Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars
Round 1
Reviewer 1 Report
My comments to the authors are as follows:
1. In Figure 3b, line-graphs corresponding to the 0.02mx0.0004m, 0.02mx0.0005m, 0.025mx0.0004m, and 0.025mx0.0005m bus bars are generated for vibration amplitudes ranging from 0 to 5 mm at a vibration frequency of 120 Hz. The mentioned bus bars correspond to the plate fins considered in Reference [15]. In [15], the fins were analyzed at vibration frequencies 29, 40, 50 and 59 Hz and a velocity ratio ranging from 0 to 20. Moreover, the plate fins were installed horizontally with a vertical major axis and they were vibrated horizontally as well. It would be useful for the authors to generate these graphs for the installation method from [15], with vibration frequencies from [15], and different vibration amplitudes corresponding to the velocity ratios from [15]. For example: to change vibration amplitudes from 0 to 5 mm at a vibration frequency of 50 Hz for the 0.02mx0.0004m, to change vibration amplitudes from 0 to 5 mm at a vibration frequency of 59 Hz for the 0.02mx0.0005m, etc. And to compare such results with the corresponding ones from [15].
2. The following statement "Specifically, the discrepancy between the simulated and existing experimental data is less than ±10%." has been taken directly from Reference [15]. This should be checked for correctness based on the results that will be obtained when responding to the first comment.
3. The results that will be obtained when responding to the first comment should be presented graphically together with the corresponding experimental data from Reference [15]. This will contribute to the experimental validation of the accuracy of the proposed analytical thermal model.
4. Some of the results that will be obtained when responding to the first comment should also be verified numerically in COMSOL. The results shown in Figure 12 should be replaced with these results.
5. All simulations that will be performed based on the previous comments should be performed under the assumption that there is no heat dissipation between the top and bottom surfaces of these four bus bars (or flat fins) so that the analytical and numerical simulations correspond to the experiment from [15]. In particular, the top and bottom surfaces should be considered adiabatic boundaries.
Author Response
Dear Reviewer 1,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to Comment 1 of Reviewer 1: As requested, the comparison between simulated and experimental data has been performed. A sub-section dealing with this comparison has been added and labeled with the ordinal number 4.1.
Response to Comment 2 of Reviewer 1: The correctness of the mention statement has been checked and the following modification: “According to Figure 2, the normalized Nusselt number represented by Equation (10) agrees well with the experimental data from [21], where the discrepancy is only in two cases beyond the ±10% limits.” has been introduced in Sub-section 4.1.
Response to Comment 3 of Reviewer 1: In connection with this comment, Figure 2 illustrating the requested comparison has been added to Sub-section 4.1.
Response to Comment 4 of Reviewer 1: As requested, the verification of the proposed analytical model using the FEM and relevant experimental data has been performed. A sub-section dealing with the verification has been added and labeled with the ordinal number 4.2.
Response to Comment 5 of Reviewer 1: The assumption that the top and bottom surfaces of the plate fins from the experiments used are adiabatic has been applied in Sub-section 4.1.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 2 Report
The manuscript "Modeling the Effects of Horizontal Transverse Vibrations on 2 the Thermal Behavior and the Ampacity of Rectangular Bus Bars in an Indoor Environment." introduced a good presentation of the Effects of Horizontal Transverse Vibrations on the Thermal Behavior. However, the paper needs more revision to be suitable for publication.
comments
1- In the introduction, the last two paras should be rewritten to show the contribution of the work clearly.
2- This work seems similar to the work in [16]. please explain your novelty and the advantage of the method that you used.
3. In Figure 8, please explain the reason for the difference in curves. some of them short while others long.
4. The authors used COMSOL for simulation. Please explain the steps that you applied in COMSOL for this work to get the results.
5. In my opinion the references should be more thane 25 references.
English Language for this paper is OK.
Author Response
Dear Reviewer 2,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to Comment 1 of Reviewer 2: The last two paragraphs of the introduction have been rewritten, and the contributions of the work have now been shown in a more appropriate way.
Response to Comment 2 of Reviewer 2: The difference between the previous and current contributions of the authors has been highlighted as requested. In this regard, the following sentence: “The proposed analytical thermal model is implemented in the BUBBAR.m program, which was already used in [16], while all FEM-based verifications are performed in COMSOL 4.3 [17].” of the introduction has been modified as follows: “The proposed analytical thermal model is implemented in the BUSBAR.m program, whose first version can only solve problems with pure free or forced convection without the effects of vibrations [22]. Whilst all FEM-based verifications are performed in COMSOL 4.3 [23].” The ordinal numbers of the references have been changed because the list of references has been expanded.
Response to Comment 3 of Reviewer 2: Reasons for the errors related to Figures 3 and 8 have been identified in Equation (18) and accordingly eliminated. Thank you very much for this comment. All the content has been rewritten and corrected in accordance with this comment.
Response to Comment 4 of Reviewer 2: Sub-section 3.2 dealing with the FEM-based thermal modeling has been completely rewritten and reorganized. All missing data are provided in the revision of this sub-section. The steps how COMSOL was applied in this paper to obtain the results are also explained.
Response to Comment 5 of Reviewer 2: The list of references has been expanded and now has 32 instead of 24 references.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 3 Report
Dear Authors,
I have the following observations:
1. The title is tangled and need to be revised wrt the problem statement.
2. The abstract needs the additional information of structural dynamics and the vibrational theory. By simply putting as " Horizontal Transverse" is not going to serve the purpose rather making it confusing for the readers.
3. The section, "Geometry/materials/assumption" is also not making a better representation of content. How many assumptions did you make? For the material what are assumptions? For the phenomenon? etc. Pl look into it.
4. How you are going to approximate the response for every set of data? I didnt see such of vibrational parameters in first part of the paper which must be there, as it initiates from this effect. The logical sequence is very important.
5. The simplified geometry is fine for the type of problem you are doing research for?
6. Mathematical model is dragged too much and some redundant formulation is also there. Revise and put the relevant part only.
7. FEM part is not well defined. Details missing for the purpose and how to you validate, with what?
8. The boundary conditions and load data must be represented in initial few sections.
9. The comparison and validation needs to be performed in a better way. It is not advisable to ignore the important sections.
10. Dont drag the conclusion part too much.
Needs a revision.
Author Response
Dear Reviewer 3,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to Comment 1 of Reviewer 3: The title has been changed and now reads: “Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars”.
Response to Comment 2 of Reviewer 3: According to the template of Applied Sciences, i.e., according to https://www.mdpi.com/journal/applsci/instructions, the abstract is limited to no more than 200 words. The present abstract consists of 200 words. Accordingly, there is no space for additional details from structural dynamics or vibrational theory in the abstract. The authors sincerely regret that they were unable to do so. Moreover, for instance, according to https://www.matec-conferences.org/articles/matecconf/pdf/2018/75/matecconf_pts2018_01015.pdf, https://courses.physics.illinois.edu/phys406/sp2017/Lecture_Notes/Waves/PDF_FIles/Waves_2.pdf, https://ccrma.stanford.edu/~jos/pasp/Horizontal_Vertical_Transverse_Waves.html, etc., the term “horizontal transverse vibration” has been used by other researchers and professors in the same context.
Response to Comment 3 of Reviewer 3: Section entitled “2. Geometry, Material Properties and Assumptions” has been completely rewritten and reorganized. In the revised version of this section, the assumptions are grouped in one place and it is indicated exactly which of the assumptions refer to the materials. The vibration phenomenon was already graphically presented in Figures 1b and 1d, and also described/mentioned below Figure 1. This was done in accordance with the way of presenting the phenomenon of vibrations in the research papers of other scientists.
Response to Comment 4 of Reviewer 3: The vibrational parameters considered have now been mentioned in Section 2 in the following sentence: “. Specifically, the effect of vibration parameters (vibration amplitude in m or/and vibration frequency in Hz) on free convection from the side, top or bottom surface of a rectangular bus bar is included on the basis of the coefficient , or , respectively.”
Response to Comment 5 of Reviewer 3: In regard with this comment, the authors added the following: “Such volume elements of rectangular bus burs having width W (in m), height H (in m) and length L (in m) are shown in Figure 1. The unit length of the bus bars was chosen because the process of solving two-dimensional heat transfer problems in COMSOL implies that the default length of any geometric model (i.e., default depth when an object or solid is displayed on a two-dimensional computer screen) is L=1 m. Thus, the representations of the problems in Figure 1 are three-dimensional, and the problems solved in COMSOL are two-dimensional of unit length.” in Section 2.
Response to Comment 6 of Reviewer 3: The part of the mathematical model related to pure free convection has been excluded, some of the important formulas from that part have been transferred to the appropriate places in the part related to vibration-assisted convection, and at the end of the analytical thermal model the following has been emphasized: “It should be emphasized here that the case of vibration-assisted convection can be reduced to the case of free convection when m or Hz is set.” The whole model has been reformulated and revised in order to exclude similarities with the previous work, as well as expanded with the part related to the introduction of a non-adiabatic assumption for the bus bar surfaces having the characteristic lengths equal to or less than 5 mm.
Response to Comment 7 of Reviewer 3: Sub-section 3.2 dealing with the FEM-based thermal modeling has been completely rewritten and reorganized. All missing data are provided in the revision of this sub-section. The purpose of validation and associated data have also been highlighted in the revision.
Response to Comment 8 of Reviewer 3: Within Sub-section 3.2, the boundary conditions have been presented in a more convenient manner. In particular, the radiation boundary condition has been corrected.
Response to Comment 9 of Reviewer 3: As requested, the comparison between simulated and experimental data has been performed. A sub-section dealing with this comparison has been added and labeled with the ordinal number 4.1.
Response to Comment 10 of Reviewer 3: The content of the conclusion has been compressed, improved and optimized as requested.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 4 Report
The authors presented analytic and numerical studies on the effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars in an Indoor Environment.
The novelty of the paper is to be clearly stated; the considered geometry is very simple; the analytical and numerical studies are very basic.
The introduction is relatively short and may be extended.
How is Qtg,v evaluated?
The numerical method is to be detailed.
A figure presenting the used mesh is to be added.
The results of the grid sensitivity test are to be presented, it is not sufficient to mention that you performed it.
A verification of the numerical model is to be performed.
Have you considered a 2D or 3D configurations; in Fig 1 you presented 3D geometries, in line 288 you mentioned that you solve 2D equations and the results of Fig 12 you are speaking about cross-section. This is very confusing, it should be clarified.
How is the vibrating boundary condition is imposed in comsol?
I can not find any novelty in the presented work, in addition the scientific soundness is relatively low.
The paper is to be checked against misprints and grammatical errors.
The paper is to be checked against misprints and grammatical errors.
Author Response
Dear Reviewer 4,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to Comment 1 of Reviewer 4: The authors agree with Reviewer 4 that the analyzed geometry is very simple and that the analytical and numerical thermal models are not complex. However, it is the real geometry of the analyzed solids, and such geometry cannot be modeled in a more complex manner. In addition, the analytical thermal model has been further improved, experimentally validated in a more convenient manner, and numerically verified using the FEM in a more appropriate manner. Furthermore, the novelties stated in the abstract are evident and real, while the obtained results are original and cannot be found in the existing literature.
Response to Comment 2 of Reviewer 4: The introduction has been expanded and significantly improved in terms of the presentation style.
Response to Comment 3 of Reviewer 4: In the first version of this manuscript, after Equation (33), the following was already given: “… is the volume power of heat sources defined by Equation (2) in W×m–3.” Accordingly, the volume power of heat sources was evaluated using Equation (2).
Response to Comment 4 of Reviewer 4: Sub-section 3.2 dealing with the FEM-based thermal modeling has been completely rewritten and reorganized. All missing data are provided in the revision of this sub-section.
Response to Comment 5 of Reviewer 4: In regard with this comment, Figure 3a of the revision presents the FE mesh used.
Response to Comment 6 of Reviewer 4: The results of the FE mesh independence tests have been presented in Table3 of the revision.
Response to Comment 7 of Reviewer 4: The verification of the proposed model has been performed as requested. The details on the verification can be found in the sub-section entitled “4.2. FEM-Based Verification of the Proposed Analytical Model”.
Response to Comment 8 of Reviewer 4: In regard with this comment, the Authors added the following: “Such volume elements of rectangular bus burs having width W (in m), height H (in m) and length L (in m) are shown in Figure 1. The unit length of the bus bars was chosen because the process of solving two-dimensional heat transfer problems in COMSOL implies that the default length of any geometric model (i.e., default depth when an object or solid is displayed on a two-dimensional computer screen) is L=1 m. Thus, the representations of the problems in Figure 1 are three-dimensional, and the problems solved in COMSOL are two-dimensional of unit length.” in Section 2. Therefore, the two-dimensional heat transfer problems have been solved in COMSOL 4.3. The authors sincerely hope that it is now clear what kind of problem was solved and how.
Response to Comment 9 of Reviewer 4: In regard with this comment, the following explanation: “The effect of horizontal transverse vibrations on free convection from any rectangular bus bar is included in the corresponding FEM-based model using the convection heat transfer coefficient in the following manner: – for its side surfaces, – for its top surface, and – for its bottom surface.” has been added to the text placed immediately after the equation representing the convection boundary condition.
Response to Comment 10 of Reviewer 4: In Reference [1], the following: “Busbars are subject to mechanical forces since each is carrying a current though the magnetic fields caused by currents in other bars. When alternating currents are flowing, the forces have a steady component, but also a vibrational component at twice the frequency of the alternating current. Under normal working conditions these forces are of little consequence.” can be found. In this regard, we found that under normal service (operating and environmental) conditions these forces are of significant importance. Accordingly, our finding is the opposite of the standardized hypothesis used for decades in the design process of bus bur conductors. The authors sincerely hope that they have now better presented the scientific contribution of this study.
Response to Comment 11 of Reviewer 4: The revised manuscript has been checked for grammatical and typographical errors as requested.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 5 Report
The authors of the paper “Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus 3 Bars in an Indoor Environment” presents an analytical study, i.e., a numerical simulation study, on the evolution of ampacity in particular situations. The paper is referenced in the literature at a minimum acceptable level. This paper is a continuation of other papers on the same topic by the authors. For this reason, the elements of novelty presented can be identified at the limit, and in the way they have been formulated it is questionable whether they are really new or just variations on the same theme. I recommend the authors to clearly motivate this study in relation to the literature respectively to their previous contributions. What new conclusions, different from the known ones, does this new study bring?
The paper is well written without noticing major revisions from this point of view other than those that may be possible to correct in the publication process anyway.
The paper contains many tables or figures which in the present form of writing often leave the impression that another page was needed. They are too technical, too much like a technical manual and are not sufficiently presented from an academic perspective, starting from the elements of novelty invoked. There are a lot of pages and my suggestion is to restrict them to the elements of maximum interest and that really bring elements that support the novelty of this new version.
As a rule, an article paper must contain an experimental section and any scientific paper loses much of its value without experimental validation and even a comparative study with data taken from the literature can rarely provide satisfaction.
It must be proven and described how to apply these results in the perspective of a future technology that will enhance the theoretical, simulated and eventually experimentally validated results. In the application area, less useful are "interesting" discoveries that have no useful application in the future.
The research effort of the authors for the elaboration of this article, which is a continuation of previous works, is not substantial and I recommend its revision from the point of view of content, starting from the previous motivations.
Author Response
Dear Reviewer 5,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Responses to the first set of comments of Reviewer 5: The literature review has been improved and the reference list now has 32 instead of 24 publications. The difference between the previous and current contributions of the authors has been highlighted in the revision. In this regard, the following sentence: “The proposed analytical thermal model is implemented in the BUBBAR.m program, which was already used in [16], while all FEM-based verifications are performed in COMSOL 4.3 [17].” of the introduction has been modified as follows: “The proposed analytical thermal model is implemented in the BUBBAR.m program, whose first version can only solve problems with pure free or forced convection without the effects of vibrations [22]. Whilst all FEM-based verifications are performed in COMSOL 4.3 [23].” The ordinal numbers of the references have been changed because the list of references has been expanded. The novelties and contributions have now been highlighted in a more appropriate manner, while the motivation is now clear for the readership. New conclusions are highlighted in relation to earlier conclusions of the authors and the literature in general. All these changes were made within the introduction, and the conclusion itself was partially modified.
Response to Comment 2 of Reviewer 5: The authors would like to thank Reviewer 5 for this positive assessment.
Response to Comment 3 of Reviewer 5: As requested, the amount of tabulated data has been reduced to an academic level. In connection with this, two tables from Appendix A have been removed.
Response to Comment 4 of Reviewer 5: As requested, the comparison between simulated and experimental data has been performed. A sub-section dealing with this comparison has been added and labeled with the ordinal number 4.1.
Response to Comment 5 of Reviewer 5: How to apply the results of this study in the perspective of a future technology has been provided at the end of conclusion. Specifically, our results can be included in the procedure of designing bus bar installations.
Response to Comment 6 of Reviewer 5: Our manuscript has been completely revised from the content point of view, of course, starting from the previous motivations. The motivation to address the existing research gaps is now much clearer.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 6 Report
The authors have presented steady-state heat transfer in and around rectangular bus bars installed horizontally in an indoor environment and to estimate the corresponding ampacities, considering the effects of horizontal transverse vibrations caused by electro- magnetic forces. This thermo-electro-magneto-mechanical problem is solved analytically using correlations determined experimentally by other researchers, while the accuracy of the obtained results is verified numerically using the finite element method (FEM).
In my opinion, the authors just have used the available formula to obtain their results for their specific boundary conditions. Hence, I cannot see any analytical novel solution in the present study to be recommended for publication.
1- The literature review denotes the existence of lots of papers on thermal induced vibration of different structures. In the introduction section, limited studies are reviewed. The authors must rewrite this section by reviewing more studies.
2- The novelties and research highlights of present study must be presented in the last paragraph of introduction section point by point and more clearly.
3- The authors have verified their results by COMSOL. The authors must verify their result by previous research not their simulation in COMSOL.
4- How can the authors prove that the applied frequencies lead to transverse vibration? Maybe the longitudinal modes be excited.
5- It is better to change the rectangular Bus bar in the title to rectangular bars.
6- The convergence study in COMSOL must be presented.
7- The authors have presented 3 novelties for their research “The novelties of the developed model
are as follows. First, modeling the effects of horizontal transverse vibrations on free convection from the top and bottom surfaces of rectangular bus bars via forced convection. Second, modeling the effects of vibration amplitudes and vibration frequencies on the bus bar ampacity. Third, introducing the existing vibration classes into the analytical and FEM-based thermal analyses” But, they have cited each formula by some Refs. I cannot see any analytical novel solution in the present study. The authors just have used the available formula to obtain their results for their specific boundary conditions.
It needs minor corrections.
Author Response
Dear Reviewer 6,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to the general opinion of Reviewer 6: The authors agree with the opinion of Reviewer 6 that existing empirical correlations were used in the analytical thermal model and that the authors did not propose novel analytical equations. However, the aim of the authors was not to derive new correlations for convection heat transfer, but to apply existing ones, to create a new thermal model and to quantify some already unquantified effects. Thus, the derivation of new correlations would go beyond the scope of this study.
Response to Comment 1 of Reviewer 6: In regard with this comment, the sentence: “However, this review paper did not include numerous references, including the older ones used to conduct this study.” of the introduction has been modified as follows: “However, these reviews did not include some relevant references, including the older ones used to conduct this study.” The part of the introduction dealing with the review of relevant literature has been improved, expanded and now reads: “A review of the literature to find possible gaps in the knowledge concerning the effect of vibrations on convection heat transfer from a vertical plate was already carried out by Abdu-Razak, Abbas, and Tahseen in 2020 [5]. In the same year, another relevant review on active and passive methods of enhancing heat transfer from a plate fin by means of vibrations was conducted by Rahman and Tafti in Reference [6]. Based on the content of References [5] and [6], it is logical that these reviews also cover the case of a bus bar installed horizontally with a vertical or horizontal major axis. However, these reviews did not include some relevant references, including the older ones used to conduct this study. For instance, in [5,6] there are no studies on free or forced convection heat transfer from: a longitudinally vibrating vertical plate [7], vertical cylinders with vertically oriented plate fins [8], bus bars under short-circuit conditions [9], bus bars used to supply a test bench with high currents [10], and so on. Accordingly, all relevant references that were published in 2020 and later can be regarded as state-of-the-art for this area. The state-of-the-art directly-related to bus bars addressed the following research gaps: finite element method- (FEM-) based electrodynamic modeling of bus bars carrying high currents [11,12]; FEM-based modeling of bus bars in terms of coupling electromagnetic and thermal phenomena with fluid flow [13]; and vibration response of a bus bar enclosure considering the effect of a strong electric field [14]. In a broader context, this state-of-the-art has also closed research gaps, such as: the effect of internal plate vibrations on heat transfer in a dryer [15]; visualization of a vibrating plate in a boiling bubble resonator [16]; mixed convection from a vertical plate subjected to periodic oscillations [17]; as well as the effect of vibrations on the phenomena of heat transfer and flow along heat exchange surfaces [18]. Within this broader context, the effects of square and sinusoidal wave-shaped vibrations on forced convection from a heat sink [19] and modeling of the thermal behavior of different vibrating blades [20] were also addressed. According to this literature review, there is no study dealing with the effect of any vibrations on the ampacity of a bus bar in normal operation.”
Response to Comment 2 of Reviewer 6: In the last paragraph of the introduction, the novelties and other contributions have been highlighted in a clearer manner.
Response to Comment 3 of Reviewer 6: As requested, we have verified our results with relevant experimental data from the literature in combination with FEM-based simulations in COMSOL, rather than using COMSOL simulations alone. The details on the verification can be found in the sub-section entitled “4.2. FEM-Based Verification of the Proposed Analytical Model”.
Response to Comment 4 of Reviewer 6: For instance, the response to the question “How can the authors prove that the applied frequencies lead to transverse vibration?” can be found in References [1], [19], etc. Specifically, Reference [1] states the following: “When alternating currents are flowing, the forces have a steady component, but also a vibrational component at twice the frequency of the alternating current.” (that is, 120 Hz is twice the frequency of the alternating current of 60 Hz), “However, if the bars are mounted on supports, each section will have a resonant frequency. If this frequency is close to twice the supply current (or any significant harmonic current), then resonant vibration of these beams may occur.” (that is, 240 Hz is the frequency of the second order harmonic current, 360 Hz is the frequency of the third order harmonic current, etc.), and so on. The details related to the frequencies considered were already provided in the following paragraph: “The vibration amplitudes considered here assuming a vibration frequency of 120 Hz are: 0 m – for the case of free convection; 8.541 mm – for the case of twice the power system frequency [1]; 1 mm – for the case of the vibration class A [4]; 1.6 mm – for the case of the vibration class B [4]; 3 mm – for the case of the vibration class C [4]; and 4 mm and 5 mm – for the case of improper selection of supporting insulators and normal operating conditions [13]. The last two vibration amplitudes are chosen to match those of the experiment performed for the purpose of study [15]. The vibration frequencies considered here assuming a vibration amplitude of 3 mm are: 0 Hz – for the case of free convection; 2.75 Hz – critical frequency for vibrations due to wind eddies [1]; 11.09 Hz – critical frequency for the vibration classes A and C [4]; 29 Hz – natural frequency determined experimentally in [15]; 120 Hz – twice the value of the power system frequency [1]; 240 Hz – twice the value of the frequency of the second order harmonic current [1,19]; and 360 Hz – twice the value of the frequency of the third order harmonic current [1,19]. The last two vibration frequencies are chosen to illustrate and quantify the potential effects of frequencies higher than twice the power system frequency.” In the first manuscript version, the given paragraph was provided after Equation (20). Therefore, all the considered frequencies were logically selected and not randomly.
Response to Comment 5 of Reviewer 6: The title has been changed and now reads: “Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars”. However, it was not appropriate to replace the term “bus bar” with the term “bar” because the first term implies the flow of electricity through a conductor and the second does not. The definition of the term “bus bar” can be found at https://circuitglobe.com/electrical-bus-bar-and-its-types.html.
Response to Comment 6 of Reviewer 6: The results of the FE mesh independence tests performed in COMSOL have been presented in Table 3, within the sub-section entitled “4.2. FEM-Based Verification of the Proposed Analytical Model”.
Response to Comment 7 of Reviewer 6: This study aimed to apply existing empirical correlations for free and vibration-assisted convection, to create a new thermal model and to quantify some already unquantified effects, not to derive new correlations for convection heat transfer. As mentioned above, the derivation of new correlations would go beyond the scope of this study. The authors are sincerely sorry that they did not meet the expectations of Reviewer 6.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Reviewer 7 Report
This article deals with modeling the influences of Horizontal Transverse Vibrations on the thermal response and the Ampacity of Rectangular Bus Bars surrounded by Indoor Environment by employing finite element approach. Based on reviewer opinion, the paper is well written and organized. Besides, it has positive impact on scientific society. I strongly recommended it for publication
This article deals with modeling the influences of Horizontal Transverse Vibrations on the thermal response and the Ampacity of Rectangular Bus Bars surrounded by Indoor Environment by employing finite element approach. Based on reviewer opinion, the paper is well written and organized. Besides, it has positive impact on scientific society. I strongly recommended it for publication
Author Response
Dear Reviewer 7,
First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. Also, based on your comments, as well as the comments of other reviewers, the authors noticed an error in the equation that was labeled with (18) in the first version of the manuscript. This equation is denoted as (10) in the revised version of the manuscript. By correcting that error, all results became comparable with the relevant experimental data from the literature. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.
Response to the comments of Reviewer 7: The authors would like to thank Reviewer 7 for the confidence and positive opinion given as well.
Sincerely Yours,
Prof. Dr. Dardan Klimenta
On behalf of all the authors.
Round 2
Reviewer 1 Report
I am very satisfied with authors responses.
Thank you for answers.
Reviewer 3 Report
The article is improved.
Moderate
Reviewer 4 Report
the paper is very basic.
the used mesh is very coarse
the scientific soundness of the paper still very low
Reviewer 5 Report
In the revised version of the paper "Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars " the authors have responded in detail to the observations and recommendations of the original version. In this version of the paper new information is highlighted which gives more consistency to this review paper. I think that the paper has interesting elements and is useful for developing applications or guiding future research according to the current trend. I recommend acceptance for publication of the article in revised form.
Reviewer 6 Report
The paper is well revised and can be accepted in the present form.
Minor editing is needed.
