A Variational Formulation for Fins with Nonzero Contact Thermal Resistance at the Base
, Rogério Pazetto Saldanha da Gama 1, Vinicius Vendas Sarmento 2 and Maria Laura Martins-Costa 2
Round 1
Reviewer 1 Report
The authors considered the steady-state heat transfer process in a fin with a Robin boundary condition at the base (instead of the usual Dirichlet boundary condition at the base). This Robin boundary condition models the effect of the thermal resistance between the base of the fin and the surface on which the fin is placed. The work presents an equivalent minimum principle, represented by a convex and coercive functional, ensuring the solution's existence and uniqueness.
The findings are interesting. However, a major revision is recommended.
1. The term "its" should be removed from the title. "... at its the base..." doesn't make sense.
2. The limitations of the mathematical model presented in Section 2 should be discussed.
3. Punctuation marks have been used very poorly throughout the manuscript. Most of the equations do not end with a full stop. Correct them all.
4. Why use the word "coerciveness" just after equation (23)?
5. Existence and uniqueness of solution in section 4 needs more elaboration. The proof is not clear at present.
6. Explain how the established results are applied in section 4.
7. The references are not written uniformly. Correct them.
Author Response
The findings are interesting. However, a major revision is recommended.
- The term "its" should be removed from the title. "... at its the base..." doesn't make sense.
RESPONSE ### The manuscript has undergone a revision by a native speaker.
- The limitations of the mathematical model presented in Section 2 should be discussed.
RESPONSE ### This issue was discussed in the revised version.
- Punctuation marks have been used very poorly throughout the manuscript. Most of the equations do not end with a full stop. Correct them all.
RESPONSE ### The manuscript has undergone a revision by a native speaker.
- Why use the word "coerciveness" just after equation (23)?
RESPONSE ### The text was improved in order to clarify this issue.
- Existence and uniqueness of solution in section 4 needs more elaboration. The proof is not clear at present.
RESPONSE ### I believe that the proof is complete. The convexity and the coerciveness were proven (as pointed out in your comments above). This is enough for this end.
- Explain how the established results are applied in section 4.
RESPONSE ### This issue was considered in the new text.
- The references are not written uniformly. Correct them.
RESPONSE ### OK.
Reviewer 2 Report
Abstract: considers should be consider
Line 145 "in which" should be "In which"
Reference should be in a same style
Author Response
Comments and Suggestions for Authors
Abstract: considers should be consider
RESPONSE ### The manuscript has undergone an English editing.
Line 145 "in which" should be "In which"
RESPONSE ### The manuscript has undergone an English editing.
Reference should be in a same style
RESPONSE ### OK.
Reviewer 3 Report
Formats around the equations seem to offset. Hard to recognize the segments.
The authors describe problems by numbers. Are they equal to equation number??
Ln 180, is eta a 'variable'?
It seems like the minimization of the functional is quite essential. The equivalence of the governing equation and the functional should be described for ordinary readers' understanding.
The authors declare their work handled the contact resistance. Is it possible to describe the resistance simply by a temperature drop to Ts?? The fin temperature distribution, efficiency, and effectiveness can be derived numerically in seconds. The authors should explain the merit of the proposed lengthy math.
Author Response
Comments and Suggestions for Authors
Formats around the equations seem to offset. Hard to recognize the segments.
RESPONSE ### I do not understand what the reviewer proposes…
The authors describe problems by numbers. Are they equal to equation number??
RESPONSE ### Yes!
Ln 180, is eta a 'variable'?
RESPONSE ### Yes! But I have clarified this issue in the revised version.
It seems like the minimization of the functional is quite essential. The equivalence of the governing equation and the functional should be described for ordinary readers' understanding.
RESPONSE ### See response for the next comment.
The authors declare their work handled the contact resistance. Is it possible to describe the resistance simply by a temperature drop to Ts?? The fin temperature distribution, efficiency, and effectiveness can be derived numerically in seconds. The authors should explain the merit of the proposed lengthy math.
RESPONSE ### “Simply drop Ts” is not enough, since the contact resistance effect occurs on the heat transfer. The temperature distribution, for nonlinear cases, is not a simple task. Once the temperature distribution is known, the efficiency and the effectiveness are quite straightforward. The “proposed lengthy math” serves for answering the previous question (from this referee)…
Round 2
Reviewer 1 Report
I believe this manuscript still needs major improvements.
Author Response
This reviewer has not pointed out any specific comment/suggestion. In this way, the paper was carefully revised and several improvements were addressed.
In special, the conclusions and the results were quite improved.
Reviewer 3 Report
1. First-person statements and descriptions are inappropriate.
2. The first sentence in the section 3. Variational Formulation
"Problem (7)" is ambiguous. Does that mean Equation (7)?
3. The description before Equation (27) should state the inclusion of thermal radiation. The definition of sigma, Stefan-Boltzmann constant, should be appeared earlier.
4. Problem (27) should be changed to Equation (27). The misusages between the problem and equation are very confusing.
5. The x- and y-captions can be improved.
6. While the authors used an example to demonstrate their proposed methodology, there was no description of how the proposal was superior to others by the end of Section 5.
7. The first sentence of Appendix: When (2) holds...
Again, does that mean equation (2)??
Author Response
Comments and suggestions for authors
1) First-person statements and descriptions are inappropriate.
response: The whole manuscript was wholly revised, avoiding first-person statements and descriptions.
2) The first sentence in Section 3. Variational Formulation. “Problem (7)” is ambiguous. Does that mean Equation (7)?
response:Yes, Thank you for the comment. Problem (2), problem (7), and problem (27) have been substituted by equation (2), equation (7), and equation (27) throughout the text.
3) The description before Equation (27) should state the inclusion of thermal radiation. The definition of sigma, Stefan-Boltzmann constant, should appear earlier.
response:A statement that thermal radiation was included has been made. Also, the definition of the Stefan-Boltzmann constant was moved to just after equation (27).
4) Problem (27) should be changed to Equation (27). The misusages between problem and equation are very confusing.
response:Again, thank you for the comment. Problem (27) has been substituted by equation (27), throughout the text, along with other analogous cases.
5) The x- and y-captions can be improved.
response:Figures 4 and 5 were modified to improve the x- and y-captions.
6) While the authors used an example to demonstrate their proposed methodology, there is no description of how the proposal was superior to others by the end of Section 5.
response:When comparing this methodology to others, the main advantage of this method is the equivalence between a minimum principle and the original problem. This equivalence provides a convenient tool for carrying out numerical simulations by means of a minimization process.
7) The first sentence of the Appendix: When (2) holds ….. Again, does that mean equation (2)?
response:Problem (2) has been substituted by equation (2) throughout the text, and it was stressed that we were referring to equations (7).
Round 3
Reviewer 1 Report
Just marginally improved.
Reviewer 3 Report
Some typesetting jobs are required and collaborated with staff.
