#### Abstract

The present work used ANFIS, an adaptive neuro-fuzzy inference system modeling to analyze the effect of the variable parameters of helically pierced twisted tape inserts on the Nusselt number, friction factor, and thermo-hydraulic heat exchanger tube performance. The experimental data utilized for ANFIS modeling considered a diameter ratio ranging from 0.57 to 0.80, a relative pitch ratio ranging from 0.046 to 0.107, a perforation index ranging from 5% to 20% as variable twisted tape parameters and flow parameters. The Reynolds number varies from 4000 to 30000. The analysis showed that the maximum thermo-hydraulic performance was obtained at a diameter ratio of 0.65, a relative pitch ratio of 0.085, and a perforation index equal to 10%. The result predicts that the ANFIS model and experimental results are in good agreement as they have only ±0.53% deviations.

#### 1. Introduction

Heat exchangers are broadly utilized in designing applications, for example, refrigeration and cooling systems, automobiles, thermal power plants, textile and chemical handling industries, and so forth. The efficiency of the heat exchanger is decided on the basis of the effective heat transfer between two working fluids [1, 2]. Numerous methods and approaches were instigated for the augmentation of heat transfer to improve thermal efficiency. The ultimate aim of these approaches is to increase the heat transfer and provide the stability of the heat exchanger [3–6].

Rounded tubes are prominently used in most engineering industries because of their compact structure for a given available space [7, 8]. Nakhchi and Esfahani [9] studied experimentally the thermal performance of a heat exchanger tube fortified with cross-cut twisted tape using nanofluid. The outcomes showed that the thermal performance of nanofluid flow in the plain tube is lesser than the tubes equipped with the cross-cut twisted tapes. Xiaowen et al. [10] performed experimental studies on a domestic water-cooled air conditioner (WAC) and reported that the COP of WAC increases to 12.3% with the insertion of the heat recovery option. Ishak et al. [11] evaluated the Nusselts number for the bundles of the flat tube and found that increases, whereas the friction factor decreases, with an escalation in the mean air velocity. Fullerton and Anand [12] and Jang and Yang [13–16] analyzed the heat transfer enhancement techniques on the heat exchangers.

Modern investigations are more focused on soft computing fields and computational intelligence. Computational intelligence includes computational fluid dynamic (CFD), artificial neural networks (ANN), fuzzy inference system (FIS), genetic algorithm (GA), particle swarm optimization (PSO), and fuzzy logic [17]. The fuzzy sets play important role in artificial neural network [18] and inference system [19]. The fuzzy models can be pooled with ANN to produce ANFIS. The modeling of a nonlinear system is now quite easier with ANFIS as ANFIS has the benefits of neural and fuzzy logic systems [20, 21]. Kiran and Rajput [22] determined that soft computing tools, such as FIS, ANN, and ANFIS, provide a modest but influential technique for predicting the performance of a heat exchanger.

Suparta and Samah [23] predicted rainfall by exploring the application of the ANFIS model with various input structures and membership functions. The analyses of six-year rainfall data on a monthly basis in South Tangerang city, Indonesia found that the rainfall prediction based on the ANFIS time series is promising, where 80% of the data testing is well-predicted. Elijah Onu et al. [24] carried the comparative analysis of RSM, ANN, ANFIS, and mechanistic modeling in the Eriochrome black-T (EBT) dye adsorption using modified clay. They found that ANFIS is the best predictive model, whereas RSM is the least in the adsorption of EBT dye. Mehrabi et al. [25] and Esen et al. [26] used ANFIS, whereas Beigzadeh and Rahimi [27, 28] used ANFIS and GA for modeling the influence of the essential parameters of the heat exchangers. Esen and Inalli [29], Hayati et al. [30], and Esen et al. [31] predicted using novel geometry in a heat exchanger using ANFIS.

Chen et al. [32] and Mohammad [33] studied experimentally the and in a double tube heat exchanger using ANN. The 99.76% and 99.54% of data regression coefficients for and , respectively, illustrated the accurateness of the method applied. Gill and Singh [34], Zarei et al. [35], and Abadi et al. [36] adopted the ANFIS approach for predicting the energetic performance analysis and found that the ANFIS predictions agreed well with the experimental results with an absolute fraction of variance in the range of 0.994–0.998, a root mean square error in the range of 0.0018–0.1907, and a mean absolute percentage error in the range of 0.103–0.897%. Onyelowe et al. [37] implemented ANFIS and its evolutionary hybrid techniques, ANFIS‐PSO and ANFIS‐GA, to forecast the coefficients of curvature and the uniformity of unsaturated lateritic soil and concluded that ANFIS and its evolutionary hybrids techniques showed great accuracy. Marjani et al. [38] used the application of ANFIS to obtain the results of CFD modeling to facilitate the prediction of the pressure of the nanofluid convective flow. The ANFIS predictions show a good agreement with the CFD results. Saee et al. [39], Beiki [40], Bahiraei et al. [41], Yashawantha and Vinod [42], Bahl et al. [43], Safarzadeh et al. [44], and Safarzadeh et al. [44] used the ANFIS model for different heat transfer enhancement applications, and their major findings are listed in Table 1.

From the literature review, it can be concluded that ANFIS is a better modeling system as it is an amalgamation of ANN combined with FIS to improve the speed, adaptiveness, and fault tolerance. It can assimilate the linguistic variables that are a part of human language, reasoning, and understanding [46–48]. The use of modern and advanced techniques leads to the saving of time, energy, and material by analyzing them on the basis of the performance dominance parameter [49]. Furthermore, the literature review shows so many studies on predicting the performance of the heat exchanger. However, very limited research has been found on the passive methods with helically pierced twisted tape inserts using ANFIS. In the present study, ANFIS modeling is used to predict and of the heat exchanger tube. It is also used to determine the geometrical parameter values by finding out their dominance and involvement in the performance assessment. The novelty of the present work is the prediction of the geometric parameter that delivers the maximum heat transfer inside a heat exchanger tube. The ANFIS method determines the dominating parameter on the basis of thermal performance to lower the experimental runs and saves time and money. The determined best-suited parameters can be used in a heat exchanger tube to enhance the heat transfer with the lowest possible pressure drop penalty.

#### 2. Range of Parameters

The variable geometrical parameters of the helical pierced twisted-tape inserts and the corresponding range taken for the investigations [50] are as follows: diameter ratio ranging from 0.57 to 0.80, relative pitch ratio ranging from 0.046 to 0.107, perforation Index ranging from 5% to 20%, and Reynolds number ranging from 4000 to 30000. For the graphic representation of the helical pierced twisted tape inserts, see Figure 1.

#### 3. Experimental Setup Details

The heat exchanger tube is made of galvanized iron with outer and inner diameters of 68 mm and 65 mm, respectively. The heat exchanger tube has three sections, viz., the inlet, outlet, and test section, which are of of 2.5 m, 1.5 m, and 1.4 m, respectively, as shown in Figure 2 [50]. The fluid flow across the tube is carried by a centrifugal blower. A tailored Nicrome wire heater is employed to maintain a 1000 W/m^{2} constant heat flux in the test section. The pressure drop across the test section is determined by a digital micromanometer (TESTO-510) with a least count of 1 Pa. The temperature is determined by 12 thermocouples attached on the test section, 3 thermocouples at the outlet, and 1 thermocouple at the inlet section [50]. The thermocouples have been calibrated in laboratory conditions against a dry block temperature calibrated instant (Presys Instruments T-25N, 2004), having the least count of 0.01°C. The thermocouple to be calibrated was placed in the calibration bath where a constant temperature was maintained. The response of the thermocouple and the standard probe were noted with the help of a digital temperature indicator for various preset values of the standard probe, and the error between the reading of the standard probe and the thermocouple were calculated.

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#### 4. ANFIS Model

ANFIS is an adaptive network that utilizes the features of ANN and fuzzy logic. ANFIS implicitly executes these two approaches. In this study, Takagi-Sugeno fuzzy inference system with a five-layered structure is employed. The structure of the proposed model (ANFIS) is represented in Figure 3 [42], whereas the plotted membership function of the input and output parameters are demonstrated by Figure 4. To regulate the output parameters in the model, the structured rules are given in Table 2.

For effortlessness, we use two inputs and and corresponding one output . Two criteria were used in the approach of “if-Then” for Takagi–Sugeno model, as follows: Criteria 1 = If is and is , Criteria 2 = If is and is ,where and are the membership functions for input . Similarly, and are the membership functions for input . , , , , , and are the linear parameters of Takagi–Sugeno fuzzy inference model.

ANFIS model comprises of five layers, and the brief narrative of all these is as follows [21]: Layer 1: Each node of this layer acclimates with a parameter function and output of each node is a degree of membership, which is given by the input of the membership functions. where and are the degree of the membership functions of fuzzy sets and , respectively, whereas , , are the parameters of the membership function. Layer 2: In this layer, each node is nonadaptive and categorized as . The output node is the outcome of the multiplication of signal coming into the node and carried out to the next node. The outputs of these nodes are given as follows: where output represents the firing strength of each rule. Layer 3: Each node in the third layer is categorized as N. Every node is a calculation of the ratio between the *i*^{th} rule and the sum of all rules. Layer 4: Every node in layer four is an adaptive node to an output that is defined as [21] follows: Layer 5: The single node of layer five is labeled as , which calculates the whole output of all received signals of the earlier nodes.

#### 5. Data Reduction

From the experimental data recorded for the heat exchanger under the steady state conditions, , , , and were computed as follows [50, 51]:

across the test section is calculated using the Darcy equation as follows [50, 51]:where (∆P)_{d} = 9.81×(∆h)_{d}× *ρ*_{m}.

is determined from the followingequation:where,

The useful heat transfer rate of the fluid is given by,

The heat exchanger with the pierced twisted tape inserts thermal performance compared to a smooth tube is obtained as follows [50, 51]:

#### 6. Uncertainties Analysis

The uncertainty calculation majorly relies on the errors linked to the measuring instruments [50]. The uncertainty evaluation is performed on a single test run with a single set of geometric parameters. The uncertainty results are presented in Table 3 [50].

#### 7. Validation of Experimental Results

The smooth tube experimental data for was validated with the Dittus-Boelter equation (13), and by the Blasius equation (14) [25, 35, 47, 50, 51].

The comparative data of the experimental and standard correlations for and are displayed in Figure 5, respectively. An equitably validation data is seen that ensures the accuracy of the data collected in the experimentation [50].

#### 8. Results and Discussion

The experimental [50] and ANFIS values of the Nusselt number with the Reynolds number for a selected diameter ratio range with other parameter values, such as and , being fixed are represented in Figure 6(a). A continuous increase in is observed by for incremental range. Both experimental and ANFIS results showed that increases with an increase in from 0.57 to 0.65. However, with a further increase in the value of , starts to decrease. The maximum and minimum values of are achieved for the diameter ratio of 0.65 and 0.80, respectively. with the diameter ratio of 0.65 helically pierced twisted tape is higher by approximately 27.11% than the diameter ratio of 0.80 helically pierced twisted tape that provides a low heat transfer rate. The helical ring diameter is the reason for the heat transfer increment. The turbulence is enhanced by an increase in the diameter that breaks the boundary layer leading to heat transfer enhancement. Any further increase in the diameter beyond a certain limit tends to decrease the rate of heat transfer because of less attachment and detachment locations on the heated tube.

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Figure 6(b) displays the experimental and ANFIS results of variation in with at selected values, and the other parameters and are kept constant. It is noticed that is enhanced by increasing the diameter ratio. The maximum is achieved at of 0.80. The minimum and maximum values of are found for the diameter ratio of 0.57 and 0.80, respectively. The friction factor with the diameter ratio of 0.80 helically pierced twisted tape is higher by approximately 10.69% than the diameter ratio of 0.57 helically pierced twisted tape that provides a low pressure drop. The increase in the diameter leads to a higher resistance in the path of the fluid flow. This development is detected because an increase in the diameter resists the flow, and higher turbulence is achieved. However, the pressure drop increases, which enhances . The main cause behind this disparity is the diameter of the helical ring.

Figure 7(a) illustrates the experimental and ANFIS results on the effect of on with varying , keeping other geometrical parameters constant, such as and . It is seen that is boosted by an increase in , and the maximum is at of 0.086. A further increase in decreases , and the trend observed is because of a smaller number of attachment and detachment points. The maximum and minimum values of are found for the pitch ratio of 0.086 and 0.046, respectively. with of 0.086 helically pierced twisted tape is higher by approximately 10.57% than of 0.046 helically pierced twisted tape that provides a low heat transfer rate. The increases in the twist ratio provides less twists on the test length that generates a lower secondary flow inside the tube. This low number of twists on the tube decreases the heat transferring spots, and hence, the heat transfer rate is reduced.

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The experimental and ANFIS values of with for a varying range of with other parameter values, such as and being fixed are represented in Figure 7(b). It is seen that as increases, decreases continuously because of a lower interference offered by a smaller number of helixes on the tape. The highest and lowest values of the friction factor are found for the pitch ratio of 0.046 and 0.107, respectively. The friction factor with the pitch ratio of 0.046 helically pierced twisted tape is higher by approximately 24.48% than the pitch ratio of 0.107 helically pierced twisted tape that provides a low pressure drop. It is because a decrease in in the test section occurs as the value increases, which is because the surface of the tape tends to become parallel to the flow direction.

The experimental and ANFIS results on the effect of on for varying flow are represented in Figure 8(a). The plot displays an increased with an increase in and produces the maximum for of 10%. The maximum and minimum values of are found for the perforation index of 10% and 20%, respectively. with the perforation index of 10% helically pierced twisted tape is higher by approximately 9.33% than the perforation index of 20% helically pierced twisted tape that provides a low heat transfer. A reduction in is seen for increasing the value of beyond 10%. A reduction in the turbulence intensity inside the tube is observed because of a larger perforation area. At lower perforation, the small dimension diameter delivers in the form of jet, thus producing a high turbulence. A further increase in the value beyond 10% allows the fluid to flow through the larger perforation, and thus, a low-intensity turbulence is produced.

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Figure 8(b) illustrates the experimental and ANFIS results on the variation of on against the . A decreasing trend of is observed by boosting up the percentage. The higher and the lower values of the hostility factor are found for the perforation index of 5% and 20%, respectively. The friction factor with the perforation index of 5% helically pierced twisted tape is higher by approximately 16.17% than the perforation index of 20% helically pierced twisted tape that provides a low pressure drop. As is leveled up from 5% to 20%, goes down, and this consequence occurs because of a large open area available for fluid flow with a lower flow resistance.

The thermal hydraulic performance of the heat exchanger incorporated with the helical pierced twisted tape comprises of the simultaneous assessment of and as related to the smooth tube. Figure 9(a) illustrates the effect of on . It is seen that is observed to elevate the value of up to 0.65, and thereafter, any increase in reduces . The higher value of is 2.13.

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Figure 9(b) illustrates the effect of on , the maximum is attained corresponding to , and the value is found to be 2.08. for is represented in Figure 9(c), which illustrated the effect of in the range of 5% to 20%. The maximum is found at of 10%, and the maximum is found to be 2.09. Thus, the inference is that the optimum value of takes place at the values of , , and of 0.65, 0.8, and 5%, respectively.

Figures 10(a)–10(c) illustrates the comparison between the experimental and ANFIS-predicted results for , , and . It may be seen that the ANFIS-predicted results and experimental results are in good consideration with each other, which assures the correctness of the information generated.

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#### 9. Conclusions

This article deals with the analysis of the effect of flow and geometric parameters on the thermal performance of the heat exchanger tube fitted with a pierced twisted tape using the experimental and ANFIS models. The experimental and ANFIS models used four input parameters , , , and , and three output parameters , , and . The inferences drawn are as follows:(1)The experimental and ANFIS results observed that the value of increases with an increase in , and it attains the highest value at the value equal to 0.65. Then, it starts decreasing with a further increase in the value of . However, continuously increases with an increase in the value of .(2)The experimental and ANFIS results showed that the value of increases with an increase in and reaches to a higher value at the value of 0.086. With more rise in the value of , decreases. However, increases with a decrease in the value of and attains a higher value in relation to a value of 0.046.(3)The experimental and ANFIS results showed that the value of increased with an increase in and attained the highest value corresponding to the value of 10%. With a further increase in the value of , decreases. However, increases with a decrease in the value of and reaches to an extreme value corresponding to the value of 5%.(4)The maximum thermal hydraulic performance was obtained with the value of 0.65, the value of 0.085, and the value of 10%. The prediction of the , , and with the ANFIS model agrees with the experimental investigation with a higher error of less than 0.53.(5)It is evident from the ANFIS and experimental results that the enhancement of heat transfer mainly depends on the type of geometrical parameters and the nature of fluid. Hence, in future, the ANFIS model can be used to predict the heat transfer and pressure drop of a nanofluid flow through twisted tape heat exchangers. Also, the Particle Swarm Optimization (PSO) algorithm can be employed to improve the ANFIS model for prediction.

#### Nomenclature

: | Area of test section, |

: | Diameter of tube, m |

: | Diameter of helical tape, m |

: | Diameter ratio |

: | Heat transfer coefficient, W/m^{2}·K |

: | Energy, |

: | Friction factor for twisted tape inserts |

: | Friction factor for smooth surface |

: | Length of test section, m |

: | Mass flow rate, kg/s |

: | Pitch of helical pierced tape, m |

: | Relative pitch ratio |

: | Perforation Index |

: | Total area of helical tape, m^{2} |

: | Nusselt number for twisted tape inserts |

: | Nusselt number for smooth surface |

: | Pressure, Pa |

: | Average pressure drops, Pa |

: | Heat transfer rate, W |

: | Reynolds number |

V: | Mean velocity of fluid, m/s |

: | Thermohydraulic performance parameter. |

#### Data Availability

The data used to support the findings of the study are included within the article.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this article.

#### Acknowledgments

This study was funded by the University of Jeddah, Jeddah, Saudi Arabia.