Mixed Convection Heat Transfer and Fluid Flow of Nanofluid/Porous Medium Under Magnetic Field Influence
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe study examines the synergistic impacts of magnetic fields and nanoparticle volume fractions on heat transport, fluid dynamics, and entropy production within a lid-driven porous enclosure containing TiO2-water nanofluid. The work employs the finite element approach and a projection algorithm to assess the effects of differing Richardson and Hartmann numbers, as well as solid volume percentages of nanoparticles. The findings indicate that augmenting the volume percentage of nanoparticles elevates the average Nusselt number while decreasing fluid temperature. The study examines the impact of various arrangements of moving vertical walls on streamfunctions, isotherms, heatlines, and entropy generation.
The title correct ‘’ Medi-Um’’ by ‘’ Medium’’
What is the innovation of the paper? A number of analogous studies are present in the literature.
The introduction should be improved by including recently published studies.
In figure 1, replace ‘’insulated’’ by ‘’adiabatic’’
the authors mentioned that they are using the FEM, then they mention that used a grid of 70x70 also they mentioned the number of elements, this is very confusing; please provide the figure presenting the mesh where 70x70 grid is used.
The title of table 2, should be more precise; all the fixed parameters are to be mentioned.
The paper is full of uncommon words, for example What do you mean by: ‘’Mathematical Formularization and Emulation’’ also ‘’ Simile between the results’’ , ‘’ regular magnetic field’’, ‘’prompted magnetic field’’…….., it seems that the authors are using a paraphrasing site without checking the generated text. Several non-academic and unusual words are used, this is the biggest issue with this paper
What is the used value for Pr?
The viscosity is missing in Table 1.
In the entropy generation analysis, you mention that temperature differences contribute most significantly to total entropy. Could you provide a deeper explanation of how viscous and ohmic dissipation specifically contribute to the entropy profile at high Hartmann numbers?
The authors have to present a qualitative verification (2D flow structure and temperature field ) of their model.
The titles of the figures are to be changed, give all the parameters, for example putting just ‘’streamlines’’ as figure title doesn’t give any idea on the used parameters in this specific figure.
The authors studied the mixed convection, but in fig 1 there no indication on the driven lid.
The use value of phi =0.15 is completely wrong, in fact it is well known that for nanoparticles volume fractions higher than 0.05, the nanofluid change the behaviour to non-Newtonian .
Is the variation of Ri based on a fixed Ra and varied Re or the reverse? What is the fixed value?
What is the interest of adding the undulations at the top wall? Why the effect of the number of undulations is not studied?
in figure 1 there are 2 heat sources? What is the dimension of the heat sources?
in figure 7, the authors presented the local Nu on the heat source, without indicating if it is the left or right one. In addition from this figure it seem that the dimension of the heat source is 0.4, so the total dimension of the 2 sources is 0.8, which is not in concordance with fig 1.
The scientific soundness of the paper is very low, and is full of scientific mistakes.
Comments on the Quality of English Language
The paper is full of uncommon words, for example What do you mean by: ‘’Mathematical Formularization and Emulation’’ also ‘’ Simile between the results’’ , ‘’ regular magnetic field’’, ‘’prompted magnetic field’’…….., it seems that the authors are using a paraphrasing site without checking the generated text. Several non-academic and unusual words are used, this is the biggest issue with this paper
Author Response
Comments 1: The study examines the synergistic impacts of magnetic fields and nanoparticle volume fractions on heat transport, fluid dynamics, and entropy production within a lid-driven porous enclosure containing TiO2-water nanofluid. The work employs the finite element approach and a projection algorithm to assess the effects of differing Richardson and Hartmann numbers, as well as solid volume percentages of nanoparticles. The findings indicate that augmenting the volume percentage of nanoparticles elevates the average Nusselt number while decreasing fluid temperature. The study examines the impact of various arrangements of moving vertical walls on streamfunctions, isotherms, heatlines, and entropy generation.
Response 1: Thank you for your valuable feedback on our manuscript. We appreciate your attention to detail and your suggestion in the manuscript. We have carefully reviewed the entire manuscript and have ensured that all comments are revised. Modifications have been made on data interpretations and discussions in the revised manuscript by referencing the reviewers’ comments. The grammatical errors have been revised by authors’ careful checking. All modifications have been reflected in the revised version and are marked in red font.
Comments 2:The title correct ‘’ Medi-Um’’ by ‘’ Medium’’
Response 2: The title has been corrected.
Comments 3: What is the innovation of the paper? A number of analogous studies are present in the literature.
Response 3: Thanks for the reviewer for the positive comments on our study. This paper differs from previous studies by focusing on headline and entropy analysis, which are often not considered. Additionally, the consideration of two separate heat sources sets this research apart.
Comments 4:The introduction should be improved by including recently published studies.
Response 4: Thank you very much. We are grateful for your positive feedback on our paper’s clarity and analysis. Your question regarding the introduction section is well-received. We explained and addressed all the problems mentioned by reviewers.
Comments 5:In figure 1, replace ‘’insulated’’ by ‘’adiabatic’’
Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we have update it to adiabatic.
Comments 6: the authors mentioned that they are using the FEM, then they mention that used a grid of 70x70 also they mentioned the number of elements, this is very confusing; please provide the figure presenting the mesh where 70x70 grid is used.
Response 6: Thank you for your valuable feedback. We apologize for the confusion regarding the mesh and FEM details. We included a figure depicting the 70x70 grid and the corresponding finite element mesh in the revised manuscript on pp.9. This will provide a clearer visualization of the numerical model used in our analysis.
Comments 7: The title of table 2, should be more precise; all the fixed parameters are to be mentioned.
Response 7: Many thanks for your valuable feedback. The title has been revised.
Comments 8: The paper is full of uncommon words, for example What do you mean by: ‘’Mathematical Formularization and Emulation’’ also ‘’ Simile between the results’’ , ‘’ regular magnetic field’’, ‘’prompted magnetic field’’…….., it seems that the authors are using a paraphrasing site without checking the generated text. Several non-academic and unusual words are used, this is the biggest issue with this paper
Response 8: Thank you for your valuable feedback. We have carefully reviewed the manuscript and have made necessary corrections. We have also engaged a professional proofreader to further enhance the clarity and coherence of the text.
Comments 9:- What is the used value for Pr?
Response9: The authors acknowledge the reviewer's feedback and clarify that by adding Prandtl number value (Pr = 6.2) to Table 1 on pp.6.
Comments 10: The viscosity is missing in Table 1.
Response 10: Thank you for pointing out the missing viscosity data in Table 1. We apologize for the oversight. The viscosity value has been added to table 1 on pp.6.
Comments 11: In the entropy generation analysis, you mention that temperature differences contribute most significantly to total entropy. Could you provide a deeper explanation of how viscous and ohmic dissipation specifically contribute to the entropy profile at high Hartmann numbers?
Response 11: Thank you for bringing up an essential point. As shown in Figure 5 and equations (14-17), the constant (χ̃) is inversely proportional to entropy generation. Therefore, increasing temperature (or heat flux) diminishes the impact of the Hartmann number (Ha) on entropy generation, particularly at high Darcy number (Da).
Comments 12: The authors have to present a qualitative verification (2D flow structure and temperature field ) of their model.
Response 12: We thank the reviewer for the valuable suggestion. While adding a new comparison graph at this stage may be time-consuming due to the required approvals, we will consider incorporating qualitative verification of the 2D flow structure and temperature field in future work.
Comments 13: The titles of the figures are to be changed, give all the parameters, for example putting just ‘’streamlines’’ as figure title doesn’t give any idea on the used parameters in this specific figure.
Response 13: Many thanks. All captures of figures have been revised based on your recommendation.
Comments 14: The authors studied the mixed convection, but in fig 1 there no indication on the driven lid.
Response 14: We are grateful for this comment. Fig.1 has been updated (see pp.4).
Comments 15: The use value of phi =0.15 is completely wrong, in fact it is well known that for nanoparticles volume fractions higher than 0.05, the nanofluid change the behaviour to non-Newtonian .
Response 15: While many studies have focused on volume fractions (Ï•) of 0.05, our research investigates a broader range, extending up to Ï• = 0.15. This focus on a higher volume fraction allows us to explore the potential benefits of using a more concentrated nanofluid, while still maintaining the characteristics of a Newtonian and incompressible fluid (limited to a mass fraction of ≤ 0.15). This choice aligns with recent research that has demonstrated the effectiveness of nanofluid with higher volume fraction (e.g., doi.org/10.1016/j.rinp.2023.106648 and doi.org/10.1016/j.proeng.2015.05.028).
Comments 16: Is the variation of Ri based on a fixed Ra and varied Re or the reverse? What is the fixed value?
Response16: The Grashof number is assumed to be constant for all cases at 104, and three different values of Ra based on three values of number Ri=1, 10, and 100.
Comments 17: What is the interest of adding the undulations at the top wall? Why the effect of the number of undulations is not studied?
Response 17: The undulated top wall is designed to improve heat transfer and fluid mixing. By disrupting the boundary layer and increasing the heat transfer surface area, undulations can enhance thermal performance, especially with the presence of lid driven surface. This study focuses on a specific undulation configuration, but future research will explore the impact of varying the number and amplitude of undulations to optimize heat transfer efficiency.
Comments 18: in figure 1 there are 2 heat sources? What is the dimension of the heat sources?
Response 18: Many thanks. The base wall is divided into two equal parts, each acting as a heat source with a length equal to 0.2 of the base length (see pp. 10). This information has been added to the problem description in the revised manuscript.
Comments 19: in figure 7, the authors presented the local Nu on the heat source, without indicating if it is the left or right one. In addition from this figure it seem that the dimension of the heat source is 0.4, so the total dimension of the 2 sources is 0.8, which is not in concordance with fig 1.
Response 19: The heat source is 0.2 of the bottom walls.
When X (dimensionless) = 0.2 to 0.4 (length 0.2) means the first heat source (left side).
When X (dimensionless) = 0.6 to 0.8 (length 0.2) means the second heat source (right side).
Comments 20: The scientific soundness of the paper is very low, and is full of scientific mistakes.
Response 20: We appreciate the reviewer's feedback and take their concerns seriously. We have carefully reviewed the manuscript and addressed the specific scientific issues raised. We also acknowledge that studying a heat function with entropy generation using a homemade program presents challenges. However, our approach, coupled with rigorous validation and verification, provides a reliable and accurate assessment of the system's thermal performance. We have also considered relevant literature to support our findings and methodology.
Comments 21: Comments on the Quality of English Language
Response 21 : All modifications have been made on data interpretations and discussions in the revised manuscript by referencing the reviewers’ comments. The grammatical errors have been revised by authors’ careful checking.
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
The manuscript applsci-3298820-v1 needs some improvement.
Include a Table with the Pi-groups related with the problem physics; it is important to present a physical interpretation of each non-dimensional parameter.
The sensitivity of both Reynolds number and Richardson number should be better clarified.
Include some comment concerning the investigated problem behaviour under transition to turbulence and turbulence. What is expected for?
What is expected for the Nusselt number behavior as the Reynolds number increases, and the transition appears?
It is unclear if the Boussinesq approximation has been adopted. Please, clarify that question and include some short discussion about it.
It is recommended a better discussion about entropy generation.
The capture of effects of buoyancy forces must be suitably discussed too.
Remove Figure 8 of “section “Conclusions” to “section 5.7”.
The limitations of the present methodology and results must be commented including suggestions/direction for future.
With regards.
Author Response
Summary Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions in yellow highlighted changes in the re-submitted files.
Comments 1: Include a Table with the Pi-groups related with the problem physics; it is important to present a physical interpretation of each non-dimensional parameter.
Response 1: Thank you for pointing out the need to update the equations. While a revision at this stage would necessitate renumbering the equations, we will certainly incorporate this feedback into our future work.
Comments 2: The sensitivity of both Reynolds number and Richardson number should be better clarified.
Response 2: We concur with the reviewer's assessment. While the impact of the Richardson number is significant, this study assumed a constant value due to page constraints. A dedicated study exploring the effects of varying Richardson number is currently under review.
Comments 3: Include some comment concerning the investigated problem behaviour under transition to turbulence and turbulence. What is expected for?
Response 3: Thank you for your insightful comment. While a comprehensive analysis of the system's behavior under turbulent flow conditions is beyond the scope of this current study, we acknowledge the importance of this aspect. As you correctly point out, turbulent flow introduces significant complexities. We plan to investigate this behavior in future work, employing turbulence models such as the k-epsilon model to capture the intricate dynamics. We appreciate your understanding and look forward to sharing our findings on turbulent flow in a future publication.
Comments 4: What is expected for the Nusselt number behavior as the Reynolds number increases, and the transition appears?
Response 4: Thanks a lot. As the Reynolds number increases, the flow transitions from laminar to turbulent. This transition is accompanied by significant changes in the flow structure, including the formation of vortices and increased mixing. Consequently, the heat transfer rate, quantified by the Nusselt number, is expected to increase substantially compared to laminar flow. A detailed analysis of this behavior, including quantitative predictions, will be presented in a future publication.
Comments 5: It is unclear if the Boussinesq approximation has been adopted. Please, clarify that question and include some short discussion about it.
Response 5: The Boussinesq approximation was employed in the momentum equation (Eq. 3). This approximation assumes that all fluid properties, except density, remain constant. Density variations, induced by temperature differences, result in a body force term in the vertical momentum equation.
Comments 6: It is recommended a better discussion about entropy generation.
Response 6: Regarding your suggestion, we have carefully considered and revised the discussion on entropy generation. While a detailed analysis of entropy generation is beyond the scope of this current study, we have included a concise discussion that highlights the key findings. A more in-depth exploration of entropy generation will be presented in a forthcoming work.
Comments 7: The capture of effects of buoyancy forces must be suitably discussed too.
Response 7: Thank you for your comment. The Boussinesq approximation was employed in the momentum equation, assuming constant fluid properties except for density. While this approach is valid for many nanofluid applications, the impact of variable thermophysical properties on buoyancy forces will be investigated in future studies.
Comments 8: Remove Figure 8 of “section “Conclusions” to “section 5.7”.
Response 8: Figure 8 has been moved to section 5.7 in the revised manuscript.
Comments 9: The limitations of the present methodology and results must be commented including suggestions/direction for future.
Response 9: Future work could explore turbulent and transient flow regimes, different nanofluid types and base fluids, and investigate the effects of variable thermophysical properties and non-uniform nanoparticle distribution. Given the extensive range of potential future research avenues, we defer specific recommendations to the discretion of future investigators.
Reviewer 3 Report
Comments and Suggestions for AuthorsIn this paper, the author discusses the impact of a constant magnetic field on heat transfer, flow of fluid, and entropy generation of mixed convection. But the work still needs more efforts to make this paper published. The following concerns should be clarified beforehand.
1. Introduction The third paragraph of the literature review should be summarised. The advantages and disadvantages of single-phase and two-phase models are detailed and the methodology used in this paper is named.
2. In this paper, numerical methods are used to study multiphase flow heat transfer, and it is suggested to increase the research discussion related to multiphase modelling and interphase coupling. The following documents can provide some help: DOI: 10.1016/j.powtec.2024.120150. Investigation on Cryogenic Cavitation Characteristics of an Inducer Considering Thermodynamic Effects.
3. Is the distribution density of nanoparticles negligible in nanoflow heat transfer? Please provide a detailed argument.
4. How are the boundary conditions of the model set? Can they be justified in more detail?
5. CFD simulation results usually need to be validated against experimental data to ensure their accuracy. It is desirable to learn more about the validation methods of the simulation results in this paper, including error analysis and experimental comparisons, as well as the way in which the simulation accuracy is assessed.
Comments on the Quality of English LanguageNo
Author Response
In this paper, the author discusses the impact of a constant magnetic field on heat transfer, flow of fluid, and entropy generation of mixed convection. But the work still needs more efforts to make this paper published. The following concerns should be clarified beforehand.
Thank you for your valuable feedback on our manuscript. We appreciate your attention to detail and your suggestion in the manuscript. We have carefully reviewed the entire manuscript and have ensured that all comments are revised.
Comments 1:. Introduction The third paragraph of the literature review should be summarised. The advantages and disadvantages of single-phase and two-phase models are detailed, and the methodology used in this paper is named.
Response 1: We appreciate your feedback. A comprehensive review of single-phase and two-phase models is presented in [8]. Considering the advantages and limitations of each approach, a one-dimensional single-phase model was deemed appropriate for our specific case.
Comments 2: In this paper, numerical methods are used to study multiphase flow heat transfer, and it is suggested to increase the research discussion related to multiphase modelling and interphase coupling. The following documents can provide some help: DOI: 10.1016/j.powtec.2024.120150. Investigation on Cryogenic Cavitation Characteristics of an Inducer Considering Thermodynamic Effects.
Response 2: Thank you for your valuable feedback. The current study utilizes a one-phase model, as outlined in our assumptions. A manuscript exploring a two-phase model is currently in preparation. We are grateful for your suggestion of the paper "Investigation on Cryogenic Cavitation Characteristics of an Inducer Considering Thermodynamic Effects" (DOI: 10.1016/j.powtec.2024.120150), which will be incorporated into our future research.
Comments 3: Is the distribution density of nanoparticles negligible in nanoflow heat transfer? Please provide a detailed argument.
Response 3: Thank you for your insightful comment. While the distribution of nanoparticles within the base fluid can influence heat transfer mechanisms, especially at higher concentrations, our study focuses on dilute nanofluids with a volume fraction of nanoparticles ≤ 0.15. At such low concentrations, the nanoparticles are assumed to be uniformly distributed within the base fluid, and their impact on the overall fluid properties is relatively minor. This assumption is commonly adopted in the literature for nanofluid heat transfer studies, as it simplifies the analysis without compromising the accuracy of the results. However, we acknowledge that the distribution of nanoparticles can become more significant at higher concentrations, leading to deviations from the classical Newtonian fluid behavior. Our future studies may explore the effects of non-uniform nanoparticle distribution on heat transfer enhancement.
Comments 4: How are the boundary conditions of the model set? Can they be justified in more detail?
Response 4: Thank you for bringing up an essential point. To maintain brevity, the boundary conditions are presented in a concise manner. The boundary conditions are set for all four walls as follows:
The bottom wall has two different boundary conditions depending on the location of the elements. From X=0 to X=0.2 is adiabatic surface, from X=0.2 to X=0.4 is a constant heat flux, from X=0.4 to X=0.6 is insulated surface, from X=0.6 to X=0.8 is a constant heat flux, and from X=0.8 to X=1 is insulated surface. Vertical walls have velocity and constant cold temperature, while the upper wall is diabetic and fixed.
Comments 5: CFD simulation results usually need to be validated against experimental data to ensure their accuracy. It is desirable to learn more about the validation methods of the simulation results in this paper, including error analysis and experimental comparisons, as well as the way in which the simulation accuracy is assessed.
Response 5: Many thanks. To address the reviewer's suggestion, the comparison was added to the revised manuscript on pp. 10.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors satisfactorily answered the questions that were asked. Therefore, I suggest that the article be accepted.
Author Response
Comment 1: The authors satisfactorily answered the questions that were asked. Therefore, I suggest that the article be accepted.
Response 1: Thank you for your valuable feedback on our manuscript. The authors greatly appreciate all the helpful suggestions and comments from the reviewers. The comments permitted the authors to make better modifications, deepen the interpretation, and improve the quality of the manuscript. The authors have taken into account of the comments and made the modifications.
