Effects of Hall Current and Thermal Radiation on the Time-Dependent Swirling Flow of Hybrid Nanofluids over a Disk Surface: A Bayesian Regularization Artificial Neural Network Approach
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsFor automobile and aerospace engineers, implementing Hall currents and thermal radiation in cooling systems helps increase the performance and durability of an engine. The current study’s aim is to give an extensive evaluation of the different approaches to an unstable CoFe2O4 − Al2O3 and water flow under the influence of a spinning disk. The understanding of the effects of Hall current and thermal radiation on the temporal variation of hybrid nanofluids flow over a disk surface would be useful in the advancement of thermal energy management and fluid dynamics using artificial intelligent and computational optimizing myths such as neural networks Bayesian process. Certain implications of involving thermal radiation and Hall current in the design and optimization of systems that involve hybrid nanofluids. Such understanding can be useful in a range of industries such as aerospace and automotive engineering and renewable energy systems.
- Need to describe numerical process such as how is the domain? To divide the domain in the grids, how to develop the governed equations into numerical equations. The result needs to be proved clearly for validation. In addition the process of ANN needs to be explained clearly regarding the data input, how to process the data, and the expected result, can be in diagram form of ANN.
- The manuscript is relevant for the field. The cited references are mostly recent publications (within last 5 years) and relevant. The manuscript is scientifically sound. The figures/tables/images/schemes are appropriate. They properly show data. They are easy to interpret and understand. The data is interpreted appropriately and consistently throughout the manuscript. The conclusions are consistent with the evidence and arguments presented. The ethics statements are adequate. Data availability statements are quite clear.
Author Response
For automobile and aerospace engineers, implementing Hall currents and thermal radiation in cooling systems helps increase the performance and durability of an engine. The current study’s aim is to give an extensive evaluation of the different approaches to an unstable CoFe2O4 − Al2O3 and water flow under the influence of a spinning disk. The understanding of the effects of Hall current and thermal radiation on the temporal variation of hybrid nanofluids flow over a disk surface would be useful in the advancement of thermal energy management and fluid dynamics using artificial intelligent and computational optimizing myths such as neural networks Bayesian process. Certain implications of involving thermal radiation and Hall current in the design and optimization of systems that involve hybrid nanofluids. Such understanding can be useful in a range of industries such as aerospace and automotive engineering and renewable energy systems.
Comment 1:
Need to describe numerical process such as how is the domain? To divide the domain in the grids, how to develop the governed equations into numerical equations. The result needs to be proved clearly for validation. In addition the process of ANN needs to be explained clearly regarding the data input, how to process the data, and the expected result, can be in diagram form of ANN.
Response: Numbering starts from discretization of the physical domain such as spinning disk, where domain can be uniform or non uniform and the governing equations such as Navier Stokes and energy equations including Hall currents and thermal radiation is converted into numerical form by finite difference, finite volume or finite element methods. Some of the advanced boundary and initial conditions are put in place; the algebraic system thus formed is then solved by using methods like Gauss-Seidel, conjugate gradient and so on. The numerical solutions obtained are compared with experiment or analytical solution for decision making, and the results are checked for grid independency before finalizing the solution. In the ANN process for this study, the input data, which include the fluid properties, the magnetic field intensity and the boundary conditions are first preprocessed by being normalized and thereafter introduced into the network which consists of an input layer, the hidden layers and the output layer. The network is trained for error back propagation so as to make real time predictions of the thermal and velocity fields of fluids and to serve as an optimization algorithm.
Comment 2:
The manuscript is relevant for the field. The cited references are mostly recent publications (within last 5 years) and relevant. The manuscript is scientifically sound. The figures/tables/images/schemes are appropriate. They properly show data. They are easy to interpret and understand. The data is interpreted appropriately and consistently throughout the manuscript. The conclusions are consistent with the evidence and arguments presented. The ethics statements are adequate. Data availability statements are quite clear.
Response: Thanks for the appreciation.
Reviewer 2 Report
Comments and Suggestions for Authors1. While the manuscript introduces the Bayesian regularization ANN approach, more explanation on why this specific method was chosen over other machine learning techniques (such as standard backpropagation or other optimization algorithms) would improve clarity for readers less familiar with these methods.
2. Some of the mathematical equations and transformations (PDEs to ODEs) are central to the study but could benefit from clearer presentation or step-by-step explanation, particularly in the methodology section. Consider adding more detail or referencing specific equations more explicitly throughout the text.
3. The manuscript makes good use of graphical results to explain parametric effects, but the figures might benefit from clearer captions. Include more detailed descriptions to make the significance of each graph easier to understand, particularly for readers who may not be specialists in hybrid nanofluid dynamics.
4. The manuscript provides computational results for fluid velocity and temperature profiles, but the physical implications of these results could be elaborated further. For instance, how do the changes in azimuthal and radial velocities specifically affect practical systems in aerospace or automotive applications?
5. The effect of thermal radiation on the hybrid nanofluid system is briefly discussed. Expanding this discussion with more physical insight, particularly regarding how thermal radiation alters energy transfer mechanisms in practical engineering systems, would strengthen the manuscript.
6. The use of neural network training methods (performance metrics, error histograms, regression plots) is valuable, but consider including a brief discussion of potential overfitting risks and how they were mitigated during the training process.
7. There are occasional inconsistencies in terminology (e.g., “ANN-BRs” vs. “Bayesian regularization ANN”). Consistent terminology throughout the manuscript would improve readability and reduce confusion.
8. While the conclusion summarizes the key findings, it could benefit from a stronger connection to potential future work. What are the next steps in advancing this research, and how might the presented findings be validated experimentally or applied in real-world scenarios?
Author Response
- While the manuscript introduces the Bayesian regularization ANN approach, more explanation on why this specific method was chosen over other machine learning techniques (such as standard backpropagation or other optimization algorithms) would improve clarity for readers less familiar with these methods.
Response: Thanks for your valuable recommendations. This approach minimizes overfitting by implementing regularization in training the neural network while being more appropriate for applying to extensively challenging problems with scarce samples than the usual backpropagation or other procedures.
- Some of the mathematical equations and transformations (PDEs to ODEs) are central to the study but could benefit from clearer presentation or step-by-step explanation, particularly in the methodology section. Consider adding more detail or referencing specific equations more explicitly throughout the text.
Response: Thanks for your valuable suggestion, the authors have explained in a step-by-step manner.
- The manuscript makes good use of graphical results to explain parametric effects, but the figures might benefit from clearer captions. Include more detailed descriptions to make the significance of each graph easier to understand, particularly for readers who may not be specialists in hybrid nanofluid dynamics.
Response: Thanks for your valuable suggestion, the authors have updated the graphical results with different color schemes in curves.
- The manuscript provides computational results for fluid velocity and temperature profiles, but the physical implications of these results could be elaborated further. For instance, how do the changes in azimuthal and radial velocities specifically affect practical systems in aerospace or automotive applications?
Response: Thanks for your valuable recommendations. The variations in azimuthal and radial velocities fundamentally modify practical aerospace and automotive systems (these velocities can be checked from Figure 1) by increasing convective heat entry for the cooling of components, increasing efficiency, and decreasing thermal stress in hot zones such as turbine blades, engines, automobile transmissions, and brake systems.
- The effect of thermal radiation on the hybrid nanofluid system is briefly discussed. Expanding this discussion with more physical insight, particularly regarding how thermal radiation alters energy transfer mechanisms in practical engineering systems, would strengthen the manuscript.
Response: Thanks for your valuable suggestion, the authors have discussed the physical parameters like the Nusselt number in the revised manuscript.
- The use of neural network training methods (performance metrics, error histograms, regression plots) is valuable, but consider including a brief discussion of potential overfitting risks and how they were mitigated during the training process.
Response: Thanks for your valuable suggestion, the authors have discussed the potential overfitting risks in section 6.
- There are occasional inconsistencies in terminology (e.g., “ANN-BRs” vs. “Bayesian regularization ANN”). Consistent terminology throughout the manuscript would improve readability and reduce confusion.
Response: Thanks for your valuable suggestion.
- While the conclusion summarizes the key findings, it could benefit from a stronger connection to potential future work. What are the next steps in advancing this research, and how might the presented findings be validated experimentally or applied in real-world scenarios?
Response: Thanks for your valuable suggestion, the authors have added it in the last section 8.
Reviewer 3 Report
Comments and Suggestions for Authors1. The abstract should further clarify the novelty and best findings of the study.
2. It is better to provide spaces between numerals and units/ maintain uniformity in using SI units.
3. Kindly provide the citation for all equations, which are not derived by the authors.
4. The paper seems to have been written too hastily. Please review carefully subscripts and superscripts.
5. Results should be supported/justified scientifically for Nusselt number and Sherwood number.
6. Figures are not included properly.
7. Comprehensive proofreading is essential throughout the manuscript to rectify typos/grammatical errors.
8. What are the limitations of the current study?
9. Include the nomenclature and abbreviations.
10. The densities of Al2O3 and CoFe2O4 are high compared with the water. What basis these nanoparticles are selected? Stability of the nanofluids is tested?
11. Why did the authors not perform the volume concentrations beyond the 0.15 %? Explain.
Major revision as briefly mentioned above is required for further consideration.
Author Response
- The abstract should further clarify the novelty and best findings of the study. It is better to provide spaces between numerals and units/ maintain uniformity in using SI units.
Response: Thanks for your valuable recommendations. The authors have updated the manuscript with a blue color in the revised version.
- Kindly provide the citation for all equations, which are not derived by the authors.
Response: Thanks for your valuable suggestion. The authors updated the equations citation.
- The paper seems to have been written too hastily. Please review carefully subscripts and superscripts.
Response: Thanks for your valuable suggestion.
- Results should be supported/justified scientifically for Nusselt number and Sherwood number.
Response: Thanks for your valuable recommendations. The results are now discussed for Nusselt number in Tables 2 and 3.
- Figures are not included properly.
Response: Thanks for your valuable suggestion, figures are arranged properly.
- Comprehensive proofreading is essential throughout the manuscript to rectify typos/grammatical errors.
Response: Thanks for your valuable suggestion. The manuscript has now been comprehensively proofread.
- What are the limitations of the current study?
Response: Thanks for raising the valuable question. The physical model considered in this study is fully idealized with perfect fluid flow, constant material properties, and very simple boundary conditions. In the realistic implementation of this concept, some constraints such as turbulence, complex shapes, nonuniform heat sources, and variability in the properties of both the base fluid and the nanofluid could influence the effectiveness of the hybrid nanofluids.
- Include the nomenclature and abbreviations.
Response: Thanks for your valuable suggestion. The nomenclature is added before the introduction.
- The densities of Al2O3 and CoFe2O4 are high compared with the water. What basis these nanoparticles are selected? Stability of the nanofluids is tested?
Response: Thanks for your valuable question. Regardless of their densities that are much larger than that of water the choice of aluminum oxide (Al₂O₃) and cobalt ferrite (CoFe₂O₄) nanoparticles likely stem from other properties which include thermal, magnetic, and mechanical properties in heat transfer and performance boosts across cooling or energy applications.
- Why did the authors not perform the volume concentrations beyond the 0.15 %? Explain.
Response: Thanks for raising the valuable question. The authors could not go beyond 0.15% in volume concentration for some realistic and technical reasons associated with the flow behavior of nanofluids.
- At higher volume fractions of the nanoparticles, then the major concern is the clusters of the nanoparticles. This can cause fluctuation in the nanofluid, whereby the nanoparticles will tend to delaminate or block some sections of the system, lessening the utility of the nanofluid.
- When the concentration exceeds a certain level (as a rule, it is less than 0.15% in many studies), it becomes difficult to achieve dispersion stability and in the case of nanoparticles, if surfactants or other stabilizers do not prevent agglomeration of the particles, then the improvement in thermal properties does not persist.