Changes in cooling range as a function of concentration and flow rate

Experiments have been performed under relatively constant environmental conditions using different operating fluids (distilled water, MWCNTs, and TiO₂ nanofluids) and five levels of the RSM method. During the experiments, the flow rate of passing air and operating fluid was constant at 7.97 kg/min and 4 kg/min, respectively. After reaching the steady-state, the inlet hot water and outlet cold water temperatures were recorded, and the cooling range was calculated.

The design of experiment table for MWCNTs and TiO₂ nanofluids by the CCD-based RSM method is presented in Table 6. The experimental design points of the response procedure were used in the factorial method. It means, instead of conducting 13 experiments for each nanofluid,29 experiments were performed, and the results were analyzed in the Historical Data section of the software. The total number of tests was 58, 29 for each nanofluid.

The analysis of variance (ANOVA) table for cooling range data of the tower using TiO₂ nanofluid is given in Table 7. According to the software definition, terms with a P-value (>) 0.1 are not significant and have little effect on the final equation and responses. Therefore, it is better to remove them from the final equation to increase the model’s validity. All terms have a P-Value (<) 0.1 and are not excluded from the final equation. The P-value of the Lack of Fit term is more than 0.05 and is not significant. The Lack of Fit F-value of 1.92 indicates that the Lack of Fit is insignificant compared to the pure error. A “Lack of Fit F-value” of this magnitude has a 27.84 percent chance of occurring due to noise.

The software presented a quadratic equation as the model equation. Equations (18) and (19) demonstrate the actual and coded equations to predict the effect of TiO₂ nanofluid flow rate and concentration on the cooling range.

To evaluate the proposed model’s validity, the model’s descriptive statistics for the tower using TiO₂ nanofluid are given in Table 8.

The coefficient of variation (C.V.) has a low value showing low data scatter. ({R}^{2}=) 0.9937 demonstrates that the proposed model can describe 99.37% of the cooling range changes. The Adj-R² reveals the conformity degree between the experimental data and the model by considering the degree of model freedom and the number of experiments, and Adj-R² (=) 0.9923 indicates a 99.23% correlation between the model and experimental data. The ability of the model to predict points outside the defined levels is also significant and has a value of 99.01%. The difference between Pred-R² and Adj-R² is insignificant (based on the software default, Pred-R² and Adj-R² should not have more than 0.2 differences). Adeq Precision also has a significant value of 71.3596, which implies the favorable conditions of the model for use in industry. To use the predicted model for industrial purposes, the Adeq Precision must have a value higher than 4.

Figure 7 illustrates the normal plot of residuals for the cooling range and the acquired experimental values compared to the predicted cooling range data for TiO₂ nanofluid. It was observed that actual and predicted values have a good agreement in accordance with the obtained ({R}^{2}) coefficient. Moreover, the residuals have acceptable proximity to the normal line. The color of the dots can detect different values of the actual cooling range. The same procedures were conducted, and similar results were obtained for MWCNTs nanofluid²⁸.

Figure 8 represents the effect of flow rate and nanofluid concentration on the cooling range of TiO₂ nanofluid. As the flow rate of the TiO₂ nanofluid increases, the temperature of outlet fluid decreases since the passing time of the fluid in the bed and the time for mass and heat transfer are reduced. The temperature of the inlet fluid decreases as the velocity of the circulating fluid increases due to the constant heating power; therefore, the cooling range of the tower is reduced. The same trend was seen for MWCNTs nanofluid. According to the obtained results considering two nanofluids, it can be concluded that increasing the flow rate led to lower performance of the cooling tower, and the cooling range is not dependent on the type of nanofluids²⁸.

The 3D Surface and contour plot of the effect of independent variables on the cooling range using TiO₂ nanofluid.

The effect of concentration on the cooling range can be analyzed by considering two states: low flow rates and high flow rates. Increasing the concentration of TiO₂ nanofluid at low flow rates increased the cooling range. Based on the reported outcomes in the literature review, the addition of small amounts of nanoparticles to the base fluid could significantly improve the conductive heat transfer and, accordingly, the cooling range. At higher concentrations, in the range of 0.1 wt%, the trend becomes almost constant or slightly decreasing due to the agglomeration of nanoparticles and poor heat and mass transfer properties. It is observed that the cooling range in the range of 0.1 wt% is still higher than water, so the use of nanofluids, in any case, improves heat transfer and increases the cooling range of the tower.

The presence of the (AB) term in the model equation becomes more highlighted at higher flow rates. The effect of flow rate on the cooling range is greater than the concentration at higher flow rates, demonstrating the interaction of flow rate and concentration on the response (cooling range). As a result, the impact of nanofluids on cooling tower performance is minimal at higher flow rates, and the lower the flow rate, the more significant the impact of nanofluids on cooling tower performance.

The effect of flow rate on cooling range compared to MWCNTs nanofluid concentration is known in all experiments. When the flow rate and concentration increase simultaneously, a kind of interactive competition is formed between these two factors affecting the cooling range, and the winner is the flow rate. According to the diagrams, the best flow rate for using MWCNTs nanofluid is also the lowest²⁸.

The average inlet and outlet temperatures of the operating fluid and cooling range of the five flow rates are presented in Fig. 9. The outlet cold water temperature is almost constant. However, increasing nanofluid concentration slightly increases the inlet temperature and the cooling range. Despite the equality of the received energy and the residence time of the fluid inside the heater, the nanofluid temperature rose more than water since the specific heat capacity of water in the operating temperature range of the tower was about six times that of TiO₂, as the concentration of nanoparticles increased, the total heat capacity of the nanofluid decreased. As a result, a further rise in the temperature of the nanofluid relative to water with the same received energy could be related to the reduction in the specific heat capacity of the nanofluid compared to water.

The average values of the inlet and outlet temperatures of the operating fluid and the cooling range of the five flow rates.

Figure 10 exhibits the variation of the average cooling rates of five flow rates using specified concentrations of nanofluids. At the flow rate of 2–6 kg/min of circulating nanofluid, the optimum concentration of TiO₂ nanofluid for the cooling process was 0.085 wt%. At this concentration, the average cooling range increased by 7.4%, while using MWCNTs nanofluid increased the cooling performance by 15.8%. Thus, using MWCNTs nanofluid had a significant enhancement impact on the cooling range than TiO₂ nanofluid²⁸.

The effect of using nanofluid on the average cooling rates of five flow rates Using specified concentrations of TiO₂ nanofluid relative to water.

Changes in effectiveness as a function of concentration and flow rate

Firstly, the experiments were performed based on the listed data in Table 6, then using Eq. (2), the effectiveness of the tower was calculated and entered into the software. Table 9 lists the ANOVA table for tower effectiveness data of TiO₂ nanofluid. The P-value of the Lack of Fit term is greater than 0.05 and is not significant, which indicates an acceptable agreement between the model and experimental results.

According to the significant terms of the model in the ANOVA table, the model equation is a modified cubic equation in which the insignificant terms were removed. To predict the effect of TiO₂ nanofluid concentration and flow rate on the effectiveness, Eqs. (20) and (21) as the final equations in terms of actual and coded factors are presented herewith:

To evaluate the validity of the proposed model, the descriptive statistics of the model for the effectiveness of CFCT using TiO₂ nanofluid is given in Table 10.

The low value of the C.V. shows low data scatter. The R² (=) 0.9952 confirms the model’s ability to predict changes in the effectiveness of CFCT. The Adj-R² (=) 0.9936 indicates a 99.36% correlation between the model and experimental data. The model’s power in predicting points outside the defined levels is significant and had a value of 99.07%. Moreover, the difference between Pred-R² and Adj-R² is negligible, and Adeq Precision also has a substantial value of 71.322, showing the favorable conditions of the model for industry purposes.

For MWCNTs nanofluid, the insignificant terms were removed from the ANOVA table to increase the validity of the model. The P-value of the Lack of Fit term was more significant than 0.05 and negligible. The software presented a quadratic equation with ({R}^{2}=) 0.9997 as the model equation, and the normal plot of residuals showed the good proximity of the residues to the normal line and in the diagram effectiveness values Predicted vs. Actual good agreement were observed between experimental and model data.

Figure 11 represents the normal effectiveness plot of residuals and compares the acquired experimental values with the predicted effectiveness values of TiO₂ nanofluid. The proximity of the data to the normal line and the conformity of the predicted data with the experimental data is acceptable.

(a) Residual normal dispersion diagram for CFCT effectiveness (b) the comparison of the acquired experimental values with the predicted effectiveness values of TiO₂ nanofluid.

The effect of flow rate and concentration of TiO₂ nanofluid on the effectiveness of CFCT is shown in Fig. 12. The velocity of the circulating fluid increased with the increase of flow rate, leading to a decrease in the fluid’s residence time inside the bed. Therefore, a heat and mass transfer time limit reduced the cooling range. On the other hand, the effectiveness of CFCT was influenced by its cooling range. Thus, the trend of changes in the tower’s effectiveness was similar to the cooling range. It was observed that with increasing concentration up to about 0.08 wt%, the effectiveness initially increased and then decreased. The maximum effectiveness was in the concentration range of 0.08 wt%. Increasing the flow rate had a similar effect on the effectiveness of CFCT using MWCNTs nanofluids²⁸.

The effect of flow rate and concentration using TiO₂ nanofluid on the effectiveness of CFCT, two-dimensional (contour) and three-dimensional diagrams.

Figure 13 shows the average effectiveness of the five flow rates at specific concentrations. Also shown is the percent change in average effectiveness using nanofluids compared to pure water at specific concentrations. Nanofluid at 0.085 wt% showed the most remarkable improvement in effectiveness compared to pure water with a change of 4.1%, while the highest effectiveness using MWCNTs nanofluids at a similar concentration was 10.2%. Therefore, the use of MWCNTs shows better performance than TiO₂ nanoparticles in improving the effectiveness²⁸.

The average effectiveness and the percentage variation in the average effectiveness at specific concentrations in all the flow rates using nanofluids compared to pure water.

Changes in Merkel number (transfer characteristic) as a function of concentration and flow rate

By performing the experiments considering data in Table 6 and Eq. (14), the Merkel number (transfer characteristic) of CFCT was obtained and entered into the software for verification. Tables 11 and 12 show the ANOVA data for the Merkel number of CFCT using MWCNTs and TiO₂ nanofluids, respectively. The model’s terms with a P-value (>) 0.1 were removed from both tables, and the final values are provided in Tables 11 and 12. The Lack of Fit term is unimportant for both nanofluids, which revealed an acceptable agreement between the experimental and model results.

According to the ANOVA table, the cubic model has the necessary conditions to fit the experimental data for both nanofluids. The P-value is less than 0.05 for the model and greater than this value for the Lack of Fit term, demonstrating that the model is significant, and the Lack of Fit data is not significantly related. The ({R}^{2}=) 0.9959 for MWCNTs nanofluids and ({R}^{2}=) 0.9985 for TiO₂ nanofluids represent the high accuracy of the models presented for both nanofluids in describing response changes at surface points of independent variables (Tables 13 and 14).

According to the significant terms of the model in the ANOVA table for MWCNTs and TiO₂ nanofluids, the model equation for both nanofluids is the modified cubic equation, from which insignificant terms were removed. Equations (22) and (23) present the coded and realistic model equations for predicting the effect of concentration and flow rate of MWCNTs nanofluid, respectively. Also, Eqs. (24) and (25) are provided for TiO₂ nanofluids.

According to the ANOVA table and the presented equations, the main difference between the two models is the terms that indicate the interaction of the final response between the two affecting factors, flow rate and concentration. In the TiO₂ nanofluid model equation, flow rate and concentration interact with the final Merkel number due to (AB) and ({AB}^{2}) terms. In contrast, in the MWCNTs nanofluid model equation, these terms were removed from the final equation due to the large P-value.

Figure 14 shows the normal residual diagrams of TiO₂ and MWCNTs nanofluids comparing the expected Merkel number and experimental values. The data for both MWCNTs and TiO₂ nanofluids are near the normal line showing a good agreement between the acquired experimental values with the predicted values.

The normal residual diagrams of TiO₂ and MWCNTs nanofluids comparing the expected Merkel number and experimental values.

Figure 15 depicts the influence of MWCNTs and TiO₂ nanofluid concentration and flow rate on the Merkel number of CFCT in three-dimensional and contour diagrams. The Merkel number decreased as the flow rate of nanofluids increased, lessening the tower performance. Although raising the flow rate raised the Reynolds number and therefore the mass and heat transfer coefficient, the decrease in residence time and transfer time had a more significant effect, confirming the inverse relation between Merkel number and circulating fluid flow rate.

The influence of MWCNTs and TiO₂ nanofluid concentration and flow rate on the Merkel number of CFCT in three-dimensional and contour diagrams.

According to Fig. 15, the Merkel number was affected differently depending on the concentration of different flow rates. The change in Merkel number was more reliant on the concentration change at lower flow rates of both nanofluids. However, the influence of the concentration change on the Merkel number was minor at higher flow rates. The explanation for this is evident in Merkel’s numerical relations. The mass transfer coefficient and total heat transfer coefficient increased as the concentration increased. As a result, the Merkel number increased.

Nevertheless, as previously explained, increasing the flow reduces the Merkel number. The increasing effect of concentration was higher than the decreasing effect of flow rates on the Merkel number at lower flow rates. However, flow rates highly affect the Merkel number at higher flow rates. The highest Merkel number for CFCT using MWCNTs and TiO₂ nanofluids was reported at 0.08 and 0.06 wt%, respectively.

Figure 16 presents the average Merkel number of CFCT at diverse concentrations and five specified flow rates considering MWCNTs and TiO₂ nanofluids. It is observed that the Merkel number for MWCNTs and TiO₂ nanofluids improved by about 28 and 5% compared to pure water, respectively. Furthermore, at almost all concentrations, the performance of MWCNTs nanofluids was better than TiO₂ nanofluids.

The average Merkel number of CFCT at diverse concentrations and five flow rates considering MWCNTs and TiO₂ nanofluids.

Optimization

The CFCT is optimal when the tower’s cooling range, effectiveness, and Merkel number are at their highest possible values based on the process circumstances. Two independent variables, flow rate and concentration, must be set to maximize the abovementioned responses. The optimal values were obtained at low concentrations and high flow rates. Since the optimal condition was reported at lower concentrations, the cost-effectiveness of this process can be determined. Table 15 lists the software’s optimization criteria for both nanofluids. The importance of each parameter in optimization was assigned a value between 1 and 5. For example, maximizing effectiveness is three times more important than minimizing nanofluid concentration. This decision was made owing to the importance of tower performance.

The best conditions for each parameter using MWCNTs and TiO₂ nanofluids selected by the program are listed in Table 16. Desirability, which has a value between zero and one, reflects how simple it is to achieve stated goals. The desirability of one implies that the stated goals are incredibly accessible and easy to attain. The program will likely give a large number of optimum spots. It is also more challenging to propose software to create targets to improve the value of optimization, and the ideal point reached.

The desirability of 0.571 presented for MWCNTs nanofluids shows that by adjusting the flow rate to 2.092 kg/min with a concentration of 0.069 wt% and a probability of 57.1%, the cooling range, effectiveness, and Merkel number of the tower will be 23.496, 55.736%, and 0.639, respectively. In addition, for TiO₂ nanofluids, with a flow rate adjustment to 2.116 kg/min with a concentration of 0.033 wt% and a probability of 65%, the cooling range, efficiency, and Merkel number of the tower will be equal to 20.551, 50.796%, and 0.510, respectively.

The tests were repeated three times under optimal point circumstances to validate the optimal point, and the mean values are shown in Table 17. The reported values are inside the anticipated range and verify the optimal value’s correctness. This illustrates the effectiveness of the response surface approach in optimizing cooling tower performance.