The Effects of Buoyancy on Laminar Heat Transfer Rates to Supercritical CO2 in Vertical Upward Flows
Round 1
Reviewer 1 Report
The authors presented a numerical simulation on the Effects of Buoyancy on Laminar Heat Transfer Rates to Supercritical CO2 in Vertical Upward Flows.
The introduction is short and should be extended.
Table 2 is to be replaced under section 2.
The numerical method is to be detailed.
Why the governing equations are time independent?
A grid sensitivity test is to be performed.
The boundary conditions are to be expressed mathematically.
A validation or verification of the numerical model is to be performed.
What is the convergence criterion ?
Qualitative results (2D flow structure and temperature field) are to be added and discussed.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The end of the introduction must be improved (presentation of your work) and write some novelty statements for the manuscript.
The end of the introduction must be improved (presentation of your work).
Is there any specific scientific approach to selecting the Reynolds number like 100 and 400?
Why specific heat is suddenly rising at the temperature of Tpc=309K and all other properties change the behavior at this temperature
Nu value increases beyond 4.36 giving a specific region.
Correct the reference value “for each scenario based on Error! Reference source not found..” at line number 269.
Try to add the Uncertainty and Errors of measurement.
Try to add Code Validation.
Try to add Grid independent test GIT.
Try to add Grid independent test GIT.
There are some language and syntax errors. Please check the manuscript.
Try to compare the results of this study with the result of previous studies.
Conclusions: Relate your conclusions to your findings. State the limitations.
Check the format of references.
Comments for author File: 
Comments.pdf
Author Response
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Author Response File: Author Response.docx
Reviewer 3 Report
The author studied the buoyancy effects in vertical upward laminar flows, which result in an augmentation in heat transfer rates to supercritical CO2 (sCO2) near its pseudocritical temperature (TPC). This is in contrast to the corresponding (upward) flows in the turbulent regime or laminar sCO2 flows (with minimum buoyancy effects) where a deterioration in heat transfer near TPC has been observed. To exploit these sCO2 heat transfer enhancement characteristics and improve heat exchange efficiencies, the location of the TPC pinch point and the variables controlling these buoyancy effects need to be identified. After highlighting the lack of heat transfer correlations for laminar sCO2 upward flows numerical simulations of sCO2 (at inlet: 8.2 MPa, 265 K) in vertical circular tubes of diameters (D: 0.2 mm - 2 mm), heated with constant wall heat fluxes (Q: 1 – 4 kW/m2) and inlet Reynolds (Re: 100, 400) were carried out to fill this void. Tube lengths were varied to maintain an exit temperature of 320 K (TPC ~309 K).
The article is written well, but before it is accepted, I will suggest some changes that must be included in the revised version.
1. The authors use the Navier-Stokes equation of motion in Eq. 2, providing the mathematical expression for the shear stress in Eq. 2.
2. The authors state the conservation of mass in Eq. 1, and the author considers CO2 fluid, so is density variable or constant?
3. If the density is constant and the fluid is compressible, then provide the expression for shear stress.
4. Boundary conditions are not provided in the manuscript. Check the articles and cite them in the introduction as well as see the boundary conditions if the authors needed, they can write from these articles.
Energy recovery mechanism of air injection in higher methane cut reservoir
OpenFOAM for computational hydrodynamics using finite volume method
OpenFOAM for computational combustion dynamics
Computation of thermal energy in a rectangular cavity with a heated top wall
Mathematical analysis of flow passing through a rectangular nozzle
Simulation of turbulence flow in OpenFOAM using the large eddy simulation model
The modified KdV equation for a nonlinear evolution problem with perturbation technique
Mathematical analysis of heat and fluid flow in a square cavity
5. The headings of the sections and subsections must be shifted to the next page if the text starts on the next page; see conclusion.
6. Which method is used for problem solving (see above references)? For the readers' understanding, provide some references.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
the authors responded adequately to most of the comments, except the validation/verification of the numerical model.
the validation means the comparison with experimental results and verification means the comparison with numerical results. the aim is to check the validity of the numerical model.
Author Response
Thank you for your kind comment and we agree with you completely regarding the definitions of "verification" and "validation."
As highlighted in Table 1 of our manuscript, lack of experimental measurements at the investigated conditions (0.2 - 2 mm tube diameter, laminar flow) precluded a rigorous validation in this study. However, since grid independent, laminar flow numerical data were generated, this data set may be considered as equivalent to "validation quality, benchmark data" similar to how DNS data may be considered as "validation quality, benchmark data" in the turbulent regime. In conclusion,
Verification in this study was accomplished by using constant fluid properties and ensuring that Nu converged to 4.36.
While validation was not rigorously demonstrated (due to lack of experimental measurements), our data was grid independent (free from numerical discretization errors) and free from epistemic uncertainties (since no turbulence model was employed). Therefore, the generated data set may be considered equivalent to a "benchmark." Furthermore, since the primary focus of the manuscript the data was to provide (phenomenological) insights into the main variables (Re, Gr) influencing buoyancy induced heat transfer augmentation in the investigated regimes, we feel confident that the numerical precision of this study was at a fine enough resolution to garner these useful insights.
I hope this helps clarify! Thank you!
Reviewer 2 Report
This is an interesting study and the authors have collected a unique dataset using the cutting-edge methodology. I am satisfied with the author’s responses to my questions/issues raised in my initial review.
Author Response
Thank you for your kind feedback!
Reviewer 3 Report
The modified form is acceptable for publication
Author Response
Thank you for your kind feedback!
