Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions
Round 1
Reviewer 1 Report
This paper aims to establish a numerical model for convective-radiative fin, which can easily be used as a collocation method and obtain stable computational results as FEM. This paper is organized as follows: The physical and mathematical models are presented in section 2. The principle of EDM and the discretized scheme of the nonlinear heat transfer equation of convective-radiative fin are described in section 3. The validation of this method is verified from the analytical solution in section 4. Then, the results and discussions are stated in section 5. Finally, conclusions are summarized in section 6.
This research has important value. However, before publication, there are still some areas in the article that need to be improved. Below is my comment.
The Introduction should be expanded and reflect current research on the topic of the article. Of the 34 references, only 5 are dated after 2018. Therefore, the Introduction must be redone.
The authors in some lines abuse citations (see line 102) 8 citations for a sentence! This is not acceptable unless the authors give full credit to each reference or reduce them to a reasonable number. Please check this issue elsewhere in the article.
Section 3 should start on a new page.
Authors must check the font styles of the paper.
The research design is appropriate. The methods and results are adequately described. The data are presented in figures, and equations are correctly valued and interpreted in the paper. The results are clearly presented. The conclusions are supported by the results.
In general, the article makes a good impression, is devoted to an interesting and topical problem of heat conduction in convective-radiative fin.
Author Response
Comments of Reviewer #1:
This paper aims to establish a numerical model for convective-radiative fin, which can easily be used as a collocation method and obtain stable computational results as FEM. This paper is organized as follows: The physical and mathematical models are presented in section 2. The principle of EDM and the discretized scheme of the nonlinear heat transfer equation of convective-radiative fin are described in section 3. The validation of this method is verified from the analytical solution in section 4. Then, the results and discussions are stated in section 5. Finally, conclusions are summarized in section 6.
This research has important value. However, before publication, there are still some areas in the article that need to be improved. Below is my comment.
Reply: We are grateful for this reviewer’s positive opinion of our manuscript.
- The Introduction should be expanded and reflect current research on the topic of the article. Of the 34 references, only 5 are dated after 2018. Therefore, the Introduction must be redone.
Reply: Thank you for your suggestion. We have updated our literature survey by referring to the most relevant references in the near 5 years.
- The authors in some lines abuse citations (see line 102) 8 citations for a sentence! This is not acceptable unless the authors give full credit to each reference or reduce them to a reasonable number. Please check this issue elsewhere in the article.
Reply: Thank you for your suggestion. We have reduced these references [27-33] and give full credit to each reference.
- Section 3 should start on a new page.
Reply: Thank you for your suggestion. The style of the manuscript has been revised.
- Authors must check the font styles of the paper.
Reply: Sure, we have revised the font styles according to Authors’ Guidelines.
- The research design is appropriate. The methods and results are adequately described. The data are presented in figures, and equations are correctly valued and interpreted in the paper.
Reply: Thank you for your positive comments.
- The results are clearly presented. The conclusions are supported by the results.
Reply: Thank you for your positive comments.
In general, the article makes a good impression, is devoted to an interesting and topical problem of heat conduction in convective-radiative fin.
Reply: We appreciate the reviewer's positive comments.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The Authors present the application of a mathematical method to the description of non-Fourier conduction within a fin subject to periodic boundary conditions and internal heat generation.
The paper is difficult to understand at times, especially in the 'Results and discussion' section (e.g. r. 240-245) and the language must definitely be reviewed. However, the single main issue is related, as is usually the case with this kind of papers, to the actual significance of the results for real-life examples: it is therefore strongly recommended that the Authors investigate a dimensional case, so that the actual differences between a Fourier and a non-Fourier treatment of the problem can be evidenced, if any.
Minor issues:
- In the definition of the relaxation time, the meaning of n is unclear: the symbol is usually employed for the kinematic viscosity, which is obviously meaningless here.
- A nomenclature should be provided, given the vast amount of symbols and quantities employed;
- The legend in Fig. 11 has typos (all plots are given as 'Non-Fourier').
In view of the above considerations, this reviewer feels that the paper should undergo a major revision before being accepted for publication in this journal.
Author Response
Response to Reviewer #2 Comments:
The Authors present the application of a mathematical method to the description of non-Fourier conduction within a fin subject to periodic boundary conditions and internal heat generation.
The paper is difficult to understand at times, especially in the 'Results and discussion' section (e.g. r. 240-245) and the language must definitely be reviewed. However, the single main issue is related, as is usually the case with this kind of papers, to the actual significance of the results for real-life examples: it is therefore strongly recommended that the Authors investigate a dimensional case, so that the actual differences between a Fourier and a non-Fourier treatment of the problem can be evidenced, if any.
Reply: Thank you for your suggestion. We have rewritten the ‘Results and discussion’.
Sure, the real-life examples of non-Fourier heat transfer is very important for investigation this problem. Similar to Li et al. (Liu Y.; Li L.; Zhang Y.W. Numerical simulation of non-Fourier heat conduction in fins by lattice Boltzmann method. App. Thermal Eng. 2020, 166(5): 114670.), for the case of heat dissipation in microelectronic elements, the heat source changes dramatically or the time of the transient problem is too short, the non-Fourier model should be considered.
Minor issues:
- In the definition of the relaxation time, the meaning of n is unclear: the symbol is usually employed for the kinematic viscosity, which is obviously meaningless here.
Reply: τ=α/v2 represents relaxation time, where α is the thermal diffusivity, and v is the velocity of the heat wave.
Revisions: Main text <line 36-37, page 1 >
- A nomenclature should be provided, given the vast amount of symbols and quantities employed;
Reply: Thank you for your suggestion. The nomenclature has been added to the revised manuscript.
Revisions: Main text <line 328-388, pages 13-14>
- The legend in Fig. 11 has typos (all plots are given as 'Non-Fourier').
Reply: Sure, we have revised this mistake.
Revisions: Main text <line 265, page 10>
- In view of the above considerations, this reviewer feels that the paper should undergo a major revision before being accepted for publication in this journal.
Reply: We appreciate the reviewer's comments and excellent suggestions to improve the quality of the manuscript.
Finally, we would like to express our acknowledgments to the editor and all reviewers for their comments and excellent suggestions to improve the quality of the manuscript.
Sincreley yours,
Jing Ma, Yasong Sun, Sida Li
Author Response File: Author Response.docx
Reviewer 3 Report
After reading carefully this paper, I can say that authors have studied a numerical investigation on Element differential method for non-Fourier heat conduction in the convective-radiative fin with mixed boundary conditions. The element differential method is validated by several numerical examples with analytical solutions.
This paper is well written in English, but, there are some modifications as follows:
1. The improvement is needed in the introduction part for the discussion of recent papers of interfacial heat transfer and thermal transport. ( Case Studies in Thermal Engineering 28, 101488, 2021; Mathematics and Computers in Simulation 171, 152-169, 2020; Case Studies in Thermal Engineering 23, 100809, 2021)
2. The crystal clear objective of the present work should be included.
3. The author should explain is there any practical application for using the present geometry?
4. The authors have considered in the present study thermal conductivity, surface emissivity, heat transfer co- efficient and internal heat generation rate. Are there they any other method available to find thermal conductivity, surface emissivity?
5. But the dimensionless temperature distribution in the distance 0.5 £ c£ 1 is almost the same for different values of μ. Justify the reason.
6. How the author choosing the value of μ? Justify it.
7. Written English/Typing of the paper has to be improved and thoroughly checked.
Briefly, after these modifications, this paper may be reconsidered for the further steps on the way of publishing.
Author Response
Response to Reviewer #3 Comments:
After reading carefully this paper, I can say that authors have studied a numerical investigation on Element differential method for non-Fourier heat conduction in the convective-radiative fin with mixed boundary conditions. The element differential method is validated by several numerical examples with analytical solutions.
This paper is well written in English, but, there are some modifications as follows:
Reply: Thank you for your positive comments.
- The improvement is needed in the introduction part for the discussion of recent papers of interfacial heat transfer and thermal transport. (Case Studies in Thermal Engineering 28, 101488, 2021; Mathematics and Computers in Simulation 171, 152-169, 2020; Case Studies in Thermal Engineering 23, 100809, 2021)
Reply: Thank you for your suggestion. We have updated our literature survey, and relative references have been cited.
Revisions: Main text <lines 416-421, page 14>:
- The crystal clear objective of the present work should be included.
Reply: The objective of this manuscript has been highlighted. Please see lines 62-67.
- The author should explain is there any practical application for using the present geometry?
Reply: Similar to Li et al. (Liu Y.; Li L.; Zhang Y.W. Numerical simulation of non-Fourier heat conduction in fins by lattice Boltzmann method. App. Thermal Eng. 2020, 166(5): 114670.), for the case of heat dissipation in microelectronic elements, the heat source changes dramatically or the time of the transient problem is too short, the non-Fourier model should be considered.
- The authors have considered in the present study thermal conductivity, surface emissivity, heat transfer co- efficient and internal heat generation rate. Are there they any other method available to find thermal conductivity, surface emissivity?
Reply: Similar to Torabi and Zhang (Torabi M.; Zhang Q.B. Analytical solution for evaluating the thermal performance and efficiency of convective-radiative straight 422 fins with various profiles and considering all non-linearities. Energy Conv. Manag. 2013, 66, 199-210), the thermal conductivity, surface emissivity, heat transfer coefficient and internal heat generation rate are assumed as temperature dependent.
- But the dimensionless temperature distribution in the distance 0.5 £ c£ 1 is almost the same for different values of μ. Justify the reason.
Reply: We have deleted this statement. For non-Fourier heat transfer, the effect of parameters on instantous fin tip temperature, instantaneous fin efficiency and average fin efficiency are comprehensively analyzed.
- How the author choosing the value of μ? Justify it.
Reply: Similar to Torabi and Zhang (Torabi M.; Zhang Q.B. Analytical solution for evaluating the thermal performance and efficiency of convective-radiative straight 422 fins with various profiles and considering all non-linearities. Energy Conv. Manag. 2013, 66, 199-210), the coefficient of thermal conductivity is considered as -0.1<μ<0.1.
- Written English/Typing of the paper has to be improved and thoroughly checked.
Reply: Sure, the manuscript has been polished by a native-English scholar.
Briefly, after these modifications, this paper may be reconsidered for the further steps on the way of publishing.
Reply: We appreciate the reviewer's positive comments.
Finally, we would like to express our acknowledgments to the editor and all reviewers for their comments and excellent suggestions to improve the quality of the manuscript.
Sincreley yours,
Jing Ma, Yasong Sun, Sida Li
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
All my comments were taken into account and necessary corrections were made. The article looks much better.
Reviewer 2 Report
The Authors having addressed all relevant issues, this reviewer has no further commments and deems the paper acceptable in its present form.
Reviewer 3 Report
I accept the present version of the manuscript
