Penta-Hybrid Nanofluid Transport and Irreversibility in Stenotic Arteries Under Caputo–Fabrizio Fractional Dynamics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

“Penta-Hybrid Nanofluid Transport and Irreversibility in Stenotic Arteries under Caputo–Fabrizio Fractional Dynamics”

Based on my detailed review of the manuscript, the following comments are provided to help improve clarity, rigor, and presentation. The comments are listed sequentially and refer to specific sections and pages of the manuscript.

Comments:

1. (Abstract, Page 1)

The abstract is informative but relatively long. It would benefit from a clearer and more focused statement of the main contribution of the study, particularly how it differs from existing fractional Casson blood flow models.

1. (Abstract, Page 1, Lines 9–16)

The wording suggests that this is the first study of its kind. This claim should either be moderated or supported by a clearer comparison with closely related studies in the literature.

1. (Abstract, Page 1, Lines 19–22)

The improvement in thermal characteristics due to penta-hybrid nanoparticles is stated, but the physical or practical significance of this improvement is not clearly explained.

1. (Introduction, Pages 1–2)

The introduction provides extensive background information; however, several paragraphs repeat general concepts related to nanofluids and fractional calculus and could be condensed for better focus.

1. (Introduction, Page 2, Lines 35–47)

While the advantages of penta-hybrid nanofluids are described, the manuscript does not clearly explain why five nanoparticles are necessary compared to tri- or tetra-hybrid systems.

 

1. (Introduction, Page 3, Lines 88–94)

The justification for modeling blood as a Casson fluid is appropriate, but the specific shear-rate conditions relevant to the present study should be stated more explicitly.

1. (Introduction, Page 4, Lines 170–175)

The novelty related to coupling fractional-order modeling with entropy generation and Bejan number analysis should be more clearly distinguished from existing entropy-based blood flow studies.

1. (Section 2.1 – Flow Geometry, Page 5)

The arterial geometry is mathematically well defined; however, a brief discussion of its physiological relevance would improve the clarity of the model assumptions.

1. (Section 2.1, Page 5, Equation (1))

The mild stenosis approximation is introduced without explanation. The authors should clarify the range of stenosis severity for which this approximation is valid.

1. (Section 2.2 – Basic Flow Equation, Page 6)

The governing equations are correctly formulated, but the physical interpretation of each force term should be explained more clearly, especially for readers from biomedical backgrounds.

1. (Section 2.2, Page 6, Lines 224–229)

The assumption of uniform dispersion of five different nanoparticles in blood should be explicitly stated as an idealization, along with a brief discussion of its limitations.

1. (Section 2.3 – External Applied Electric Field, Pages 6–7)

The electrokinetic model is mathematically sound, but its physiological relevance in large arterial flows should be clarified.

1. (Non-dimensionalization, Page 7, Equation (16))

Many dimensionless parameters are introduced. A summary table explaining their physical meaning and relevance would improve readability.

1. (Fractional Model Formulation, Page 10, Equation (23))

The Caputo–Fabrizio fractional derivative is correctly defined, but its specific advantages over other commonly used fractional operators should be explained more clearly.

1. (Section 3 – Solution Methodology, Pages 10–11)

The analytical solution procedure is rigorous; however, intermediate explanations connecting the mathematics to the underlying physics are limited and should be expanded.

1. (Section 3, Page 11, Equations (38)–(42))

The convergence and numerical implementation of the obtained series solutions are not discussed and should be briefly addressed.

1. (Section 4 – Entropy Generation, Page 12)

The entropy generation formulation is appropriate, but the physical interpretation of entropy production in the context of blood flow is not sufficiently explained.

1. (Section 4, Page 13, Equation (51))

The Bejan number analysis would benefit from comparison with existing entropy–Bejan studies in biofluid mechanics to provide better context.

1. (Section 5 – Results and Analysis, Page 13)

The results are presented clearly, but many of the observed trends are expected. The authors should emphasize results that offer new or non-trivial insights.

1. (Results, Pages 13–14, Figures 2–7)

The discussion of velocity profiles is mainly descriptive. Additional physical reasoning explaining why these trends occur would strengthen the analysis.

1. (Results, Page 14, Lines 421–428)

The discussion of magnetic field effects on blood flow should be presented cautiously, with clear distinction between model-based observations and clinical implications.

1. (Results, Page 14, Lines 439–446)

Although entropy trends are explained, a quantitative comparison between penta-hybrid nanofluids and simpler nanofluid systems is missing.

1. (Discussion Section, Page 14)

The discussion focuses primarily on parameter variation. The limitations of the model and assumptions should be explicitly acknowledged.

1. (Conclusion Section)

The conclusions mainly restate the results. A more synthesized discussion of the key findings and their broader implications would improve this section.

Note:
Minor grammatical, typographical, and formatting inconsistencies are present and should be carefully corrected during revision.

 

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Thank you very much for your valuable comments and constructive suggestions.
We have carefully addressed all the points raised and revised the manuscript accordingly.

Please find the attached detailed response to the reviewer comments, where each remark is addressed point by point, along with the corresponding revisions in the manuscript.

We sincerely appreciate your time and effort in reviewing our work.

Kind regards,

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors investigate unsteady transport in a stenosed artery by modeling Casson-type non-Newtonian blood laden with a penta-hybrid nanoparticle mixture. The model incorporates a pulsatile pressure gradient, MHD effects, electro-osmotic forcing via an EDL, buoyancy in an inclined configuration, and body acceleration. The manuscript further claims novelty through the use of Caputo–Fabrizio fractional dynamics and through irreversibility analysis (entropy generation and Bejan number). The mathematical development is extensive and the parametric trends are clearly plotted. However, several key issues must be addressed to make the modeling assumptions, novelty claims, and results scientifically credible.

 

1. While a stenosis geometry is introduced, it is not sufficiently clear how the axial variation of radius is retained in the governing equations and in the final closed-form solutions. The reported solutions appear primarily as u and Θ via Bessel eigenfunction expansions, which is typical for fully developed flow in a straight circular tube. Please clarify, step-by-step, how the stenosis shape influences the solution (e.g., through a mild-stenosis approximation, local analysis, or an explicit z-dependent formulation). If the analysis effectively assumes a locally fully developed flow, then the scope, title/claims, and interpretation should be adjusted accordingly, and the limitations should be stated explicitly.

 

2. The simultaneous inclusion of EDL electro-osmosis, strong MHD damping, buoyancy in an inclined artery, and body acceleration significantly increases model complexity. However, there is no order-of-magnitude or nondimensional scale analysis demonstrating that these effects are simultaneously relevant for the targeted “artery” regime. In particular, EDL/ electro-osmotic forcing is commonly significant in micro-channels; for mm-scale arteries, the Debye length is typically orders of magnitude smaller than the vessel radius, raising questions about practical relevance without additional justification.

 

3. The manuscript’s central premise is a penta-hybrid nanoparticle mixture in blood, yet the practical feasibility and parameterization are not sufficiently supported. The paper must clearly specify the volume fractions Φ1–Φ5, their admissible ranges, and how these choices map to realistic biomedical contexts (stability, aggregation, hemocompatibility/toxicity, etc.). Without explicit values and constraints, the results are difficult to reproduce and the biomedical framing becomes speculative.

 

4. The Caputo–Fabrizio fractional operator is central to the claimed novelty, but the presentation is not sufficiently rigorous/consistent for reproducibility. The definition, notation (integration variable, derivative term), and the Laplace-transform properties used later should be clearly and consistently stated.

 

5. The manuscript provides extensive parametric plots, but it lacks verification or validation. At minimum, one should include: (i) benchmark comparisons against known limiting solutions (Newtonian limit, no-nanoparticle limit, Ha=0, no-EDL, α->1), (ii) comparison with prior published results for special cases, and (iii) numerical/series convergence information (how many terms retained; truncation error).

 

6. The introduction uses strong language (e.g., “never been considered,” “no significant research”), which is vulnerable unless the literature search is exhaustive. The novelty should be precisely stated in terms of the specific combination of assumptions (penta-hybrid + CF fractional + irreversibility metrics + specific forcing), and the claims should be softened to “to the best of our knowledge” unless comprehensive evidence is provided.

 

7. The manuscript combines multiple mechanisms (Casson rheology, penta-hybrid nanoparticles, MHD, EDL electro-osmosis, buoyancy in an inclined artery, body acceleration, and Caputo–Fabrizio fractional dynamics). Given this breadth, the paper must clearly delineate what physical regimes the proposed model can realistically represent and which important arterial-flow phenomena are inherently outside the model’s scope. Without an explicit “scope of validity/limitations” statement, the current discussion risks over-interpretation of parametric trends.

 

Minor comments (clarity and presentation)

1. The introduction uses phrasing such as “vertical artery” and later “inclined artery.” Please standardize terminology throughout.
2. Please ensure parameters (ex, Casson parameter vs. angle notation) are unambiguous.

 

Author Response

Dear Reviewer,

Thank you very much for your valuable comments and constructive suggestions.
We have carefully addressed all the points raised and revised the manuscript accordingly.

Please find the attached detailed response to the reviewer comments, where each remark is addressed point by point, along with the corresponding revisions in the manuscript.

We sincerely appreciate your time and effort in reviewing our work.

Kind regards,

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I would like to thank the authors for their detailed responses and for addressing all of my concerns. The revisions have significantly improved the clarity and robustness of the manuscript. I am satisfied with the current version of the paper