A vehicle engine cooling system is of utmost importance to ensure that the engine operates in a safe temperature range. In most radiators that are used to cool an engine, water serves as a cooling fluid. The performance of a radiator in terms of heat transmission is significantly influenced by the incorporation of nanoparticles into the cooling water. Concentration and uniformity of nanoparticle distribution are the two major factors for the practical use of nanofluids. The shape and size of nanoparticles also have a great impact on the performance of heat transfer. Many researchers are investigating the impact of nanoparticles on heat transfer. This study aims to develop an artificial neural network (ANN) model for predicting the thermal conductivity of an ethylene glycol (EG)/water-based crystalline nanocellulose (CNC) nanofluid for cooling internal combustion engine. The implementation of an artificial neural network considering different activation functions in the hidden layer is made to find the best model for the cooling of an engine using the nanofluid. Accuracies of the model with different activation functions in artificial neural networks are analyzed for different nanofluid concentrations and temperatures. In artificial neural networks, Levenberg–Marquardt is an optimization approach used with activation functions, including Tansig and Logsig functions in the training phase. The findings of each training, testing, and validation phase are presented to demonstrate the network that provides the highest level of accuracy. The best result was obtained with Tansig, which has a correlation of 0.99903 and an error of 3.7959 ×10^{–8}. It has also been noticed that the Logsig function can also be a good model due to its correlation of 0.99890 and an error of 4.9218 ×10^{–8}. Thus our ANN with Tansig and Logsig functions demonstrates a high correlation between the actual output and the predicted output.

The engine-cooling system is an essential part of a vehicle, providing the engine’s coolness and maintaining a safe temperature range for efficient operation. Engine cooling is performed through a heat transfer between the coolant running around the engine and the surrounding atmosphere through a radiator. In this process, the coefficient of thermal conductivity is critical to ensuring that the coolant can reduce the engine’s temperature to a suitable level for its operating condition [

Samylinggam et al. [

Conversely, distinct research by Raddy et al. [_{2}). Their findings indicated that the volume concentration of nanoparticles and the temperature significantly contribute to the enhancement of thermal conductivity in TiO_{2} nanofluids. Christensen et al. [_{2}O_{3}) and copper oxide (CuO) across various temperatures and nanoparticle concentrations. The authors presented findings showing that the thermal conductivity enhancement of Al_{2}O_{3} nanofluid at a volume concentration of 0.8% varies between 9.8% and 17.89%. This increase ranges from 15.6% to 24.56% nanofluid over an identical temperature range of 15°C to 50°C. Witharana et al. [_{2}O_{3} and TiO_{2}. Additional studies further explored the thermal conductivity of EG/water [

Over the past two decades, artificial neural network (ANN) deployment has become prevalent, covering various applications from regression to classification tasks [_{2}-EG/water [_{2}-water [_{2,} and calcium Carbonate (CaCO_{3}) under varying temperature and volume concentrations. Their model demonstrated remarkable accuracy, evidenced by a correction coefficient of 0.99913 and an exceedingly mean error rate of only 0.02%. While a considerable amount of research has been conducted on ANN, there remains a gap in experimental applications, particularly in employing ANN for the composition of EG/water mixtures with cellulose nanocrystals. Hence, this research aims to develop an ANN model to predict nanofluids’ thermal conductivity based on EG/water with CNC. The ANN model utilizes nanofluid concentrations, temperature, and composition details. The Levenberg-Marquardt algorithm is employed as the training mechanism. In the design of the ANN model, the various activation functions are integrated to augment its computational efficacy. This deliberate incorporation of diverse activation functions is instrumental in generating a wide range of outcomes, significantly boosting the network’s precision and efficiency. Subsequently, the performance of the neural network is evaluated and analyzed. This process is pivotal in identifying superior activation functions and establishing a correlation between the network’s actual and anticipated output.

As depicted in

The value of output

The value of

Back-propagation is a supervised learning algorithm primarily employed in the mathematical training neural networks. Its core function is to minimize the loss function, thereby enhancing the accuracy and efficiency of the neural networks. The neural network is trained by changing the weights and biases, also known as the hyperparameters, rather than the input values. The training phase of neural networks ensures that error is minimal. In backward propagation, the calculation of hyperparameter changes is performed for the learning of the ANN. Typically, the Mean Square Error (MSE) is employed as a quadratic loss metric within the framework of an error function (

Considering that,

Data points are typically subjected to pre-processing steps to normalize the dataset, ensuring that the first layer receives data with a zero mean. This diminishes the disparities in data scales and establishes a correlation among various data attributes [

We assume v′ as the normalized data, v as unnormalized data, _{minA} as –1 to normalize to an equal scale of [−1, 1]. The equation of max-min normalization for each data point is as

The max-min normalization technique plays a pivotal role in implementing neural networks. This method effectively scales the diverse range of numerical values in the dataset’s feature, standardizing them into a unified range of [−1, 1]. Such standardization is crucial for optimizing the performance and efficacy of neural networks by ensuring consistent data scales for all features. The Z-score normalization method is adeptly employed to standardize input data, thereby enhancing the efficiency of gradient descent. This approach retains the range extremities’ maximum and minimum values while incorporating critical statistical measures such as variance and standard deviation. This approach streamlines data processing and ensures a more robust and consistent data normalization framework. Assume we denote all data points as ‘

At this stage, all data points have been adjusted to zero-centred, effectively achieving a zero mean.

Maintaining consistency in the data transformation process is essential by applying the identical mean and variance in normalizing the primary dataset to subsequent datasets, including the test and validation sets. This ensures a uniform standard of normalization across all data segments.

MSE is a standard error estimation method to determine the neural network’s error rate. When the value of the MSE is high, the error value is high, and zero means the model has the correct and accurate prediction [

An adjustable hyperparameter’s learning rate plays a pivotal role in defining the speed at which a neural network model adepts and learns from a specific task. It is crucial to fine-tune this learning rate to an optimal level, significantly reducing error and enhancing the model’s efficiency. Nevertheless, there are specific challenges associated with setting learning rates. It may lead to a phenomenon known as gradient explosion in the model if the learning rate is set excessively high. Conversely, setting the learning rate too low can result in excessively prolonged training durations, leading to a scenario where the model takes an extended time to converge to a minimum or may fail to reach the minimum. Typically, learning rates are set within a spectrum ranging from 10^{−6} to 1.0. We have initiated our learning rate at 0.01, aligning it with the specific requirements and goals.

The training phase of the neural network is initiated with an assembled dataset engineered to predict the thermal conductivity of EG/water-based CNC precisely. This dataset comprises three pivotal input variables, including the proportion of EG to water, the concentration of CNC, and the elevated temperature. Additionally, it includes the output variable, which is the thermal conductivity. The utilization of these data points in training the neural network is illustrated in

The subsequent phase involves data splitting, which is performed utilizing a sophisticated technique known as data partitioning. Three distinct features enrich this dataset, comprising 1632 data points segmented into smaller subsets. These subsets play a pivotal role in the efficient training of the neural network. They are categorized into distinct phases, including training, testing, and validation, each allocated in specific, calculated ratios to optimize the learning and validation process. For this study, the distribution ratio has been set at 6:2:2. This deliberate calibration ensures that substantial data is allocated for training while sufficient data are allocated for testing and validation. Such a balanced approach is pivotal in mitigating risks associated with underfitting and overfitting, thereby fostering the development of a more accurate model. The data is randomly slit during training using the “dividerand” function as the neural network dividing mechanism. In this setup, the 6:2:2 ratio translates to 980 data points for training, 326 for testing, and 326 for validation.

As depicted in

In the context of model training, generalization is characterized by an increase in validation error, indicating that the model has exceeded its optimal capacity for accurate predictions. This phenomenon is a critical component of regularization techniques to enhance the model’s performance and reliability during training. An extensive array of activation functions was rigorously tested within the hidden layers of the neural networks. This diverse set includes the Logsig, Tansig, Softmax, Satlin, Elliotsig, Poslin, Purelin, and Hardlim. The objective was to assess their impact on the network’s efficacy and overall performance. The neural network’s performance is recorded and reiterated using various activation functions. The Mean Square Error is employed as the loss function, a standard approach in regression lasks, providing a reliable measure of model accuracy. The design of neural networks encompasses a wide array of critical hyperparameters, the specific learning rate, and the selected optimization algorithm, which are integral to fine-tuning the network’s functionality and optimizing its overall performance. The network’s training hyperparameters have been established based on the specifications outlined in

Hyperparameters | Value |
---|---|

Optimization algorithm | Levenberg–Marquardt |

Learning rate | 0.01 |

Loss function | MSE |

Epoch | 1000 |

This research uses ANN to predict thermal conductivity in EG/water mixtures with incorporated CNC. The study examines various activation functions in the hidden layers of the ANN, aiming to evaluate and enhance the accuracy and reliability of the network’s predictive capabilities. Several activation functions, including Tansig, Logsig, Hardlim, Poslin, Elliotsig, Softmax, Satlin, and Purlin, are used in the neural network’s model. ^{th} epoch, marking the conclusion of the training period. At this juncture, the model achieves a notably refined level of precision, evidenced by an MSE of 3.7959 × 10^{−8}, reflecting the culmination of optimized learning. In addition, the intricate details of the network’s architecture are elucidated in

Hidden layer neurons | Weights | Bias | ||
---|---|---|---|---|

w_{1y} |
w_{2y} |
w_{3y} |
||

1 | −0.2726 | 0.8116 | −2.2066 | 1.5956 |

2 | 2.3033 | −1.5101 | −0.1212 | −4.3488 |

3 | −1.9325 | 0.2230 | 0.4131 | 1.9189 |

4 | −0.0818 | −3.2331 | 3.4678 | 5.4702 |

5 | −0.6132 | −2.2786 | −0.3169 | 0.8475 |

6 | −6.1231 | 5.7153 | 0.0949 | 2.3003 |

7 | −2.8735 | 3.5602 | 0.7503 | 0.1842 |

8 | −1.7434 | −0.1216 | 1.8382 | 0.1931 |

9 | −0.5370 | 0.9613 | −0.8999 | −0.6623 |

10 | −1.7608 | 4.2824 | 0.9663 | 0.1224 |

11 | −0.6548 | 1.7703 | 0.0238 | −3.0588 |

12 | 2.6612 | −3.8714 | 0.2686 | 2.7306 |

13 | −0.2289 | −2.8022 | 0.2193 | −2.2740 |

14 | 1.2636 | −1.0382 | 0.2682 | 1.4219 |

15 | −1.9142 | 1.5675 | −0.7351 | −2.9052 |

Neurons | Weights | Bias | |
---|---|---|---|

1 | w_{1y} |
0.027438574 | −0.980014300 |

2 | w_{2y} |
−0.227341126 | |

3 | w_{3y} |
0.557141197 | |

4 | w_{4y} |
−0.021804455 | |

5 | w_{5y} |
−0.200701036 | |

6 | w_{6y} |
0.149936774 | |

7 | w_{7y} |
−1.208035759 | |

8 | w_{8y} |
−0.022412308 | |

9 | w_{9y} |
0.080219847 | |

10 | w_{10y} |
0.818629678 | |

11 | w_{11y} |
0.123792151 | |

12 | w_{12y} |
−3.814119540 | |

13 | w_{13y} |
−0.419235180 | |

14 | w_{14y} |
5.397284068 | |

15 | w_{15y} |
1.051245690 |

The training data plays a pivotal role in attaining the optimal configuration of the network. In this study, the data sets allocated for training substantially exceed those designated for testing and validation purposes. In particular, 60% of the data set is dedicated to network training. This training data is derived from a strategically randomized selection spanning the full spectrum of the ANN experimental results.

^{−8}) than the Logsig (4.9218 × 10^{−8}). This discrepancy can be attributed to the intrinsic properties of the Tansig activation functions, particularly its centering around zero and its superior facilitation of the neural network’s learning capabilities, as detailed [

AFs | Epoch | Time (s) | MSE | MOD% | Train | Validation | Test | All |
---|---|---|---|---|---|---|---|---|

Tansig | 46 | 19 | 3.7959 × 10^{−8} |
1.05 | 0.99904 | 0.99918 | 0.99885 | 0.99903 |

Logsig | 38 | 12 | 4.9218 × 10^{−8} |
1.11 | 0.99901 | 0.99891 | 0.99853 | 0.99890 |

Elliotsig | 459 | 1000 | 9.6291 × 10^{−8} |
1.63 | 0.99852 | 0.99742 | 0.99857 | 0.99817 |

Softmax | 955 | 94 | 5.4144 × 10^{−7} |
1.79 | 0.99574 | 0.99153 | 0.99138 | 0.99288 |

Poslin | 99 | 12 | 6.6284 × 10^{−7} |
2.02 | 0.99492 | 0.99269 | 0.99197 | 0.99319 |

Satlin | 1000 | 29 | 1.2259 × 10^{−6} |
2.68 | 0.98572 | 0.98267 | 0.97523 | 0.98120 |

Purelin | 3 | 0 | 1.8600 × 10^{−3} |
2.12 | 0.81595 | 0.81374 | 0.80698 | 0.81374 |

Hardlim | 4 | 0 | 2.7120 × 10^{−3} |
2.97 | 0.71267 | 0.71170 | 0.70906 | 0.71177 |

Additionally, several other activation functions have been identified as highly effective for this specific task, demonstrating notable accuracy. Functions such as Elliotsig, Softmax, and Poslin have all achieved a high correlation coefficient of 0.99, underscoring their suitability and effectiveness in this context. Upon comparing all activation functions that have been experimented with, it is observed that the Hardlim function exhibits the lowest accuracy, as evidenced by its correlation coefficient of 0.71177. Additionally, it presents an MSE of 0.002712, further indicating its relative underperformance compared to the other activation functions tested.

The scholarly literature extensively investigates the role of activation functions in ANNs for predicting thermal properties. This study’s focus has significantly contributed to the field, enhancing the precision and efficacy of thermal property predictions by strategically selecting and applying various activation functions in ANN models. The study in reference [^{−5}, exemplifying the model’s exceptional accuracy in the field of nanofluid thermal mechanism. Another ANN model with Tanh and linear activations functions accurately predicted the thermal conductivity of WO_{3}-CuO-Ag/water hybrid nanofluids, yielding a correlation coefficient of 0.997 and MSE of 7.0 × 10^{−6}, showing the model’s high precision in thermal analysis [^{−8} with the Tansig activation function compared to the other models.

In this research, the innovation lies in developing a new ANN model to predict the precision of thermal conductivity in a CNC nanofluid that uses a mixture of EG and water for cooling internal combustion engines. The database of the ANN model was established using our experimental data. The effects of network parameters, mainly activation functions, were investigated in the ANN modelling, and optimal ANN architecture was determined. The conclusion could be summarized as follows:

Different activation functions are used and analyzed in the hidden of the developed ANN model. The optimized network, consisting of 3 input nodes, 15 neurons in the hidden layer, and one output neuron, performed well in modeling the relationship between input and output parameters. This simulation shows that the Tansig activation function produces the best result with a correlation of 0.99903 and an error of 3.7959 × 10^{−8}.

It is observed that the characteristics of the Logsig activation function are almost similar to the Tansig activation function and attain a correlation of 0.99890 and an error of 4.9218 × 10^{−8}. Therefore, Logsig is a good alternative due to its good features.

The results of this model indicate a strong correlation between the thermal conductivity from experiments and the predicted value. As different vehicle types require different cooling parameters for the vehicle to run in various operating conditions, carmakers can use the neural network to test the thermal conductivity from the different parameters using simulation with ANN instead of live experiments, which is costly and time-consuming.

We intend to enhance the model generalization efficiency, optimize ANN industrial achievement, and improve cooling benefits. Therefore, future work is needed to develop a prediction model with enormous applicability and further enlarge the dataset to include a wide range of performance and control parameters.

The authors would like to thank Universiti Malaysia Pahang Al Sultan Abdullah (UMPSA), Malaysia, for their support in providing the laboratory facilities and financial assistance.

This work is supported by the International Publication Research Grant No. RDU223301.

Md. Munirul Hasan: Methodology, software, original draft preparation and editing; Mohammad Saiful Islam: Software; Wong Hung Chan: Data curation, methodology, software, original draft preparation; Md. Mustafizur Rahman: Supervision, idea generation, and conceptualization; Yasser M Alginahi: Reviewing and editing; Suraya Abu Bakar: Reviewing and editing; Muhammad Nomani Kabir: Supervision, conceptualization, reviewing, and editing; Devarajan Ramasamy: Experimental study.

Data can be provided on request.

The authors declare no conflicts of interest to report regarding the present study.

_{2}-MWCNT ternary hybrid nanofluid and the development of practical correlations

_{2}nanofluids

_{2}O

_{3}nanoparticles

_{2}O

_{3}and CuO nanofluids

_{3}O

_{4}hybrid nanofluids: An experimental assessment and application of data-driven approaches

_{3}O

_{4}/water nanofluid: Machine learning modeling and proposing a new correlation

_{2}-water/EG hybrid nanofluid: Experimental data and modeling using artificial neural network and correlation

_{2}/Water nanofluid using artificial neural network

_{2}-CaCO

_{3}/Water hybrid nanofluid: Proposing new correlation and artificial neural network optimization

_{2}emissions, and gas-fired power plant parameters

_{3}-CuO-Ag (35:40:25)/water hybrid ternary nanofluid with artificial neural network and back-propagation algorithm