Reviewer’s report #
1. In the Introduction; the usage of three terms for the cylinder porosity confuses the readers! cylinder porosity, free volume fraction, permeability, blockage ratio, and cylinder spacing might confuse the readers to show that there is no work on the cylinder porosity effect.

It can be also seen from this section that there are so many papers published on this topic, but the different terms used for describing the cylinder array configuration also confuses the readers, such as staggered array and triangular array as they are the same.
In addition, the authors reviewed so many references showing what they have done but without showing what they have found! For instance; Ref [25, 26, 28, 29, 32, 34, 35, 36, 37] and others.
Many irrelevant references must be omitted such as [18] (lubrication and non-newtonian fluids), [28] (unsteady flow), [45] (natural convection), and [47, 48, 49, 50, 51, 52] (forced convection.
What is the difference between the current work and that of [34, 42, 43, 44, 46] as they have the same boundary conditions and configurations of the current work? Particularly Ref [34] as the cylinders are also arranged in an equilateral triangular array!
As shown in the introduction, the parameters of porosity, Prandtl number, Richardson number, and Reynolds number are extensively examined before, so what is the difference in this study?
I think the introduction section needs to re-written as categories such as (in-line array, staggered array) or like this.
2. How much the value of Raleigh number is adopted? Where is the definition of Gr number and what is its equation?
3. In section (2.1) are authors sure that the diameter (D) of the cylinder is 1 m as mentioned in the first line of the second paragraph!!! If so, do you mean that L = 10.43 m when the cylinder spacing equals to 0.99??? is there such this heat exchanger?
The left side of equation 1 must be the distance between the centers of the cylinders L (as this distance has many names in this article !!!) not the porosity!!! As L is estimated according to the value of the porosity. Furthermore, the symbol of Pi is incorrect, it must be in greek! If the cylinder diameter is kept constant throughout the current study so why the size of cylinders in Figures 8, 9, 11, 12 seems to be varied (i.e., biggest at the porosity of 0.7 and smallest at the porosity of 0.99)?
The direction of the axes in Figure 1(a) is reversed (x must be y) and vice versa. The coordinates in this figure do not match that in the governing equations!
Whereas the L in Figure 1(b) must be the distance between the centers of the three cylinders, not just cylinders 1 and 2!!! In addition, the boundary conditions are not illustrated too!! Where is the prescription of the inlet/outlet? What is the BC of the left and right side of the physical domain? If the inlet and outlet are adopted as a periodic boundary condition, what is the code that used for prescribing the condition (write the code)? Is there any symmetry boundary condition considered?
Do authors think that the governing equations are represented in dimensionless form!!
If the symbol T in equation 5 is dimensionless, so where is its mathematical formula?
The authors mentioned that their study is transient heat transfer as reported in section 3, “The second-order implicit scheme is used to solve the transient conditions occurring in the present
scenario”, so, at what time the results are presented??? Why there is nothing illustrated in the results to show that this study is transient, not steady????
4. Section (2.2) define FD, FDP and FDF in equation 12, 13 and 14.
The symbol Cp is used for both the specific heat and pressure coefficient!! See equation 7 and 17. What are the non-dimensional equations of parameters of equation 17 (right side parameters).
5. Section (3), do authors think that convergence criteria 10-12 and 10-15 for the flow and thermal parameters, respectively it too much for 2D physical domain and mixed convection?
Why authors used triangular meshing for the physical domain whilst the square meshing provides more accurate results? They have very simple 2D geometry! Uniform structural square elements mesh can be generated easily in such very simple geometry.
How much the mesh growth ratio was?
The discrepancy between Fig. 2(a) and 2(b) is that the highest refinement mesh is seen on the cylinder wall more than the other zones in Fig 1(a) while the opposite is seen in the other!!! Moreover, the nodes on the one-fourth cylinder surface are not 50!!!
The caption of Fig. 3 must include the title of (a) and (b)! What the authors mean by 0, 0.8, and 1.6 which is shown inside Fig. 3(a)?
6. Section (5.1); Which kind of coding tools did authors use? Is it FORTRAN or ANSYS-Fluent??
All the code validations carried out are not accepted due to the only average value of the quantities are validated. Therefore, the validation must be carried out for local quantities such as wall temperature, wall Nusselt number, or even streamlines or isotherm lines. Thus, Table 2, Fig. 4, Table 3and Table 4 must be omitted.
7. Section (5.2.1.); the authors mentioned that the porosity values are 0.7, 0.8, and 0.99, while they refer to 0.7, 0.9, and 0.99 in Figures 5, 6, and 7!!!!
Figures 8, and 9; the dimensionless value of the streamlines must be shown (like that in isotherm lines figures) to ensure that the vertical left and right side of the domain is fluid symmetry, not solid symmetry!!!! From Figure 8, do you believe that the circulations happened in the pattern of 0.99 porosity and Ri = -0.5 caused by these small temperature differences and so long distance between the centers of the cylinders (10.43m)???
8. Section (5); 47 pages for a 2D numerical study is too much. The displaying of the results in 21 figures is over.
9. Figure 14 is redundant and no need.
10. Fig. 13 must be merged with Fig. 17, (14 with 18), and (15 with 19) for comprehensive comparison as the difference is just Prandtl number.
11. The equation of the heat transfer enhancement must be mentioned earlier and placed at the end of section 2.1.
12. The conclusion is written wrongly as it must conclude the parameters that have been varied throughout the study to show their effects on the output variables. Unfortunately, the authors presented the outcomes, such as the aiding/opposing buoyancy, coefficient of pressure, average drag coefficient, and isotherms. Briefly, the effect of porosity, Prandtl number, and Richardson number must be shown on the hydraulic and thermal performance such as (pressure coefficient, average drag coefficient, isotherm, streamlines, etc. ).

Regards
Reviewer #