A Similarity Model of Specific Heat Loss Determined by Dimensional Analysis

Round 1

Reviewer 1 Report

The article titled "A similarity model of specific heat loss determined by a dimensional analysis" created a mathematical model of specific heat loss based on dimensional analysis. 

The author(s) used Buckingham Pi Theorem in order to do their dimensionless model. 

Perhaps the author(s) can explain why they proposed a dimensional analysis method to solve their problems.

The results obtained were verified using an experimental model based on the mathematical model representation. The results show a good agreement between the mathematical and experimental models.

The findings obtained from this research have contributed to the new knowledge of the subject matter. 

There have several typos on this document as highlighted in the attached file. 

Therefore, this article will be considered for acceptance to be published. 

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Please find our answers to the reviewers’ questions and our statements to their comments. New texts were added in the lines indicated in each statement to a relevant comment.

Perhaps the author(s) can explain why they proposed a dimensional analysis method to solve their problems.

The explanation has been supplemented in the article in lines 22 and 23, as follows:

For the aforesaid reasons, the authors created a mathematical model for specific heat losses based on a dimensional analysis.

Reviewer 2 Report

Authors of this article have created a mathematical model of specific heat loss based on a dimensional analysis which was based on relevant dimensional quantities. this study used a database of results obtained by physical experiments conducted on two heat networks. And the results showed that: The standard deviation of a difference in heat losses identified by applying the balance method and using the proposed criterial equation for a twin pipe directly buried pre-insulated heat network was small.

However, the innovation of the paper is not strong, which needs major revisions. See the issues as follows, please.

1.    What does FEV mean? It is suggested to add in the paper.

2.     Suggest inviting native English speakers to polish the paper.

3.     Why does this paper not consider the influence of the length of the two pipes on the measurement results? A supplementary explanation is recommended.

4.     Please explain why the ambient temperature of the two pipes is set to 7.5, 10,15 ° C and 5,9,13 °  C respectively.

5.     Add information  about F test in "5. Identification of the Criterial Equation  Parameters".

6.     It is suggested  that the authors should consider heteroscedasticity and multicollinearity tests  when conducting multiple regression analysis.

7.     Figure 2 needs to  be embellished. In addition, the figure lacks legend, it is suggested to add. Moreover,Figure 3 needs to be embellished.

8.     Is there no abnormal data during the experiment? Does this paper not require data filtering?

9.     The paper has noconclusion, and it is suggested to add.

10. The format of references should be unified. For example, "in Slovak" should be changed to "In Slovak".

Dear editor, the paper currently under review has major defects and needs major revision.

Author Response

Dear Reviewer, Thank you very much for your review and support, I very appreciate it.

1.     What does FEV mean? It is suggested to add in the paper. 
The abbreviation has been corrected in line 63 to FVM.

2.    Suggest inviting native English speakers to polish the paper. 
The article has been proofread by a native speaker.

3.    Why does this paper not consider the influence of the length of the two pipes on the measurement results? A supplementary explanation is recommended. 
The article discusses specific heat losses, i.e. heat losses per one unit of a pipe length. Based on the values of the measured parameters, such as a pipe length, input and output temperatures of water in the supply and return pipes, an ambient temperature, a burial depth etc., we calculated respective values of ql (W•m-1). The calculated values of ql (W•m-1) were then used in a dimensional analysis. Lengths of the analysed pipes were therefore irrelevant to the derivation of a criterial equation.  

4.    Please explain why the ambient temperature of the two pipes is set to 7.5, 10, 15 °C and 5, 9, 13 °C respectively. 
This temperature was not set by the authors of the article. These were actual temperatures at which individual measurements were made.

5.    Add information about F test in "5. Identification of the Criterial Equation Parameters". 
The compared data sets for heat loss ql,mea, calculated while using the results of measurements, and ql,mod (obtained from the model) are mutually dependent sets (sets with paired values). Therefore, we made the evaluation by applying a t-test (specified in more detail in the article). In this case, it was inappropriate to use an F-test. 
The application of a paired t-test is conditioned by meeting the requirement of normality of differences in values, which was verified by applying the Shapiro-Wilk test of normality. The testing was carried out using the R package software.

6.    It is suggested that the authors should consider heteroscedasticity and multicollinearity tests when conducting multiple regression analysis. 
It has been supplements in line 224 and subsequent lines, as follows:
An analysis of the results indicated that the model was statistically significant. To verify multicollinearity, the Variance Inflation Factor (VIF) quotient was used. Since the VIF value lied between 1 and 5, the considered criteria did not correlate with the other criteria. Heteroscedasticity was verified using the Breusch-Pagan test. The results indicated that the regression model did not prove the heteroscedasticity. Tests were carried out using the R package software.

7.    Figure 2 needs to be embellished. In addition, the figure lacks legend, it is suggested to add. Moreover, Figure 3 needs to be embellished. 
Figures 2 and 3 were modified and inserted in the article. They will also be sent as separate files.

8.    Is there no abnormal data during the experiment? Does this paper not require data filtering?
It has been supplemented in line 210 and subsequent lines, as follows:
For the purpose of a further analysis, we had to our disposal the values of parameters obtained by a total of 216 measurements. From the set of calculated values for ql we removed the outliers. Therefore, when deriving the parameters of a criterial equation, we did not take into account 2 measurements on the DN65 network and 3 measurements on the DN100 network.

9.    The paper has noconclusion, and it is suggested to add. 
The conclusion in contained in Chapter 5.

10.    The format of references should be unified. For example, "in Slovak" should be changed to "In Slovak".
The format of “In Slovak” references has been made consistent.

Round 2

Reviewer 2 Report

Good.

Good