Mathematical Model for Quantitative Estimation of Thermophysical Properties of Flat Samples of Potatoes by Active Thermography at Varying Boundary Layer Conditions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a mathematical model for the experimental estimation of the volumetric heat capacity and thermal conductivity of flat potato samples as a test material and polymethylmethacrylate as a reference material. The samples were cooled, then heated to room temperature, with or without a weak air flow. The surface temperatures were measured with a thermal chamber and processed using the proposed model. The method is based on the determination of the Bi values from the thermal behaviour of the reference samples, which allows the application of simple formulas for the calculation of thermophysical properties. Although it is an accessible method and applicable to other plant materials. The authors highlight that it does not offer high precision and requires further improvements to reduce uncertainties.

My observations are as follows:
•    In general, more bibliographic references are needed.
•    It might be helpful to explain why polymethyl methacrylate was used as the reference sample.
•    In my opinion, it should be stated from the beginning of the calculations that water evaporation from the potato was not taken into account.
•    Was the density of the potato determined experimentally or assumed?
•    How many measurements formed the basis of this experiment?
•    Line 112 – the symbols h and D need to be explained.
•    Line 145 – an explanation should be provided for why Bi < 0.3 is assumed.
•    Lines 151 and 160 – the word “and” appears in Russian.
•    Lines 167 and 231 – a space is needed before “Bi” and “was,” respectively.
•    In Figure 7b, the label for the vertical axis is missing.

Author Response

Comments 1: In general, more bibliographic references are needed.

Response 1: references [16-20] has been added.

 

Comments 2: It might be helpful to explain why polymethyl methacrylate was used as the reference sample.

Response 2: an explanation has been added on page 3 line 124.

 

Comments 3:  In my opinion, it should be stated from the beginning of the calculations that water evaporation from the potato was not taken into account.

Response 3: this assumption has been added on page 3 line 131.

 

Comments 4: Was the density of the potato determined experimentally or assumed?

Response 4: The potato density was taken as the average value from the references [15-20]. Information has been added on page 9 line 300.

 

Comments 5: How many measurements formed the basis of this experiment?

Response 5: Information about the number of measurements has been added on page 9 line 312.

 

Comments 6:  Line 112 – the symbols h and D need to be explained.

Response 6: The explanation of the symbols is given in the sentence itself.

 

Comments 7: Line 145 – an explanation should be provided for why Bi < 0.3 is assumed.

Response 7: an explanation has been added on page 4 line 162.

 

Comments 8: Lines 151 and 160 – the word “and” appears in Russian.

Response 8: The typo has been corrected.

 

Comments 9: Lines 167 and 231 – a space is needed before “Bi” and “was,” respectively.

Response 9: The typo has been corrected.

 

Comments 10: In Figure 7b, the label for the vertical axis is missing.

Response 10: Figure 7b has been corrected.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors, I think it's good work. However, some aspects require clarification, additional validation, or deeper explanation before this manuscript can be considered for publication.

1. While the paper assumes Bi < 0.3 for simplification, the practical verification of this assumption for all experiments is not sufficiently demonstrated. How was this range ensured, especially in the case of the blown sample (sample 2)?
2. The uncertainty in the calculated value of λ (thermal conductivity) is acknowledged, but the authors should provide a more quantitative error analysis. What is the estimated range of uncertainty, and how does it compare to literature data?
3. The paper discusses moisture evaporation affecting α and recommends polyethylene film use, but in the presented experiments, the film was not applied. This weakens the claim that α_test ≈ α_reference. Could the authors provide data from film-covered samples to support this assumption?
4. The paper does not mention how many repetitions were conducted. Are the values of λ and c_v averaged over multiple samples? A statistical treatment (e.g., standard deviation, confidence interval) would improve reliability.
5. How was the thermal camera calibrated? What is its sensitivity and spatial resolution? Since the method heavily depends on accurate surface temperature measurements, this should be clearly explained.
6. The model assumes flat samples with h < D/10. Would the same model be valid for slightly thicker or differently shaped samples (e.g., hemispherical or irregular)? Some discussion would be beneficial.
7. Equation (1) would benefit from clearly defining each variable upon its first use, especially for interdisciplinary readers.
8. Figures are helpful, but more detailed axis labels (units, variable names) would improve clarity, especially in Figures 3, 5, and 7.
9. Check for consistent formatting in equations and symbols (e.g., sometimes Bi is subscripted, sometimes not).
10. The authors state that “results are in good agreement with literature,” but this should be supported with a comparative table or plot.
11. Citation [2] is labeled as 2007 but refers to a 1986 article in its DOI. Please verify and correct any inconsistencies in the reference list.
12. How sensitive is the result for c_v and λ to the estimation of the Biot number from the reference samples?
13. Could this method be extended to study thermal properties at varying humidity levels or under different ambient temperatures?
14. What steps were taken to ensure symmetry in sample geometry and temperature distribution across the thickness?
15. How would the results be affected if the test and reference samples had slightly different thicknesses due to cutting inconsistencies?
16. What are the limitations of the method in terms of the material type? Could it be applied to fibrous or highly anisotropic plant tissues?

Author Response

Comments 1: While the paper assumes Bi < 0.3 for simplification, the practical verification of this assumption for all experiments is not sufficiently demonstrated. How was this range ensured, especially in the case of the blown sample (sample 2)?

Response 1: The information has been added on page 9 line 288.

 

Comments 2: The uncertainty in the calculated value of λ (thermal conductivity) is acknowledged, but the authors should provide a more quantitative error analysis. What is the estimated range of uncertainty, and how does it compare to literature data?

Response 2: The quantitative analysis has been provided on page 8 line 273.

 

Comments 3: The paper discusses moisture evaporation affecting α and recommends polyethylene film use, but in the presented experiments, the film was not applied. This weakens the claim that α_test ≈ α_reference. Could the authors provide data from film-covered samples to support this assumption?

Response 3: Explanations have been added on page 6 line 229.

 

Comments 4: The paper does not mention how many repetitions were conducted. Are the values of λ and c_v averaged over multiple samples? A statistical treatment (e.g., standard deviation, confidence interval) would improve reliability.

Response 4: The information has been added on page 9 line 309. The results have been compared with references in Table 1.

 

Comments 5: How was the thermal camera calibrated? What is its sensitivity and spatial resolution? Since the method heavily depends on accurate surface temperature measurements, this should be clearly explained.

Response 5: The information has been added on page 3 line 137.

 

Comments 6: The model assumes flat samples with h < D/10. Would the same model be valid for slightly thicker or differently shaped samples (e.g., hemispherical or irregular)? Some discussion would be beneficial.

Response 6: The information has been added on page 11 line 341.

 

Comments 7: Equation (1) would benefit from clearly defining each variable upon its first use, especially for interdisciplinary readers.

Response 7: The variables in equation (1) are defined in the paragraph above.

 

Comments 8: Figures are helpful, but more detailed axis labels (units, variable names) would improve clarity, especially in Figures 3, 5, and 7.

Response 8: Figure 7b has been corrected due to the lack of a vertical axis designation.

 

Comments 9: Check for consistent formatting in equations and symbols (e.g., sometimes Bi is subscripted, sometimes not).

Response 9: The Bi is not signed in the case of general formulas for calculations. The Bi is signed by an index in case of calculation for specific samples.

 

Comments 10: The authors state that “results are in good agreement with literature,” but this should be supported with a comparative table or plot.

Response 10: Table 1 has been added on page 10 line 319.

 

Comments 11: Citation [2] is labeled as 2007 but refers to a 1986 article in its DOI. Please verify and correct any inconsistencies in the reference list.

Response 11: Citation has been corrected.

 

Comments 12: How sensitive is the result for c_v and λ to the estimation of the Biot number from the reference samples?

Response 12: The answer is given in the response to Comments 2.

 

Comments 13: Could this method be extended to study thermal properties at varying humidity levels or under different ambient temperatures?

Response 13: Measurements were carried out at normal relative humidity in the range of 30-45%, at room temperatures and heat exchange conditions characterized by the number Bi<0.3, determined from the experiment with flat reference samples, the thermophysical properties of which were known.  The information has been added on page 11 line 348.

 

Comments 14: What steps were taken to ensure symmetry in sample geometry and temperature distribution across the thickness?

Response 14: The symmetry of the temperature field was ensured due to the fact that the same heat exchange conditions were created on opposite surfaces of the samples (see the physical model in Fig. 2). For clarity of practical implementation, Figure 1b has been changed.

 

Comments 15: How would the results be affected if the test and reference samples had slightly different thicknesses due to cutting inconsistencies?

Response 15: The answer is given in the response to Comments 2.

 

Comments 16: What are the limitations of the method in terms of the material type? Could it be applied to fibrous or highly anisotropic plant tissues?

Response 16: The information has been added on page 11 line 359.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,
I would like to thank you for making the necessary modifications.

Author Response

Thank you for your valuable feedback and insightful comments on our manuscript. Your suggestions are greatly appreciated and helped to improve the quality of the manuscript.