Impact of bumpers position variation on heat exchanger performance: an experimental and predictive analysis using an artificial neural network

Abstract

Experimentally and numerically, the thermal performance enhancement of counterflow twin-pipe heat exchanger with bumpers position variation was explored. A set of semicircular bumpers were positioned at varying distances from the fluid flow entrance on the annulus gap of the concentric pipe heat exchanger (10–70, 70–130, and 130–190 cm). The hot water entered the inner pipe at a constant mass flow rate of 0.0167 kg/s, whereas the cold air entered the annulus gap of a concentric pipe heat exchanger at changing mass flow rates of 2 × 10⁻⁵ to 14 × 10⁻⁵ kg/s. The numerical portion comprised simulating the efficacy of the heat exchanger with a smooth pipe and varied bumper placements using an artificial neural network (ANN) model. The experimental portion of the present work consisted of a series of tests to determine the optimal position of the bumpers for maximizing heat exchanger efficiency. At a constant fluid inlet temperature and with varied mass flow rates of the cold air, the numerical model was compared to the experimental results. When the bumpers are put at a distance of 130–190 cm, the heat exchanger has the highest thermal efficiency compared to other bumper placements and a smooth pipe. In all cases of the investigation, there is a good correlation between numerical and experimental data.

Introduction

Numerous applications, including heating and cooling systems, chemical processes, compressor ventilation, and others, make extensive use of the concentric pipes heat exchanger [1,2,3,4]. Heat exchanger performance has recently been improved by inserting wire mesh, interior bumpers, and exterior bumpers inside pipes [5,6,7]. One of the techniques uses bumpers that increased the occurrence of disturbances causing to increase in the heat transfer’s surface area. The presence of the bumpers impeded the runoff flow and caused a backflow of the fluid, resulting in an increased pressure drop due to the increased heat transfer [8]. With the development of the techniques of artificial neural networks (ANN) rapidly, more of these techniques were used in many processes successfully to choose the suitable design of the heat exchanger [9,10,11,12]. ANN prediction presents a new method to predict a complex system that is nonlinear, unknown, uncertain, or without any obvious conditions about the relationship between the input and output. The ANN techniques can be used to predict the relationships of complicated nonlinear equations through network forming. This network can be used to control unknown or uncertain processes and simulate dynamically [13].

The majority of research aims to enhance heat transfer in such applications; the neural network method has been suggested for predicting heat exchanger performance. The current work reviews many studies that looked into how fluid flow and heat transfer properties evolved. Khalaf and Falih [14] used semicircular disc baffles inserted in the annulus gap of the heat exchanger and various types of twisted tape to investigate the behavior of heat transfer in a double pipes heat exchanger with counter water flow direction numerically and experimentally. Nanofluid’s effect on countercurrent flow in a double-pipe heat exchanger was examined by Noor et al. [15]. The viscosity of nanofluids was measured, and the friction factor and heat transfer coefficient were calculated at various temperatures and particle sizes. The findings revealed that existing nanoparticles played an important role in improving the heat exchanger’s effectiveness. Muataz et al. [16] used varying geometries (dimple, twisted, and corrugated) of tapes inserted into the heat exchanger’s inner pipe to implement and numerically test the method of improving heat transfer performance [17]. Jenan and Dr. Mohammed conducted a numerical analysis to determine how the addition of metal foam fins affects the air-to-water double-pipe heat exchanger’s heat transfer properties. The behavior and values of local and average heat transfer coefficients resulting were presented to show from this study that the mean coefficient of heat transfer had improved by utilizing the metal foam fins. Tongkratoke et al. [18] compared the performance of two heat exchangers with double pipes and two distinct welding techniques: argon and fire welding with parallel and counterflow water flow directions. Shanas and Arsana [19] conducted an experimental investigation into the impact of helical baffle angle variation on heat exchanger performance. This study has proven that the smallest angle of a helical baffle was given the greatest performance in the heat transfer characteristics. Amar et al. [20] conducted a series of tests to see how triangular bumpers affected the efficiency of double-pipe heat exchangers with parallel and counter-flowing water. Salem et al. [21] studied experimentally the heat transfer and the pressure drop characteristics for counter water flow through the heat exchanger under the effect of perforated baffles. Perforated baffles were fabricated with a variation of the holes spacing, ratio of the pitch, void ratio, and angle’s inclination. Anum et al. [22] investigated the effect of heat generation and thermal radiation in electrically conductive unstable Williamson fluid along porous expansion surface using ANN modeling. Khalid et al. [23] predicted the force convective heat transfer in a circular pipe using the artificial neural network with constant heat flux. Basma and Hawraa [24] analyzed the shell and double concentric tube heat exchanger numerically. CFD package was employed to solve the flowing fluid and temperature field inside the shell and tubes with existing 20 baffles and 16 tubes in this heat exchanger. Anum et al. [25] predicted the flow of the boundary layer for single-wall carbon nanotubes toward three distinct nonlinear isotropic needles of parabolic, cylinder, and cone shapes with convective limit conditions. Dr. Adnan et al. [26] simulated with ANN model to predict boiling flow and pressure drops in parallel copper multichannel using MATLAB program. Anum et al. [27] demonstrated the magnetohydrodynamic squeezing of a fluid flow toward a stretched permeable surface through a nonpartisan medium. Heat transfer properties and fluid flow were investigated with the help of nonlinear ANN modeling. Xueping et al. [28] predicted the performances of heat transfer for finned pipe heat exchangers using ANN model. Anum et al. [29, 30] showed the significance of using an artificial neural network as an alternative to traditional methods for providing reliability and important criteria for the analysis of mixed models, as well as methods for qualifying them and utilizing them in statistical calculations. Utilizing discrete twisted tapes, Nassr and Abdulrahman [31] conducted experimental research on the enhancement of heat transfer in a tube heat exchanger. Horizontal, inclined, and vertical positions were chosen for fixing discrete tapes at a long pipe section. The results demonstrate that using discrete twisted tapes enhanced the heat transfer rate, especially in the inclined position.

The purpose of this study is to compare the thermal performance of double-pipe heat exchangers with varying positions of semicircular bumpers inside the heat exchanger to that of smooth pipe using experimental and numerical methods. An artificial neural network (ANN) was used to predict heat transfer characteristics in a double-pipe heat exchanger with and without bumper position variation. The empirical correlations and the experimental data’s degrees of divergence were compared. In these engineering applications, the artificial neural network method was given preference over empirical correlations.

Experimental apparatus and data reduction

The experimental apparatus of double-pipe heat exchanger was shown schematically in Fig. 1 and photographically in Fig. 2. The inner pipe was made from stainless steel metal of 1.25 cm diameter. The outer pipe was made from PVC metal of 3.75 cm inner diameter. The outer pipe was insulated using glass wool of 1 cm thickness to minimize the loss of heat to the surrounding. The length of a concentric pipe heat exchanger is of 200 cm. Hot water has flowed through the internal pipe of the heat exchanger with a closed circuit. The hot water was heated using the electrical heater (3000 W) provided by a thermostat to control the inlet hot water temperature at a constant temperature of 60 °C. The hot water was pushed into the inner pipe of heat exchanger by water pump device. The water flow meter with the range 1–7 LPM was used to control the amount of inlet hot water and to remain constant in all tested times at 1 LPM.

Fig. 1

Schematic diagram of the experimental apparatus

Fig. 2

Photographic of the experimental apparatus

The cold air was passed through into the gap between concentric double-pipe heat exchanger. The cold air was provided by the air compressor device (Fig. 3).

Fig. 3

Photographic of the compressor (cold air supply)

The air flow meter at the range 1–20 LPM was used to control the flow rate of cold air. The amount of the cold air was changed from 1 to 8 LPM to investigate the effect of this changing of the heat transfer characteristics.

The bumpers were semicircular rings made from stainless steel metal with dimensions Rout = 16, Rin = 10, and t = 3 mm as shown in Figs. 4 and 5. A number of semicircular bumpers that have been used were 20 bumpers arranged on the zic-zac form. The semicircular bumpers were welded and installed on the outer surface of the inner pipe. The distance between bumper and another is of 3 cm. The first bumper was put after leaving 10 cm distance from the air flow into the gap between concentric double-pipe heat exchanger to avoid the backflow of the air. The semicircular bumpers were inserted at different positions of 10–70, 70–130, and 130–190 cm from the air flow inlet to investigate the effect of varying bumper positions on the characteristics of heat transfer coefficient and fluid flow.

Fig. 4

Photographic of bumper positions

Fig. 5

Dimensions of bumper

The temperatures of the two fluids at their inlet and outlet were measured using (k-type) thermocouple by connecting one of the two ends of the thermocouples with a digital thermometer. The static pressure drops between the entrance and outlet of the airflow were measured using an air manometer that was made locally as shown in Fig. 6.

Fig. 6

Photographic of air manometer

Data analysis

Rate of heat transfer and Nusselt number

The data analysis of concentric pipes heat exchangers with and without using semicircular bumpers was carried out in case of steady-state heat balance. The inlet coefficient of heat transfer can be determined by the below equation [32]:

$${\textrm{h}}_{\textrm{i}}=\frac{\textrm{Nu}\ast {\textrm{k}}_{\textrm{w}}}{\textrm{L}}$$

(1)

where Nu is Nusselt number and can be calculated from the below equation as follows:

$${\textrm{Nu}}_{\textrm{i}}=0.023\ {\operatorname{Re}}^{0.8}{\Pr}^{0.4}$$

(2)

where Reynold number Re can be found in the equation as follows:

$${\textrm{R}}_{\textrm{e}}=\frac{\uprho {\textrm{vd}}_{\textrm{i}}}{\upmu}$$

(3)

A set of hypotheses were presented to solve the equations of double-pipe heat exchanger model such as steady-state conditions, the radiation and conduction of heat transfer inside the pipe were negligible, and all the fluid properties were constant except the fluid density which was a function of the mean fluid temperatures. The heat loss from the outer heat exchanger to the surroundings was calculated from the following equations:

The calculation of heat transfer losses Q_loss was very low, around 3%, and it is calculated from the following equation:

$${\textrm{Q}}_{loss}={\textrm{h}}_{\textrm{o},\textrm{ins}.}\ {A}_s\ \left({\textrm{T}}_{\textrm{ins}.}-{\textrm{T}}_{\infty}\right)$$

(4)

The heat transfer rates for hot and cold fluids, as well as the overall heat transfer coefficient, were calculated using mathematical analysis of the current work with and without semicircular bumpers as follows:

The following equation was used to determine the hot water’s heat transfer rate ($\dot{{\textrm{Q}}_{\textrm{h}}}$) as follows:

$$\dot{{\textrm{Q}}_{\textrm{h}}}={\dot{\textrm{m}}}_{\textrm{w}}{\textrm{C}}_{\textrm{p}}\left({\textrm{T}}_{\textrm{hi}}-{\textrm{T}}_{\textrm{ho}}\right)$$

(5)

It is possible to write the heat transfer rate ($\dot{{\textrm{Q}}_{\textrm{c}}}$) ̇to cold air as follows:

$$\dot{{\textrm{Q}}_{\textrm{c}}}={\dot{\textrm{m}}}_{\textrm{a}}{\textrm{C}}_{\textrm{p}}\left({\textrm{T}}_{\textrm{co}}-{\textrm{T}}_{\textrm{ci}}\right)$$

(6)

where $\dot{\textrm{m}}$ represents the rate of mass flow and calculated by the following:

$${\dot{\textrm{m}}}_{\textrm{a}}=\uprho \textrm{v}\ast \frac{\uppi}{4}\ \left({\textrm{D}}_{\textrm{o}}^2-{\textrm{D}}_{\textrm{i}}^2\right)$$

(7)

The average rate of heat transfer can be written by the following:

$${\dot{\textrm{Q}}}_{\textrm{ave}.}=\left({\dot{\textrm{Q}}}_{\textrm{h}}+{\dot{\textrm{Q}}}_{\textrm{c}}\right)/2$$

(8)

The equation that follows can be used to determine the overall heat transfer coefficient U as follows:

$$\textrm{U}=\frac{{\dot{\textrm{Q}}}_{\textrm{ave}.}}{{\textrm{A}}_{\textrm{s}}\ast \textrm{LMTD}}$$

(9)

From the following equation can be estimated the outer heat transfer coefficient h_o [33] as follows:

$$\frac{1}{{\textrm{U}}_{\textrm{i}}{\textrm{A}}_{\textrm{i}}}=\frac{1}{{\textrm{h}}_{\textrm{o}}{\textrm{A}}_{\textrm{o}}}+\frac{\ln \left({\textrm{D}}_{\textrm{o}}/{\textrm{D}}_{\textrm{i}}\right)}{2\uppi {\textrm{k}}_{\textrm{a}}\textrm{L}}+\frac{1}{{\textrm{h}}_{\textrm{i}}{\textrm{A}}_{\textrm{i}}}$$

(10)

where the surface area of the inner surface can be determined from the following equation:

$${\textrm{A}}_{\textrm{i}}=\uppi .{\textrm{D}}_{\textrm{i}}.\textrm{L}$$

(11)

And the surface area of the outer surface without bumpers is as follows:

$${\textrm{A}}_{\textrm{o}}=\uppi .{\textrm{D}}_{\textrm{h}}\textrm{L}$$

(12)

And the surface area of the outer surface with bumpers is as follows:

$${\textrm{A}}_{\textrm{o},\textrm{b}}=\uppi .{\textrm{D}}_{\textrm{h}}.\left(\textrm{L}-06.\right)$$

(13)

The following formula was used to determine the Nusselt number along the outer pipe’s air side as follows:

$${\textrm{Nu}}_{\textrm{o}}=\frac{{\textrm{h}}_{\textrm{o}}\ {\textrm{D}}_{\textrm{h}}}{{\textrm{k}}_{\textrm{a}}}$$

(14)

where the hydraulic diameter can be determined from the following equation:

$${\textrm{D}}_h=\left({D}_o-{D}_i\right)$$

(15)

Friction factor (f)

The below Eq. 9 can be used to determine the Reynolds number as follows:

$$\operatorname{Re}=\frac{\uprho {\textrm{vD}}_{\textrm{h}}}{\upmu}$$

(16)

For (Re < 2300), the flow is laminar, and the applied equations to find the friction factor f are as follows:

$$\textrm{f}=\frac{{\textrm{h}}_{\textrm{loss}}\ast {\textrm{D}}_{\textrm{h}}\ast 2\textrm{g}}{\textrm{L}\ast {\textrm{v}}^2}$$

(17)

Effectiveness (∈)

The effectiveness (∈) of heat exchanger with and without using semicircular bumpers can be calculated from the following equation:

$$\in =\frac{{\dot{\textrm{Q}}}_{\textrm{actual}}}{{\dot{\textrm{Q}}}_{\textrm{maximum}}}$$

(18)

where:

$${\dot{\textrm{Q}}}_{\textrm{actual}}={\dot{\textrm{m}}}_{\textrm{a}}\textrm{CP}\left({\textrm{T}}_{\textrm{co}}-{\textrm{T}}_{\textrm{ci}}\right)$$

(19)

$${\dot{\textrm{Q}}}_{\textrm{maximum}}={\dot{\textrm{m}}}_{\textrm{w}}\textrm{CP}\left({\textrm{T}}_{\textrm{hi}}-{\textrm{T}}_{\textrm{ci}}\right)$$

(20)

Numerical analysis

Heat exchanger modeling analysis using artificial neural networks

The model of artificial neural networks (ANN) was utilized to analyze double-pipe heat exchanger model. ANN method was used in many applications of engineering that simulated nonlinear equations. This method did not require knowledge of the input and output such as controlling of dynamic system and prediction of thermal system performance. In last decades, ANN model was used widely in the analysis of heat exchanger models [34]. Neural network stimulates the human intelligence to a high degree which may be trained to find the right outputs and classed the training exercises. Thus, it needs to know the training inputs. After training, the flow parameters can be classed with high accuracy [35].

The two primary types of ANN are as follows:

• 1. Feed forward in which the network does not create any loops

• 2. The feedback that leads to the formation of one or more loops

Figure 7 showed three layers of the feed-forward back propagation. The ANN model was arranged in three layers based on the following: layers for input, hidden, and output. In the hidden layer, many neurons were connected to neurons in the input and output layers. Input layer included four parameters as follows: inlet hot water temperature T_{h, i}, inlet cold air temperature T_{c, i}, hot water mass flow rate${\dot{\ \textrm{m}}}_{\textrm{h},\textrm{i}}$, and inlet air mass flow rate${\dot{\ \textrm{m}}}_{\textrm{c},\textrm{i}}$. The output layer included four parameters as follows: average rate of heat transfer ${\dot{\textrm{Q}}}_{\textrm{ave}.}$, Nusselt number Nu, friction factor f, and heat transfer effectiveness ∈. The statistical parameter-squared correlation coefficient (R) serves as the foundation for making comparisons between the various algorithms. The orders of ANN’s input values may vary by many magnitude orders, and it may not show the relative importance of the input values, which are within a specific range of (−1, 1) as the maximum and minimum range. The following is a summary of the procedure for using ANN modeling to predict the output parameters [36] as follows:

Fig. 7

Architecture of artificial neural network (ANN)

1) Utilize data sets to identify training patterns.

2) Define the architecture of a neural network.

3) Set the parameters of the network.

4) Execute a program for feed-forward back propagation.

5) Analysis and comparison.

There are three equations of experimental correlations to know the number of nodes in the hidden layer N. In this present work and for forward propagation input, the following formula was used [1]:

$$\textrm{N}=\sqrt{0.43\textrm{nm}+0.12{\textrm{m}}^2+2.5\textrm{n}++0.77\textrm{m}+0.86}$$

(21)

where n and m represent the number of nods for the input and output layers respectively.

The hidden layer included seven neurons. In the hidden layer, the function that was selected is the logistic sigmoid (TANSIG), and in the output layer, the function was PURELIN. Summation of the product of each contact weight (W_jk) is from a neuron (j) to the neuron (k), input (X_j), and the bias b_i (additional weight) to obtain the sum of each neuron. Neuron i^th has a sum of the weighted input (W_ij, X_j ) and the net input P_i formed by the bais b_i as shown in the equation:

$${\textrm{P}}_{\textrm{i}}=\sum\nolimits_{\textrm{j}=1}^{\textrm{n}-1}{\textrm{W}}_{\textrm{ij}}{\textrm{X}}_{\textrm{j}}-{\textrm{b}}_{\textrm{i}}$$

(22)

where W_ij represents the connection strength from input j^th to neuroni^th, n denotes about the input vectors number, X_j represents the input vector, and b_i is the bias of the neuron. The sigmoid function is employed to determine the output of the neuron. The training process is important as a first step to form ANN model due to the training process denotes that the weights are corrected to determine the output (target) values. Training means that weights. The training process is a pair of the actual input data (XS, YS), XS represents the vector, and YS represents the corresponding target after the successful training process. When the target values YS are corrected for each vector XS, then the neural network was given a correct prediction for any input X to produce any target value Y depending on the fundamentals of the ANN model. The observed data percentage used in the ANN model is 70% as a training dataset, 15% as test dataset, and 15% as validation dataset. The performance is improved due to the difference between the observed data, and the predicted values filtered back through the system and connecting between the layers. ANN model for the training, test, and validation qualities can be evaluated by applying the correlation of the squared coefficient R as follows:

$$\textrm{R}=1-\frac{\sum\nolimits_{\textrm{j}=1}^{\textrm{n}}{\left({\textrm{y}}_{\textrm{i}-}{\textrm{y}}_{\textrm{i}}^{\textrm{t}}\right)}^2}{\sum\nolimits_{\textrm{j}=1}^{\textrm{n}}{\left({\textrm{y}}_{\textrm{i}-}{\textrm{y}}_{\textrm{o}}\right)}^2}$$

(23)

$${\textrm{y}}_{\textrm{o}}=\frac{1}{\textrm{n}}{\sum\nolimits}_{\textrm{i}=1}^{\textrm{n}}\left({\textrm{y}}_{\textrm{i}-}{\textrm{y}}_{\textrm{i}}^{\textrm{t}}\right)$$

(24)

where y_i is the output’s value of either i^th training, test, or validation and ${\textrm{y}}_{\textrm{i}}^{\textrm{t}}$ represents the value of the corresponding target [37, 38].

MATLAB software programming algorithm

MATLAB programming (version R2015b) was used to predict the experimental data using ANN model. The experimental data of the inputs and outputs values were read as a form of Excel file in workspace window. Function (nn train tool) was used in commend window to manage the data. After the input and output data were imported, the network was created after selecting a set of network properties. After then, the created network was opened to show the network configuration. Start to train the network by pressing on the “train.” It is important to show that the network’s performance was reduced when the over training occurred. Two-hundred twenty-four experimental data were considered in the ANN model. The feed-forward back propagation neural network was used to put the trained data into action. The rate average of heat transfer, Nusselt number, friction factor, and heat exchanger effectiveness with and without bumpers were predicted together depending on the testing input data, temperature of the air at the inlet, mass flow rate of hot and cold air, and temperature of the hot water at the inlet [39].

Results and discussion

In this present work, the effects of heat transfer and fluid flow on the thermal effectiveness of a double-pipe heat exchanger with and without semicircular bumpers are investigated numerically and experimentally.

ANN model predictive ability can give a satisfactory output for the flow parameters included in the ANN examples. The predictive ability can be determined using the cross-validation. This procedure is shown in that one of the compound parameters is removed from the dataset, and the neural network trains with other components to predict the hidden compound. The process is repeated for each compound in the dataset. After mutual validation, the predictive ability of the various neural networks is evaluated through cross-validation.

The performance of the neural network is a function of the number of hidden neurons. The relationship between the experimental analyzed data and the ANN predictive model was expressed by the linear combination. The number of iterations increases the ANN’s performance, but the predictive ability was reduced when the training process exceeds 1000 iterations. This is known as the excessive training process due to the very long training time. In fact, the weights obtained after excessive training contain more training set-specific information, so the prediction of the test dataset will not be really satisfactory. Therefore, when a very low error is searched in training set, the predictive ability of ANN is less successful. Predictability is an essential quality of an ANN. Thus, the effect of over-training process should be avoided [40].

Figure 8 shows the difference of inlet and outlet air temperature versus change of the air mass flow rates with and without using bumpers. Generally, it is observed that the temperature difference increases with the mass flow rate of the air due to an increase in the rate of heat transfer. The highest air temperature difference is recorded when the bumpers are inserted at position 130–190 cm to increase by about 58.94% compared to the smooth pipe.

Fig. 8

Air temperature difference versus air mass flow rate with and without bumpers

The experimental overall heat transfer coefficient is depicted in Fig. 9 as a function of the air mass flow rate. The overall heat transfer coefficient was enhanced by increasing the air mass flow rate due to increase swirl and turbulence in the region of air flow which causes to prevent formation of boundary layer thickness. Additionally, varied bumper positions at 10–70, 70–130, and 130–190 cm have an increased U that is 20.6%, 43%, and 60.3% than smooth pipe. The reason in this return is to increase in the temperature difference between the fluids at the input and output in heat exchanger.

Fig. 9

Over heat transfer coefficient versus air mass flow rate with and without bumpers

Figure 10 indicates the effect of fluid flow rate on rate of heat transfer with different positions for the bumpers at 10–70, 70–130, and 130–190 cm and with smooth pipe. A comparison between the experimental data and the predictions is shown in the figure. In general, it is shown that the rate of heat transfer increases with increasing the mass flow rate as a result of increase in the overall heat transfer coefficient. The maximum heat transfer rate is recorded at position of 130–190 cm to about 45.9% in the case of the experimental data and to about 45.76% in the case of the predictive data compared to the smooth pipe.

Fig. 10

ANN predicted and experimental heat transfer with and without bumpers

Figure 11 investigates the effect of air mass flow rate and bumper’s positions on the Nusselt number numerically by ANN mode prediction and experimentally through the experimental data. The Nusselt number is increased with the increase of the air mass flow rate due to the increase of the turbulence of airflow causing increase in the rate of heat transfer. Nu values with the varying bumper’s positions give high value when the bumpers are arranged at the position of 130–190 cm, where the Nusselt number values are enhanced to about 48.1% predictively and 59.4% experimentally compared to the smooth pipe. This is due to the thermal boundary layer close to the heat exchanger wall being largely destroyed as a result of the airflow being slowed considerably in this position.

Fig. 11

ANN predicted and experimental Nusselt number with and without bumpers

Figure 12 shows the influence of air mass flow rate and bumpers position variation on the friction factor experimentally and predictively using ANN model. Generally, it is noticed that the friction factor is decreased with an increase of the air mass flow rate as a result of the air pressure drop increases. The variation of bumpers positions decreases the friction factor highly compared to smooth pipe due to increase in the fluid recirculation near the bumpers and increases the turbulence force. Maximum reduction of friction factor is recorded with the insertion of the bumpers at position of 130–190 cm to about 28% experimentally and to about 27.2% predictively compared with the smooth pipe.

Fig. 12

ANN predicted and experimental friction factor with and without bumpers

Figure 13 shows how the predictive and experimental heat exchanger effectiveness of semicircular bumpers and the smooth pipe is affected by increasing the air mass flow rate at various positions. The effectiveness of the heat exchanger increases with fluid flow rate in all instances. This is because an increase in the pressure drop causes an increase in the rate of heat transfer due to the increase in high turbulence. The effectiveness with the bumpers at position 130–190 cm is given the best position compared to the other positions and smooth pipe. The effectiveness increases by approximately 43.4% experimentally and by approximately 42.9% predictively.

Fig. 13

ANN predicted and experimental heat exchanger effectiveness with and without bumpers

It is noticed from Figs. 10, 11, 12 and 13 that there is great convergence between the experimental data and the data which are predicted using the artificial neural network model. So, it gives evidence that the bumper’s positions are important to enhance the heat exchanger effectiveness with this engineering application.

Table 1 shows the fitting function performance with the ANN model of Q, Nu, f, and ∈ predicted together, which also lists the MSE values.

Table 1 Performance of ANN prediction with and without bumpers

Figure 14 describes the linear output regressions relative to the targets of fitting ANN function. Also, it gives the error R values and the correlations of linear regression to compare between the outputs data and target data from training, validation, testing, and all operations at bumpers position of 130–190 cm. It is noticed from the figure that the error values are more than of 0.975. So, it gives evidence of the good agreement between the output and target data.

Fig. 14

ANN performances of the training record at the air inlet at (130–190) cm

The fitting of ANN function can choose the data, build a network, and train it to solve the problems. The ANN performance is evaluated using the mean squared error (MSE), depending on the formula in Eq. 23, the mean squared difference MSE found between the predicted data (outputs data) and actual data. The better are the lower values, a value closer to zero shows that the fit is more suitable for the prediction, and zero indicates that there is no error.

$$\textrm{MSE}=\frac{1}{\textrm{n}}\sum\nolimits_{\textrm{i}=1}^{\textrm{n}}{\left({\textrm{E}}_{\textrm{i}}-{\textrm{P}}_{\textrm{i}}\right)}^2$$

(25)

where E represents the experimental data and P is the predicted output data. The experimental correlations and MSE for predicting ANN are contrasted in Table 2. It is noticed that all the MSE values of the fitting ANN function are smaller than of the correlations. This means that ANN results are better than those of correlations.

Table 2 Comparison is made between the MSE of ANN predicted model and experimental correlations with and without using bumpers

Conclusions

In the current work, the heat transfer and fluid flow characteristics were discussed experimentally and numerically, and the factor of thermal effectiveness of heat exchanger with changing of semicircular bumpers position at air mass flow rate of (2 × 10⁻⁵ to 14 × 10⁻⁵ kg/s) regimes were examined. The conclusions were included as follows:

• 1. The parameters of friction factor, overall heat transfer coefficient, and Nusselt number can be predicted accurately where the results showed that the MSE is less than 6% in all cases.

• 2. The overall heat transfer, especially at the position of the bumper 130–190 cm, is highest compared to the other bumpers’ positions and smooth pipe.

• 3. The values of Nusselt numbers and the friction factor were recorded as the best values with the presence of semicircular bumpers compared to the smooth pipe.

• 4. The change of the semicircular bumpers’ positions causes increase in the rate of heat transfer. The maximum heat transfer rate is recorded at position of 130–190 cm to about 45.9% in the case of the experimental data and to about 45.76% in the case of the predictive data compared to the other bumpers’ positions and smooth pipe.

• 5. The change of the position of the bumper causes to increase the thermal effectiveness is improved to reach the maximum values at bumpers position (130–200 cm) to about 43.4% experimentally and to about 42.9% predictively. Thus, the change in the bumper’s positions on the outer surface of the inner pipe is given important evidence on the improvement of the heat exchanger’s effectiveness in such engineering applications.

• 6. ANN model shows the ability and the high accuracy in the prediction of the heat transfer and the friction factor with and without using semicircular bumpers. The results of the experimental part are shown as a good agreement with the prediction correlations (rate of heat transfer, Nusselt number, friction factor, and thermal effectiveness). The ANN model gives a large closer to the experimental data in all cases.