Heat Transfer in Annular Channels with the Inner Rotating Cylinder and the Radial Array of Cylinders

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article discuss an importatnt topic: Heat transfer in annular channels. I want thank an authors for an article. The state of the art has been checked very well. But I have a few comments.

 

1. You calculated a Nusselt number. In order to calculate a Nusselt Number is necessary Prandtl number and Grashow number. Additionally in forced convection Rayleigh number. How You calculate / designated this numbers? How You calculated / designated Richardson number .  Please add in article.

2. Please add in abstract if  your analisys is for natural or forced convection?

3. Plaese add inform how is dependence between size of mesh, time of prepared thermal simulation and accurancy this simulations.

Author Response

Comments 1: You calculated a Nusselt number. In order to calculate a Nusselt Number is necessary Prandtl number and Grashow number. Additionally in forced convection Rayleigh number. How You calculate / designated this numbers? How You calculated / designated Richardson number.  Please add in article.

Response 1: Definitions of the Reynolds number, the Prandtl number, the Grashof number, the Rayleigh number and the Richardson number are given in equation 1. As stated in Section 4.1, the full factor experiment was conducted with the following specified numbers values: Pr=0.7; Ri = [10^-2; 10⁴]; Ra = 10⁴, 10⁵, 10⁶. We didn’t calculate their values, and they were specified. Including other factors, the total number of cases was 432.

Comments 2: Please add in abstract if your analysis is for natural or forced convection?

Response 2: The abstract was rewritten as follows: “Numerical investigations of heat transfer for forced, mixed and natural convection conditions within an annular channel are carried out. The main objective was to investigate for the first time an effect of the radial cylinder array on heat transfer in the annular channel with the rotating cylinder.”

Comments 3: Please add inform how is dependence between size of mesh, time of prepared thermal simulation and accuracy these simulations.

Response 3: Results of the grid independency test are given in Table2. The following was added to the article: “Although Mesh#4 already had an acceptable error (no more 0.87%), for further calculations, Mesh#5 was chosen to increase the accuracy of calculations with Ri<10^-1. Here, the calculation time of one case was approximately 10 CPU hours and up to 100 CPU hours for stable and unstable modes, respectively. The calculation time depended on the number of elements by a factor of approximately 1.5 - 2.”

Reviewer 2 Report

Comments and Suggestions for Authors

In the paper, a numerical study was carried out under convective heat transfer conditions (forced and free) in an annular channel with and without radial cylinders with a rotating inner cylinder. The main objective was to study for the first time the effect of the radial cylinder arrangement on heat transfer in an annular channel with a rotating cylinder.

The layout of the work is well thought out and constitutes a logical whole. The subject matter of the work undertaken in the paper is topical and of great practical and scientific importance.

I congratulate the authors on a very good and interesting paper!

I recommend to accept its present form.

Author Response

Thank you for your positive response.

Reviewer 3 Report

Comments and Suggestions for Authors

Comments

The study investigates the impact of radial cylinder arrays on heat transfer within an annular channel with a rotating inner cylinder, addressing a gap in existing literature. The work is relevant for engineering applications in energy systems, such as thermal management in industrial processes.

 

I would suggest the publication of this article if the following minor issues were addressed.

 

-       While the literature review covers various aspects of heat transfer in rotating systems, it lacks depth in discussing recent advancements and similar studies in annular geometry.

Include more recent research and critically analyze prior studies to emphasize how this work addresses specific gaps. More recent relevant papers should be included:

 

o   https://doi.org/10.1021/acsomega.1c05334

o   https://doi.org/10.1016/j.asej.2023.102374

o   https://doi.org/10.1016/j.csite.2023.103216

 

-        Frome Fi4, remove “Figure 4. Cont.” which is below the caption (a)

-        From figure 7, The Nusselt number for the inner cylinder changes with the Richardson number. Can you explain why the critical Richardson numbers (𝑅𝑖𝑚𝑖𝑛. Rimax) shift as the Rayleigh number (Ra) increases?

-        ​From Fig8, for the case with radial cylinders, why does the Nusselt number on the radial cylinders exceed that of the inner rotating cylinder in free convection modes? What mechanisms are responsible for this behavior?

-        Figure 14, the inner cylinder’s Nusselt number increases with Rr​ across all Richardson numbers. Can you explain the physical reasoning behind this trend, particularly in the transition between mixed and free convection?

-        Figure 20, the local Nusselt number distribution on the inner cylinder shows a shift in peak location with increasing rotation velocity. How does the gap size (Rr) affect this peak shift, and why?

 

-        Figure 23, The results indicate that radial cylinders lead to a more uniform temperature distribution in the annular channel. What specific changes in flow dynamics contribute to this uniformity, particularly at high Rayleigh numbers?

Author Response

Comment 1: While the literature review covers various aspects of heat transfer in rotating systems, it lacks depth in discussing recent advancements and similar studies in annular geometry.

Include more recent research and critically analyze prior studies to emphasize how this work addresses specific gaps. More recent relevant papers should be included:

https://doi.org/10.1021/acsomega.1c05334

https://doi.org/10.1016/j.asej.2023.102374

https://doi.org/10.1016/j.csite.2023.103216

Response 1: We have reviewed most of the works suitable for the conditions of the study (Pr, Ra, Ri). The most suitable of the recent ones is the work of Abd Al-Hasan et al. However, it explores the rotation of the baffle, which contributes to a stronger alteration than the smooth cylinder. We have emphasized this nuance in the paper additionally as follows: “Baffles and grooved cylinders have a more mixing effect because of their shape. Therefore, with an increase in rotation velocity, heat transfer increases in contrast to smooth cylinders.”

Of the proposed works, we have included in the paper the study of Hassen et al. (https://doi.org/10.1021/acsomega.1c05334), to once again note the effects of cylinder rotation on heat transfer even in porous media as follows: “Hassen et al. [11] conducted numerical simulations of mixed convection in a partitioned porous cavity with double inner rotating cylinders under a magnetic field. Due to the complex interaction between the natural convection, moving wall, and rotational effects of inner cylinders complicated flow field with multicellular structures was observed. In comparison with the case of motionless cylinders, rotational effects of the cylinders provided an enhance of heat-transfer approximately 5 and 5.9 times with non dimensional rotational speeds of 5 and −5, respectively.”

Comment 2: Frome Fi4, remove “Figure 4. Cont.” which is below the caption (a)

Response 2: The Figures are corrected.

Comment 3: From figure 7, The Nusselt number for the inner cylinder changes with the Richardson number. Can you explain why the critical Richardson numbers (?????. Rimax) shift as the Rayleigh number (Ra) increases?

Response 3: Follows added to the paper: “The shift of Ri_min and at the inflection point to smaller values with increasing Ra is associated with the growth of the lifting force, for the balance of which a higher rotation speed of the cylinder (lower Ri) is required. This is more noticeable for the inner cylinder, since due to the low Pr and sheer stresses, disturbances from the moving wall of the inner cylinder do not reach the outer surface, and more active interaction of forced and free convections occurs approximately in the region of its near-wall layer.”

Comment 4: From Fig8, for the case with radial cylinders, why does the Nusselt number on the radial cylinders exceed that of the inner rotating cylinder in free convection modes? What mechanisms are responsible for this behavior?

Response 4: In the paper mechanisms are explained as (corrected version): “Nu_c is higher because the cylinders act as an obstacle to the flow. They create additional mixing by increasing the vortex flow around them, compared to the more stagnant flow at the flat outer surface without radial cylinders (for example, the flows in Figures 4 e and 4 l can be compared). At the same time, heat transfer on the inner rotating cylinder remains relatively unchanged. This is especially true when the radius ratios are large, as the radial cylinders have a minimal impact on the flow structure near the inner cylinder.”

Comment 5: Figure 14, the inner cylinder’s Nusselt number increases with R_r across all Richardson numbers. Can you explain the physical reasoning behind this trend, particularly in the transition between mixed and free convection?

Response 5: Follows added to the paper: “As the gap increases, the intensity of natural convection increases (the Rayleigh number grows faster than the Reynolds number), and the two-vortex global structure is forming. In the right area (Figure 13 b, c), the reverse flow of a vortex, coinciding with the direction of the cylinder's movement, increases the air velocity around the inner cylinder. The reverse flow of the vortex in the left area, moving in the opposite direction, increase the shear mixing of the boundary layer around the inner cylinder. This leads to an increase in the intensity of heat transfer with an increase in the ratio R_r.”

Comment 6: Figure 20, the local Nusselt number distribution on the inner cylinder shows a shift in peak location with increasing rotation velocity. How does the gap size (R_r) affect this peak shift, and why?

Response 6: Most likely you meant Figure 15. Follows added to the paper: “Thus, with an increase in the radius ratio, the shift of the local distribution tends to the minimal angle. This is because with the R_r grow the natural convection prevails and an influence of rotational effects on the local distribution decreases.”

Comment 7: Figure 23, The results indicate that radial cylinders lead to a more uniform temperature distribution in the annular channel. What specific changes in flow dynamics contribute to this uniformity, particularly at high Rayleigh numbers?

Response 7: Most likely you meant Figure 4 (we have only 20 figures). In the paper, the results show radial cylinders lead to a more uniform temperature distribution “in the upper area of the annulus and around the radial cylinders”. The paper details the reasons behind this (corrected version): “A narrower plume penetrates between the upper cylinders, and it is more noticeably divided (more suppressed). The return flow from the plume along the outer wall and around the radial cylinders generates vortex fluxes around them. The radial cylinders reduce global vortices and generate small ones around them (Figure 4 i - n, streamlines). The bulk temperature in the upper area of the annulus and around the radial cylinders decreases and becomes more uniform, which indicates an increase in heat transfer intensity.”