Modeling of Heat Flux in a Heating Furnace

Round 1

Reviewer 1 Report

The paper presents the results obtained from experimental data on heating slab in a pusher heating furnace. The experimental data are represented by the change in temperature at the internal points of the slab along the height and distance from the side face. Based on the results of heating the slab, the heat fluxes on the upper and lower sides of the slab in the initial furnace and the furnace after reconstruction have been determined. Positive changes have been presented after the reconstruction of the furnace, expressed in the alignment of heat flows from the upper and lower zones of the heating furnace. Based on the results, there are several questions.

a) the purpose of the study was to determine heat fluxes. Why was the temperature on the surface of the slab not measured, which would make it possible to simplify the mathematical model?

b) Have studies been carried out on the relationship between fuel consumption and heat fluxes to the surface of the slab? This is not mentioned in the work. And how can the developed model be used by operators to control the thermal state of slabs (line 430) in the furnace if the mathematical relationship between heat flows and fuel consumption by furnace zones is not defined?

c) what do the markers on the diagrams (Fig. 9.11) marked as "Slab in the furnace" mean?

d) it is stated that the experiment was carried out with a slab 200 mm thick, but in the diagrams (Fig. 8, 10) the xmin value takes on a value greater than 200 mm.

e) line 307 refers to equations (6) and (7) and states that di is calculated in these equations, but actually tdi and cp are calculated in these equations.

f) in the line 275 the index (to, i) is not correctly specified, it should probably be (td, i).

The work is undoubtedly of interest, as it contains the results of a complex experiment. But the authors should more carefully present the results of the research and make corrections to the article.

For further research to substantiate optimal heating strategies, I recommend that the authors familiarize themselves with the work, for example, Machines 2019, 7(3), 60; https://doi.org/10.3390/machines7030060

Authors are required to use terminology more precisely. It is advisable to use one term to refer to an object throughout the entire paper. The text of the article uses different terms to refer to slabs (charge, billets, gate, pre-rolls, material), furnaces (pusher furnaces, heating furnace, ramming furnace)

Author Response

In the attached file, the responses to the individual points of the review are elaborated. I hope that we have sufficiently edited the manuscript and answered the questions. Edits according to the comments are indicated in the manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments to the Author:

A mathematical model was developed to calculate the heat fluxes of the moving charge slabs along the length of the pusher furnace to evaluate the heating of the charge in this paper. The developed mathematical heat flux model is applicable as part of the powerful tools for monitoring and controlling the thermal condition of the charge inside the furnace as well as for evaluating the operating condition of such furnaces. The structure of the article is complete, logical rigorous, has a certain innovation and research value. However, the manuscript still has some issues that need to be revision:

1. The resolution of figures are not clear enough. Please increase the resolution of figures to at least 300 dpi.

2. In page 4, line 154, what is the meaning of quality 379? The author should add more detailed statements to explain the situation of the test slab.

3. The location of the thermocouple measuring points should be marked in detail in Figure 1 to better represent the actual situation. 

4. The description of thermocouple type, embedment depth and reason of measuring points selection should be added so that readers can better understand the measurement method.

5. In page 9, line 325, the paper said “Figures 8 and 9 show the results for the test slab measurement with a heating time of 187 min. This is because of the heating comparison shown in Figure 3, where the residence time of the gate in the furnace was 171 min.”. The meaning of this description is confused, so the author needs to explain it more clearly.

6. The author need to clarify the location of t1-t3 in Figure 8, is it as description in Figure 3

7. What is the meaning of “slab in the furnace” in Figure 9 and Figure 11? The author needs to add statement to clarify the actual meaning.

8. The author should explain how the mathematical model is applied in the industrial process to show the practical value of the model.

Author Response

In the attached file, the responses to the individual points of the review are elaborated. I hope that we have sufficiently edited the manuscript and answered the questions. Edits according to the comments are indicated in the manuscript.

Author Response File: Author Response.pdf