Heat Transfer in Nanomaterial Suspension (CuO and Al2O3) Using KKL Model
, Saeed Ehsan Awan 2, Muhammad Asif Zahoor Raja 3, Muhammad Nawaz 4, Wasim Ullah Khan 5,*, Muhammad Yousaf Malik 6 and Yigang He 5,*Round 1
Reviewer 1 Report
The paper discusses a nonlinear flux model to incorporate heat-transfer effects in nano-micropylar polymer. A predictor-corrector numerical approach is proposed to solve the proposed model, and it has also been compared to the Runge-Kutta method. A good agreement is achieved with various numerical examples. Here are some concerns,
1: New numerical simulations should be performed to exhibit the order of accuracy both in time and in space for the proposed numerical approach.
2: Since all the numerical methods employed in the paper are explicit, there should have very severe numerical stability constraints. What is the time step size h for all the simulations presented in the paper? Stability analysis should be carried out to show how the time step size relies on the spatial size by some numerical examples.
3: To further justify the novelty of the model, numerical simulations should be compared to some real experiment data. Otherwise it is hard to verify whether the proposed model is more physical/real than other existed models.
Author Response
I am submitting the revised version of research article titled “Heat Transfer in Metallic Nanomaterial Suspension (CuO and Al2O3) Using KKL Model ” Tracking number Ref.: Ms. No. 1137905 by Muhammad Awais, Saeed Ehsan Awan, Muhammad Asif Zahoor, Muhammad Nawaz and Muhammad Yousaf Malik for the possible publication in your esteem journal. Authors tried their level best to address all the queries raised. Following are our humble submissions for your kind consideration please.
Reviewer 1 General Comments
The paper discusses a nonlinear flux model to incorporate heat-transfer effects in nano-micropylar polymer. A predictor-corrector numerical approach is proposed to solve the proposed model, and it has also been compared to the Runge-Kutta method. A good agreement is achieved with various numerical examples. Here are some concerns,
Author Response:
We are thankful for the constructive comments of anonymous reviewer that help definitely for the improvement of the revised manuscript. Authors tried their level best to address all the suggested queries and manuscript is modified accordingly.
Reviewer 1 Query 1:
- 1: New numerical simulations should be performed to exhibit the order of accuracy both in time and in space for the proposed numerical approach.
Author Response
Agreed. As suggested by anonymous reviewer, authors have performed new numerical simulations for exhibition of order accuracy both in time and space for different numerical computing techniques including Adam method, Backward Difference method (BDF), Explicit Runge Kutta (ERK), Implicit Runge Kutta (IRK) and Extrapolation (ET) for CuO and Al2O3.based metallic nano polymeric suspension in the KKL fluidic model. Results for Adam, BDF, ERK, IRK & ET both types of suspension are presented in Table 5 in term of computational time consumed, number of steps, ODE evaluations and different accuracy goals. Time and space accuracy for proposed numerical approaches are validated through numerical data provided in Table 5 of the manuscript.
Reviewer 1 Query 2:
Since all the numerical methods employed in the paper are explicit, there should have very severe numerical stability constraints. What is the time step size h for all the simulations presented in the paper? Stability analysis should be carried out to show how the time step size relies on the spatial size by some numerical examples.
Author Response:
Agreed. We have updated the manuscript by providing the comparative study of numerical methods (including Explicit and Implicit approaches) to have better insight for the accuracy, convergence, stability and convergence. Results for Adam, BDF, ERK, IRK & ET for CuO and Al2O3.based metallic nano polymeric suspension in the KKL fluidic model are presented in Table 5 in term of computational time consumed, number of steps, ODE evaluations and different accuracy goals. One may see that accuracy convergence, stability of all numerical approaches is validated for all four different levels of accuracy goals i.e., 10-07, 10-15, 10-22 and 10-30. However, the complexity of all algorithms increases for more stiff levels of accuracy goals, but the performance of computational time complexity as well as numbers of evaluation are generally found best for Adam numerical method in case of CuO and Al2O3.based metallic nano polymeric suspension in the KKL fluidic model for scenario based on k0 = 0.6. Results are omitted for other scenarios due to similar trends /inferences of accuracy, convergence, stability and complexity for all other cases of KKL fluidic model.
Reviewer 1 Query 3:
To further justify the novelty of the model, numerical simulations should be compared to some real experiment data. Otherwise it is hard to verify whether the proposed model is more physical/real than other existed models.
Author Response:
Agreed. We have updated the manuscript by presenting exhaustive comparison of five different numerical methods namely Adam, BDF, ERK, IRK & ET for both types of suspension as tabulated in Table 5 in term of computational time consumed, number of steps, ODE evaluations and different accuracy goals. Results proves the validity of proposed algorithms in terms of accuracy, convergence, and stability. The acquisition facility of real experimental data for the computational fluid dynamics problem is not available in our university as well as in other academic institutes of Pakistan. However, the presented study can be utilized for real experimental data and this aspect is mentioned in Conclusion section as future recommended research directions.
Reviewer 2 Report
Review of Coatings,
Title: Heat Transfer in Metallic Nano-Polymeric Suspension (CuO 2 and Al2O3) Using KKL Model
By M. Awais et al,
This paper addresses a few interesting ideas in order to approach real-life practical questions of nanofluid suspensions, however I found no convincing/conclusive results in this respect.
Using the mathematical KKL model in resolving practical problems is not well-explained.
Moreover, shear thinning and shear thickening is mentioned in the abstract, which are not addressed in the main body of the paper. Also, I find the title of this paper misleading: “metallic nano-polymeric suspension” suggests that the polymeric nature of the material being studied in this paper is important, but no discussion of that is given in the paper.
Also, the figure captions are inadequate: for instance what is the symbol “eta” in Figure 1, 2, 3, … , which is also not mentioned in the main text. Overall, much more explanations are needed to be able to understand the precise content of this paper.
Furthermore, the results are not novel neither impressive. The authors do not indicate what is new with respect to already published work, especially regarding shear-tinning and shear-thickening, as well as non-uniform flow profiles, and the temperature profiles.
Finally, the citations are not properly done. For instance, the citations in Table 3 are, incorrect and incomplete. Please cite the original work with a proper reference (for example: incorrect reference citation in Table 3: CuO-water from Ref. Heat Transfer. 2021;50:1232–1251.wileyonlinelibrary.com/journal/htj1232). Also, the reference concerning Al2O3 is misleading: the original paper is not cited.
In view of the above comments, I recommend to reject of this paper.
Author Response
I am submitting the revised version of research article titled “Heat Transfer in Metallic Nanomaterial Suspension (CuO and Al2O3) Using KKL Model ” Tracking number Ref.: Ms. No. 1137905 by Muhammad Awais, Saeed Ehsan Awan, Muhammad Asif Zahoor, Muhammad Nawaz and Muhammad Yousaf Malik for the possible publication in your esteem journal. Authors tried their level best to address all the queries raised. Following are our humble submissions for your kind consideration please.
Reviewer 2 General Comments
This paper addresses a few interesting ideas in order to approach real-life practical questions of nanofluid suspensions, however I found no convincing/conclusive results in this respect.
Author Response:
Many thanks for your valuable comments on our submitted manuscript. Additionally, authors tried their best to address each query raised by the anonymous reviewer and manuscript is modified accordingly.
Reviewer 2 Query 1:
Using the mathematical KKL model in resolving practical problems is not well-explained.
Author Response:
As suggested, we have added a paragraph in the manuscript which present the usage of mathematical KKL model in resolving recent practical problems. Please see introduction section of the manuscript.
Reviewer 2 Query 2:
Moreover, shear thinning and shear thickening is mentioned in the abstract, which are not addressed in the main body of the paper. Also, I find the title of this paper misleading: “metallic nano-polymeric suspension” suggests that the polymeric nature of the material being studied in this paper is important, but no discussion of that is given in the paper.
Author Response:
As suggested, we have addressed about the shear-thinning and shear-thickening effects in the revised version of the manuscript. Plots have been prepared showing the effects of shear-thinning and shear-thickening effects on the velocity, micro-rotation and temperature profile. The explanations about plotted graphs have been included in the revised version of the manuscript. Please see research and discussion section. Moreover the title of the script is also modified which would be more appropriate for the readers to understand the real insight of the present analysis.
Reviewer 2 Query 3:
Also, the figure captions are inadequate: for instance what is the symbol “eta” in Figure 1, 2, 3, … , which is also not mentioned in the main text. Overall, much more explanations are needed to be able to understand the precise content of this paper.
Author Response: It is stated that “eta” is the parameter as defined in Eq. 14. All profiles are functions of “eta”. We have revised the captions in the revised version to be more appropriate for the readers.
Reviewer 2 Query 4:
Furthermore, the results are not novel neither impressive. The authors do not indicate what is new with respect to already published work, especially regarding shear-tinning and shear-thickening, as well as non-uniform flow profiles, and the temperature profiles.
Author Response:
Our aim/objectives are to analyze the numerical computations for the heat transfer in nanomaterial suspension involving CuO and Al2O3 nanoparticles. Heat transfer characteristics along with micro rotation properties of micropolar fluid utilizing the KKL nanofluid theory are presented. The numerical treatment via different schemes have been performed. We have updated the manuscript by presenting exhaustive comparison of five different numerical methods namely Adam, BDF, ERK, IRK & ET for both types of suspension as tabulated in Table 5 in term of computational time consumed, number of steps, ODE evaluations and different accuracy goals. Results proves the validity of proposed algorithms in terms of accuracy, convergence, and stability. The acquisition facility of real experimental data for the computational fluid dynamics problem is not available in our university as well as in other academic institutes of Pakistan. However, the presented study can be utilized for real experimental data and this aspect is mentioned in conclusion section as future recommended research directions.
Reviewer 2 Query 5:
Finally, the citations are not properly done. For instance, the citations in Table 3 are, incorrect and incomplete. Please cite the original work with a proper reference (for example: incorrect reference citation in Table 3: CuO-water from Ref. Heat Transfer. 2021;50:12321251.wileyonlinelibrary.com/journal/htj1232). Also, the reference concerning Al2O3 is misleading: the original paper is not cited.
Author Response: Yes we agree with the referee. This is corrected in the revised version
Reviewer 3 Report
In this work, the authors have investigated a novel flux model to demonstrate the effects of nanofluids and their enhancement of heat transfer when the micropolar fluids are added. The authors trials by using KLL model for effective viscosity and thermal conductivity are interesting although the numerical scheme is not really new and normal. I guess the key observation of this article is the decay of velocity and temperature profile for positive values of K_0 and the "jump effect" around the surface.
It is more desirable if the authors can provide any experimental data together with the numerical data.
English expression is very poor and grammar is not in good condition, which the authors should extensively improve.
Are all these 21 figures total necessary?
Round 2
Reviewer 1 Report
No more comments.
