Entropy Analysis for Hydromagnetic Darcy–Forchheimer Flow Subject to Soret and Dufour Effects
Round 1
Reviewer 1 Report
The author studied the well-known unsteady stretching sheet problem along with the Soret and Dufour effects, in Darcy-Forchheimer porous medium flow under radiation. The second law analysis is also conducted against various parameters. The problem is solved by finite difference method. I have the following concern due to which I won't recommend the publication of this manuscript.
1. There are numerous studies on stretching sheet with the same physical combinations of various effects. What is need of this article?
2. The stretching sheet problem is a boundary layer flow. Why are authors considering this problem as uni-directional flow. Why boundary-layer approximations are not used?
3. In boundary layer flow the derivative "partial u by partial x" is not zero and the continuity equation doesn't reduced to v = constant.
4. The formulation of the problem must be written scientifically by explaining all the terms in the governing equations with proper assumptions and referencing.
5. There is no dependency of x variable in Eqs. 1 to 5. Why x is normalized in Eqs. 6?
6. The entropy analysis lacks the basic assumptions of entropy production in the flow and the reference.
7. The numerical solution part is not complete. Nothing has been written, for example, what Order of approximations is used for the spatial and temporal derivatives and which difference scheme is used and why.
8. Nothing mentioned how to solve Eqs. 22 and 23 at what order, what is truncation of the temporal and spatial domains and which method is used to solve algebraic equations.
9. Discussion and conclusion parts are also not written up to the mark.
10. What parametric values are used to draw figures 2-18? How can one reproduce these figures?
11. The language of the manuscript is below standard and does not reflect the language of an international scientific journal.
In conclusion, I can not recommend this article for publication.
Author Response
Now the whole manuscript revised carefully
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this article, the authors model nonlinear effects in porous medium flow through the lens of thermodynamics. The system of partial differential equations modelling the flow is reduced to a system of ordinary differential equations using similarity transformations.
I strongly recommend the authors include a narrative in section 7. The point discussed in section 7 does not provide the reader with an overview of the results. A comparison must be made with known results so that the contributions made by the authors are highlighted.
In addition to the points above, I believe the language needs to be improved.
I include some language corrections below.
On line 11 in the abstract - A decay ... not decays.
On line 21 accounted -> arise
On line 101 Engineering contents of interest
Author Response
To
Mr. Ursulescu Vlad Bogdan
Assistant Editor, MDPI Cluj
Mathematical and Computational Applications
Respected Sir,
The compliances of reviewer’s comments are enclosed for your kind perusal and necessary action at your end. We are grateful of your valuable time.
Thank you
With highest regards
Sohail Ahmad Khan
Email: sakhan@math.qau.edu.pk
Reviewer #02
In this article, the authors model nonlinear effects in porous medium flow through the lens of thermodynamics. The system of partial differential equations modelling the flow is reduced to a system of ordinary differential equations using similarity transformations.
Comment No. 1: I strongly recommend the authors include a narrative in section 7. The point discussed in section 7 does not provide the reader with an overview of the results. A comparison must be made with known results so that the contributions made by the authors are highlighted.
Reply: Now it is carefully revised.
Comment No. 2: In addition to the points above, I believe the language needs to be improved.
I include some language corrections below.
On line 11 in the abstract - A decay ... not decays.
On line 21 accounted -> arise
On line 101 Engineering contents of interest
Reply: Many thanks. Now it is done.
Reviewer 3 Report
I recommend accepting the manuscript after the authors do the major revisions included in the review report in the attachment file.
Comments for author File: Comments.pdf
Author Response
To
Mr. Ursulescu Vlad Bogdan
Assistant Editor, MDPI Cluj
Mathematical and Computational Applications
Respected Sir,
The compliances of reviewer’s comments are enclosed for your kind perusal and necessary action at your end. We are grateful of your valuable time.
Thank you
With highest regards
Sohail Ahmad Khan
Email: sakhan@math.qau.edu.pk
Reviewer #03
Authors discussed the effect of Dufour and Soret in radiative Darcy-Forchheimer flow. Ohmic heating and dissipative features are taken into consideration. Characteristics features of thermo-diffusion and diffusion-thermo are probed. Binary chemical reaction is examined. Non-linear system is computed by finite difference technique. Paper is of current interest and falls in the scope of the journal, however, there are the following suggestions authors should address and then I welcome for publication:
Comment No. 01: The abstract can be written in a more interesting fashion in an arrange form without long introduction in it and with the important numerical outcomes. The structure of the abstract needs a revision. Revise the abstract to provide (i) the significance of the study, (ii) the aim of the study, (iii) the research methodology, (iv) the major conclusion of the study.
Reply: Thank you for your valuable comment. Now it is carefully revised.
Comment No. 02: The originality of the paper needs to be further clarified in the Abstract. Please, involve the novelty of this paper not what you have done in this study.
Reply: Now it is mentioned in last paragraph of introduction.
Comment No. 03: Add some important numerical outcomes to the final abstract section.
Reply: Now it is carefully added.
Comment No. 04: It is preferable to add SI units to a Nomenclature section.
Reply: Now it is added.
Comment No. 05: How have the authors verified the validity of their results? It is preferable to include a table showing the comparison results with some published papers in limited cases from this study to verify the validity of the used code in the current study.
Reply: It is done as suggested (see Table 1).
Comment No. 07: Introduction section can be supported with some more recent related literature on Darcy-Forchheimer flow: •https://doi.org/10.1016/j.aej.2022.03.030 •https://doi.org/10.3390/mi12111395 •https://doi.org/10.1016/j.surfin.2021.101119 •https://doi.org/10.1007/s10973-020-09928-w
- https://doi.org/10.1002/mma.6956
- https://doi.org/10.1088/1402-4896/abb5c7
Reply: Many thanks. Now all the related studies are added in revised manuscript (see References).
Comment No. 08: Double check all mathematical equations.
Reply: Now it is carefully checked.
Comment No. 09: The applicability of the research findings should be mentioned. Also, figures need more consistency and harmony in the size and type of font used.
Reply Thank you for your valuable comment. The related modification is made.
Comment No. 10: Results and discussion are mainly quantitative. Please rewrite this section by including meaningful physical interpretation for broader field audiences. Figures need to be elaborated in terms of the physics of the system from chemical engineering and thermodynamic aspect rather than just a brief explanation of results and trends.
Reply: Now it is carefully revised.
Round 2
Reviewer 1 Report
The authors have improved their manuscript but I cannot see
any change made against comments 6, 7 and 8 in the manuscript.
The author must write the motivations of entropy equations.
The author must write the complete methodology part as mentioned in the previous review report.
English needs to be revised very carefully. What is Flow 1 on page 4 last sentence?
Author Response
To
Mr. Ursulescu Vlad Bogdan
Assistant Editor, MDPI Cluj
Mathematical and Computational Applications
Respected Sir,
The compliances of reviewer’s comments are enclosed for your kind perusal and necessary action at your end. We are grateful of your valuable time.
Thank you
With highest regards
Sohail Ahmad Khan
Email: sakhan@math.qau.edu.pk
Reviewer #01
The authors have improved their manuscript but I cannot see.
Any change made against comments 6, 7 and 8 in the manuscript.
Reply: Dear Reviewer the reply for above mentioned comments are in the comments 6, 7 and 8.
Comment No. 06: The entropy analysis lacks the basic assumptions of entropy production in the flow and the reference.
Reply: Many thanks. Here the entropy generation produced due to heat transfer irreversibility, joule heating irreversibility, viscous dissipation irreversibility, porosity irreversibility and mass diffusion irreversibility.
Comment No. 07: The numerical solution part is not complete. Nothing has been written, for example, what Order of approximations is used for the spatial and temporal derivatives and which difference scheme is used and why.
Reply: The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems. This method can be applied to problems with different boundary shapes, different kinds of boundary conditions, and for a region containing a number of different materials. Even though the method was known by such workers as Gauss and Boltzmann, it was not widely used to solve engineering problems until the 1940s. The mathematical basis of the method was already known to Richardson in 1910.
Here we used the finite difference method in Newton built in-shooting technique. The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial conditions that give a root. The advantage of the shooting method is that it takes advantage of the speed and adaptivity of methods for initial value problems. Also, this method which automatically discretize data analysis. Therefore, we choose this numerical scheme.
Comment No. 08: Nothing mentioned how to solve Eqs. 22 and 23 at what order, what is truncation of the temporal and spatial domains and which method is used to solve algebraic equations.
Reply Here we used the finite difference method in Newton built in-shooting technique. The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial conditions that give a root. The advantage of the shooting method is that it takes advantage of the speed and adaptivity of methods for initial value problems. Also, this method which automatically discretize data analysis. Therefore, we choose this numerical scheme.
Comment No. 09: The author must write the motivations of entropy equations.
Reply: Many thanks. Now it is mentioned in revised version (see entropy section).
Comment No. 10: The author must write the complete methodology part as mentioned in the previous review report.
Reply: Here we used the finite difference method in Newton built in-shooting technique. The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial conditions that give a root. The advantage of the shooting method is that it takes advantage of the speed and adaptivity of methods for initial value problems. Also, this method which automatically discretize data analysis. Therefore, we choose this numerical scheme.
Comment No. 11: English needs to be revised very carefully. What is Flow 1 on page 4 last sentence?
Reply: Many thanks. Now it is carefully in revised.
Flow 1 is written by mistakenly it is Fig. 1 for flow sketch. Now it is revised carefully.
Reviewer 3 Report
After reviewing the revised version, it was found that the authors made the required improvements. They also responded to many concerns. We now believe that the manuscript can be accepted for publication in the esteemed Journal. The final decision is yours and the academic editor.
Author Response
To
Mr. Ursulescu Vlad Bogdan
Assistant Editor, MDPI Cluj
Mathematical and Computational Applications
Respected Sir,
The compliances of reviewer’s comments are enclosed for your kind perusal and necessary action at your end. We are grateful of your valuable time.
Thank you
With highest regards
Sohail Ahmad Khan
Email: sakhan@math.qau.edu.pk
Reviewer #03
After reviewing the revised version, it was found that the authors made the required improvements. They also responded to many concerns. We now believe that the manuscript can be accepted for publication in the esteemed Journal. The final decision is yours and the academic editor.
Round 3
Reviewer 1 Report
Could I ask why authors did not change anything despite my repeated recommendations? If the authors could not respond on the manuscript regarding comments 7 and 8, the paper may be rejected.
Author Response
To
Mr. Ursulescu Vlad Bogdan
Assistant Editor, MDPI Cluj
Mathematical and Computational Applications
Respected Sir,
The compliances of reviewer’s comments are enclosed for your kind perusal and necessary action at your end. We are grateful of your valuable time.
Thank you
With highest regards
Sohail Ahmad Khan
Email: sakhan@math.qau.edu.pk
Reviewer #01
Comment No. 07: The numerical solution part is not complete. Nothing has been written, for example, what Order of approximations is used for the spatial and temporal derivatives and which difference scheme is used and why.
Reply: Here we used the finite difference method in Newton built in-shooting technique. The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial conditions that give a root. The advantage of the shooting method is that it takes advantage of the speed and adaptivity of methods for initial value problems. Also, this method which automatically discretize data analysis. Therefore, we choose this numerical scheme. Both the spatial and temporal derivatives is of first order of approximation.
Here we used finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems. This method can be applied to problems with different boundary shapes, different kinds of boundary conditions, and for a region containing a number of different materials.
Comment No. 08: Nothing mentioned how to solve Equ. 24 at what order, what is truncation of the temporal and spatial domains and which method is used to solve algebraic equations.
Reply Here the entropy generation equation 24 is based on velocity, temperature and concentration. Here this equation is solved for first order truncation and there is only spatial derivative which is of first order truncation.
Round 4
Reviewer 1 Report
Accepted
