent (GNPs-SDBS@DW) nanofluids showed a higher average increase in heat transfer, corresponding to covalent (GNPs-COOH@DW) nanofluids.
The average friction coefficient (\({f}_{Nanofluids}/{f}_{Basefluid}\)) of non-covalent (VNP-SDBS@DW) and covalent (VNP-COOH@DW) nanofluids is always ≈1. friction of non-covalent (ZNP-SDBS@DV) and covalent (ZNP-COOH@DV) nanofluids (\({f}_{Twisted}/{f}_{Plain}\)) for always > 3.
In both cases (45° and 90° helix angle), the nanofluids (GNPs-SDBS@DW) showed higher (\({\Delta P}_{Nanofluids}/{\Delta P}_{Basefluid}\)) 0.025 wt .% for 2.04%, 0.05 wt.% for 2.46% and 0.1 wt.% for 3.44%. Meanwhile, (GNPs-COOH@DW) nanofluids showed lower (\({\Delta P}_{Nanofluids}/{\Delta P}_{Basefluid}\)) from 1.31% for 0.025 wt.% to 1.65% is 0.05% by weight. In addition, the average pressure loss (\({\Delta P}_{Twisted}/{\Delta P}_{Plain}\) of non-covalent (GNPs-SDBS@DW) and covalent (GNPs-COOH@DW ))) nanofluids always >3.
In both cases (45° and 90° helix angles), the nanofluids (GNPs-SDBS@DW) showed a higher (\({PEC}_{Nanofluids}/{PEC} _{Basefluid}\)) @DW value), e.g. 0.025 wt.% – 1.17, 0.05 wt.% – 1.19, 0.1 wt.% – 1.26. In this case, the values ​​of (\({PEC}_{Nanofluids}/{PEC}_{Basefluid}\)) using (GNPs-COOH@DW) nanofluids are 1.02 for 0.025 wt.%, 1.05 for 0, 05 wt. % and 1.02 is 0.1% by weight. In addition, at Re = 11,000, 0.1 wt%-GNPs@SDBS showed higher values ​​(\({PEC}_{Twisted}/{PEC}_{Plain}\)), such as 1.25 for 45° helix angle and 90° helix angle 1.27.
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