Calculation of Effective Thermal Conductivity for Human Skin Using the Fractal Monte Carlo Method

Round 1

Reviewer 1 Report

In this revised manuscript, the authors made significant improvement according to my comments. But some minor revisions should be further made before this manuscript can be accepted for publication. Here are my detailed comments.

1.  The citation of Eq. (18) was incomplete because the method and model were first proposed by Wu and Yu in 2007, and in fact Eq. (18) is the same as that derived by Wu and Yu, see Eq. (12) in Wu and Yu’s paper (J. Wu and B. Yu, A fractal resistance model for flow through porous media, Int. J. Heat Mass Transfer 50, 3925-3932 (2007)). Citation should be given to a theory/model/method founder(s) as the earliest as possible.
2.  The citation of Eq. (27) was missing, and the citation should be given to Ref. [50], and citation should be provided immediately before citing it.
3. After line 179, the authors should add a brief discussion: Feng et al. [?] compared the ratios of λ_min/λ_max in Eq. (27) with the experimental data (see Fig. 2 in Feng et al.’ paper, A generalized model for the effective thermal conductivity of porous media based on self-similarity, J. Phys. D. Applied Physics, 37, 3030-3040(2004)) reported in literature and found that the ratio of λ_min/λ_max ≅ 10^-3 is more suitable to most data.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The problem is interesting, high level research and the results are important, but, the paper needs the following points are noted:

1. The paper should be carefully revised for punctuation, grammar, spelling mistakes and sentences structuring.

2. The author should explain the novelty clearly in the abstract and conclusion.

3. What are the advantages of the proposed new model?

4. The authors should include scientific reasoning for graphical results in details.

5. What are the advantages of the method used?

6. English should be improved on the paper.

7. References must be arranged as per the journal style.

8. The literature survey might be improved on adding some relevant references as:

• "Generalized Bio-Heat Transfer Model Combining with the Relaxation Mechanism and Non-Equilibrium Heat Transfer."Journal of Heat Transfer (2022).
• "A numerical study of space‐fractional three‐phase‐lag bioheat transfer model during thermal therapy."Heat Transfer 1 (2022): 470-489.
• "Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data", J. Therm. Biol., 85. https://doi.org/10.1016/j.jtherbio.2019.102421.
• "Thermal response of cylindrical tissue induced by laser irradiation with experimental study", Int. J. Numer. Methods Heat Fluid Flow. 22(7), 4013-4023. https://doi.org/10.1108/HFF-10-2019-0777.
• "Mathematical modeling of heat transfer in biological tissues (bioheat transfer)."Principles and Technologies for Electromagnetic Energy Based Therapies. Academic Press, 2022. 1-24.
• "Analytical estimation of temperature in living tissues using the TPL bioheat model with experimental verification", Mathematics. 8(7). https://doi.org/10.3390/math8071188.
• "The effect of fractional time derivative of bioheat model in skin tissue induced to laser irradiation", Symmetry. 12(4), 1-10. https://doi.org/10.3390/SYM12040602.
• "Numerical simulation of three‐phase‐lag bio‐heat transfer model for generalized coordinate system amidst thermal ablation." Heat Transfer.
• "Theoretical analysis of thermal damages in skin tissue induced by intense moving heat source", Int. J. Heat Mass Transf., 124 1011-1014. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.018.

In view of all the points given above the paper needs to be modified and can be recommended for publication.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors' addressed my minor scientific and clarity concerns and the manuscript appears ready for publication.