Model of Complex Heat Transfer in the Package of Rectangular Steel Sections
Round 1
Reviewer 1 Report
Review report for the paper “Model of complex heat transfer in the package of steel rectangular sections” written by Rafał Wyczółkowski, Marek Gała and Vazgen Bagdasaryan
The authors introduced a thermo-electric analogy to estimate the estimation of the total thermal resistance for regularly arranged packages of steel rectangular sections. The paper may be useful for those dealing with heat treatments of such packages. The authors should consider the following comments seriously before its possible publication:
1. The coefficient e eq for the equivalent gas thermal conductivity is simply “Nusselt number based on the vertical height of the rectangular enclosure and the temperature difference between its upper and lower walls”. The authors should indicate so. The reader may not be familiar with the term "equivalent gas thermal conductivity".
2. The definition of the Rayleigh number Ra should be given.
3. When evaluating Ra, the temperature difference between the upper and lower walls is needed. How, did the authors estimate it?
4. What does the lower case letter t in Eqs. (16) to (19) indicate? Is it absolute temperature or what? The authors should provide Nomenclature.
5. The authors should also provide the portions of the resistances, namely, conductive one, convective cone, radiative one and contact resistance. It appears to this reviewer that the contact resistance dominates the others. In any case, the information for such contact resistance should be provided more, how to establish the correlations (16) and (17).
Author Response
Responses to the comments from Reviewer 1
Comment 1: The coefficient eeq for the equivalent gas thermal conductivity is simply “Nusselt number based on the vertical height of the rectangular enclosure and the temperature difference between its upper and lower walls”. The authors should indicate so. The reader may not be familiar with the term "equivalent gas thermal conductivity".
Response: We agree. This comment is obvious and has been incorporated throughout the paper. The eeq coefficient has been substituted by the Nusselt number. Therefore, equations (9), (10), (11) and (15) have been adjusted.
Comment 2: The definition of the Rayleigh number Ra should be given.
Response: Thank you for this comment. We have added the suggested content to the manuscript. The definition of the Rayleigh number has been introduced – in equation (12) and lines 111-115 in the text.
Comment 3: When evaluating Ra, the temperature difference between the upper and lower walls is needed. How, did the authors estimate it?
Response: The temperature difference Dt between the lower and upper wall of a section which is necessary for calculating the Ra number was determined by conducting experimental research. It has been described in the lines 116-123. The values of the Dt parameter obtained this way are presented in fig. 5a. We hope that it is now clear.
Comment 4: What does the lower case letter t in Eqs. (16) to (19) indicate? Is it absolute temperature or what? The authors should provide Nomenclature.
Response: Thank you for this suggestion. However, the content of the article indicates that a lower case letter t denotes the temperature in degrees Celsius – see lines 138 and 182. The absolute temperature in [K] was denoted by upper case letter T – see line 148. There is no ‘Nomenclature’ section as all the symbols are explained immediately when they appear in the text.
Comment 5: The authors should also provide the portions of the resistances, namely, conductive one, convective cone, radiative one and contact resistance. It appears to this reviewer that the contact resistance dominates the others. In any case, the information for such contact resistance should be provided more, how to establish the correlations (16) and (17).
Response: Agree. We have introduced some modifications to the text to emphasize this point. A more detailed explanation on how the relationships concerning contact resistance were determined is presented in lines 159-179 – after the editing the equations are now denoted by (20) and (21). Also, figures 6 and 7 have been added. The influence of each mechanism of heat transfer on the values of the analysed resistances has been described in lines 200-234. Moreover, figures 8 and 9 as well as table 1 have been added.
Additional clarifications:
In addition to the above corrections, the following passages have been incorporated into the content of the paper:
- additional information on the resistance Rto (lines 69-71),
- additional conclusions on the passages which have been added according to Reviewers’ comments – lines (302-306),
- additional references [7], [10], [15], [16].
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript introduced using heat transfer network to calculate the total equivalent heat resistance for the package of steel rectangular sections. My main concern is the novelty of the method and the results. The heat transfer network is a very common way to solve the heat transfer problem in an analytical way. The investigated application, a package of steel rectangular section, is also very common. It would be good if the authors can provide more information about novelty or uniqueness about the proposed method and results.
There are several minor issues:
1: There is a typo in Abstract. It should be 20-700, not a “divide”
2: Why the final value of the section thermal resistance is Eq.4?
3: Are the parameter values in Eq.16 and 17 calibrated from experiment measurements?
4: It would be good if more details about how the experimental measurements were implemented.
Author Response
Responses to the comments from Reviewer 2
A general comment: The manuscript introduced using heat transfer network to calculate the total equivalent heat resistance for the package of steel rectangular sections. My main concern is the novelty of the method and the results. The heat transfer network is a very common way to solve the heat transfer problem in an analytical way. The investigated application, a package of steel rectangular section, is also very common. It would be good if the authors can provide more information about novelty or uniqueness about the proposed method and results.
Response: We appreciate the Reviewer’s feedback. However, we believe that the explanation concerning the novelty or uniqueness of the proposed model has been presented in the introduction to the article, in lines 53-59.
Comment 1: There is a typo in Abstract. It should be 20-700, not a “divide”.
Response: Thank you for pointing this out. The „¸” has been substituted by the „-” sign.
Comment 2: Why the final value of the section thermal resistance is Eq.4?
Response: The final value of the section thermal resistance was calculated from the equation (4) since the values of resistances Rst-a and Rst-b obtained for individual section divisions are different – which results from different assumptions for heat transfer. The explanation of this problem has been described in lines 91-95. We hope that it is now clear.
Comment 3: Are the parameter values in Eq.16 and 17 calibrated from experiment measurements?
Response: The mentioned equations (after editing they are denoted by (20) and (21)) have been determined based on experimental research. The detailed description of the methodology of determining these correlations has been presented in lines 159-179. Also, pictures 6 and 7 have been added to emphasize this point.
Comment 4: It would be good if more details about how the experimental measurements were implemented.
Response: Thank you for this suggestion. The experimental measurements were necessary to determine:
- the value of Nusselt number,
- the values of contact resistance,
- the verification of the model.
As suggested by the Reviewer, more details on how the experimental measurements were implemented have been added. The use of measurements concerning the Nusselt number has been described in lines 116-143. The research concerning contact resistance has been described in lines 158-186. The research concerning the verification of the model, which consists in determining the value of Rto resistance in an experimental way, has been described in lines 265-272.
Additional clarifications:
In addition to the above corrections, the following passages have been incorporated into the content of the paper:
- additional information on the resistance Rto (lines 69-71),
- additional conclusions on the passages which have been added according to Reviewers’ comments – lines (302-306),
- additional references [7], [10], [15], [16].
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The revised version has addressed all my comments and concerns. It is good to be accepted.
