Natural Convection Heat Transfer from an Isothermal Plate
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
The Abstract is rewritten, but I couldn't find a way to highlight the
text inside the Abstract.
| The authors performed a new approach by introducing the harmonic
| mean as the characteristic length metric for vertical and
| downward-facing plates.
The rewritten conclusion hopefully makes clearer the achievements:
Using a novel methodology based on streamline photographs,
dimensional analysis, and the thermodynamic constraints on
heat-engine efficiency, this investigation:
derived from first principles a previously unknown comprehensive
heat transfer formula for upward-facing convection;
extended the scope of vertical and downward-facing formulas from
rectangles to other shapes with convex perimeters using the
harmonic mean for the characteristic-length metric; and
unified the $Pr$ dependence of vertical and downward-facing
plates.
| The work presented in this paper must be reformulated because it
| presents an old theory based on old bibliographical references.
The abstract now begins:
Using boundary-layer theory, natural convection heat transfer
formulas which are accurate over a wide range of Rayleigh numbers
($Ra$) were developed in the 1970s and 1980s for vertical and
downward-facing plates. A comprehensive formula for upward-facing
plates remained unsolved because they do not form conventional
boundary-layers.
From the thermodynamic constraints on heat-engine efficiency, the
novel approach presented here derives formulas for natural
convection heat transfer from isothermal plates.
So my paper addresses a long-standing open problem. As for the age of
the references, in the discussion section I wrote:
Much of the subsequent natural convection literature investigates
local flow properties. Such studies do not inform this
investigation's systemic-invariant analysis. However, streamlines
photographs were crucial to characterizing the flow topologies and
deriving the present formulas.
External turbulent natural convection is not amenable to CFD, so I
have found few recent articles on this subject.
| The work can be considered as a review paper because it highlights
| a several flow topologies. There are a lot of theoretical
| equations and parameters which they have not been explained or
| given physical explanation.
The "Generalization" section enumerates the parameters tied to
physical attributes:
L is characteristic-length; Nu_0 is static conduction; E is the
count of 90-degree changes in direction of fluid flow; B is the sum
of the mean lengths of flows parallel to the plate divided by L; C
is the plate area fraction responsible for flow induced heat
transfer; D is the effective length of heat transfer contact with
the plate divided by L; p is 1/2 when E=1 without side-walls, and 1
otherwise.
| The Authors should give more information on the novelty of the
| paper.
Done in the introduction:
System-wide thermodynamic constraints cannot be enforced locally,
requiring a radical departure from boundary-layer analysis (which is
based on local flow solutions of the Navier-Stokes equations). This
investigation solves algebraic equations in terms of average fluid
velocity, heat conduction, and power flux.
| "Introduction" section is out-of-date. Please enrich the mentioned
| section through the reviewing those published in the last five
| years. Some references in this field can enrich the introduction
External turbulent natural convection is not amenable to CFD, so I
have found few recent articles on this subject.
| Nomenclature should be added in the text in order to explain all
| undefined parameters.
Done. I believe all parameters are introduced at first appearance; a
specific parameter would have been helpful.
| Some spelling and language-related mistakes were encountered. In
| my opinion, the manuscript would need to be considerably improved
| before sending it out elsewhere, as there are some concerns
| regarding the methodology, presentation of results, and discussion
Reviewer 2 Report
The authors presented a theoretical study on the Natural Convection Heat Transfer from an Isothermal Plate.
The paper is very basic and full of well-known formulas used in heat transfer textbooks.
I cannot find any novelty in this paper.
It is not sufficient to consider the study only from mathematical point of view, physical interpretations are to be added to the discussion.
Author Response
The Abstract is rewritten, but I couldn't find a way to highlight the
text inside the Abstract.
| The authors presented a theoretical study on the Natural Convection
| Heat Transfer from an Isothermal Plate.
| I cannot find any novelty in this paper.
I have addressed this concern in the rewritten abstract:
Using boundary-layer theory, natural convection heat transfer
formulas which are accurate over a wide range of Rayleigh numbers
(Ra) were developed in the 1970s and 1980s for vertical and
downward-facing plates. A comprehensive formula for upward-facing
plates remained unsolved because they do not form conventional
boundary-layers.
From the thermodynamic constraints on heat-engine efficiency,
the novel approach presented here derives formulas for natural
convection heat transfer from isothermal plates.
...
| The paper is very basic and full of well-known formulas used in heat
| transfer textbooks.
The prerequisite formulas are found in textbooks. The derived upward
and downward facing formulas and use of the harmonic mean are new.
Prior to this work, there was no upward-facing formula covering 12
orders of magnitude of Rayleigh numbers.
The new "Detail" subsection says:
Were this theory derived using the usual fluid-mechanics techniques,
derivation detail would be unnecessary. However, this powerful new
methodology is unlike those techniques. The first derivations
provide more detail to enable readers to adapt the present
methodology to other fluid mechanics problems.
| It is not sufficient to consider the study only from mathematical
| point of view, physical interpretations are to be added to the
| discussion.
I added a subsection to the introduction addressing this:
Not Empirical
Empirical theories derive their coefficients from measurements,
inheriting the uncertainties from those measurements. Theories
developed from first principles derive their coefficients
mathematically. For example, the Blasius model of laminar flow
coefficient 0.3320+ is the solution of a differential equation.
Another example is the heat conduction shape factor for one face of
a disk, which is exactly twice its diameter.
The present theory derives from first principles; it is not
empirical. Each equation term is tied to an aspect of the plate
geometry, orientation, and flow diagram.
The "Generalization" section enumerates the parameters tied to
physical attributes:
L is characteristic-length; Nu_0 is static conduction; E is the
count of 90-degree changes in direction of fluid flow; B is the sum
of the mean lengths of flows parallel to the plate divided by L; C
is the plate area fraction responsible for flow induced heat
transfer; D is the effective length of heat transfer contact with
the plate divided by L; p is 1/2 when E=1 without side-walls, and 1
otherwise.
Reviewer 3 Report
The goal behind this research is not well clear in the paper,
The introduction, the discussion, and even the conclusion are poor,
The paper is not organized as a research paper, the paper is written as exercises and corrections.
I recommend to re-write the paper, to illustrate the results and discussion section and improve the introduction and conclusion.
Minimize the number of equations in the main text, the rest of the equations could be written in the Appendix.
The paper could be considered for publication after a Major revision.
Author Response
The Abstract is rewritten, but I couldn't find a way to highlight the
text inside the Abstract.
| The goal behind this research is not well clear in the paper,
The second paragraph of the Introduction states:
... This investigation seeks to predict the overall steady-state
heat transfer rate from an external, flat, isothermal surface
inclined at any angle in a Newtonian fluid.
| The introduction, the discussion, and even the conclusion are poor,
I have rewritten much of the introduction and conclusion and a bit of
the discussion in the revised paper.
| The paper is not organized as a research paper, the paper is written
| as exercises and corrections.
The paper is unusual in that it solves plate natural convection with a
technique based on thermodynamics, which is novel to fluid mechanics.
That novelty motivated the explicit derivations, as explained in the
"Detail" paragraph below.
| I recommend to re-write the paper, to illustrate the results and
| discussion section and improve the introduction and conclusion.
I have rewritten much of the introduction and conclusion and a bit of
the discussion in the revised paper.
| Minimize the number of equations in the main text, the rest of the
| equations could be written in the Appendix.
I added a subsection "Detail":
Were this theory derived using the usual fluid-mechanics techniques,
derivation detail would be unnecessary. However, this powerful new
methodology is unlike those techniques. The first derivations
provide more detail to enable readers to adapt the present
methodology to other fluid mechanics problems.
| The paper could be considered for publication after a Major revision.
Reviewer 4 Report
The article has a proper structure and can be published after a series of corrections.
Better articles in this field should be mentioned in the introduction, and you should explain the innovation of your work in more detail. If you want, you can get help from articles in this field.
[1] "A Review on the Mechanisms of Heat Transport in Nanofluids," Heat Transfer Engineering, vol. 30, no. 14, pp. 1136-1150, 12/01/2009.
[2] "Studies on natural convection within enclosures of various (non-square) shapes – A review," International Journal of Heat and Mass Transfer, vol. 106, pp. 356-406, 2017/03/01/2017.
[3] "Review and Comparison of Nanofluid Thermal Conductivity and Heat Transfer Enhancements," Heat Transfer Engineering, vol. 29, no. 5, pp. 432-460, 2008/05/01 2008.
[4] "Nanofluids: Physical phenomena, applications in thermal systems and the environmental effects - a critical review," Journal of Cleaner Production, p. 128573, 2021/08/11/2021.
[5] "A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid," vol. 8, no. 9, p. 1011, 2020.
Table 1 should be modified.
The article needs a nomenclature.
Explain about choosing this interval for Rayleigh number.
The article should be reviewed and corrected in terms of writing and language.
Author Response
The Abstract is rewritten, but I couldn't find a way to highlight the
text inside the Abstract.
| The article has a proper structure and can be published after a series
| of corrections.
| Better articles in this field should be mentioned in the introduction,
In the Discussion section:
Much of the subsequent natural convection literature investigates
local flow properties. Such studies do not inform this
investigation's systemic-invariant analysis. However, streamlines
photographs were crucial to characterizing the flow topologies and
deriving the present formulas.
External turbulent natural convection is not amenable to CFD, so I
have found few recent articles on this subject.
I modified the introduction to restrict the paper's scope to Newtonian
fluids.
| and you should explain the innovation of your work in more detail.
Done in Introduction and Conclusions.
| Table 1 should be modified.
Done.
| The article needs a nomenclature.
Done.
| Explain about choosing this interval for Rayleigh number.
I added this to the introduction:
This investigation tests its theory on prior works' measurement data
with as wide a range of Ra and Pr as possible.
| The article should be reviewed and corrected in terms of writing and
| language.
Round 2
Reviewer 1 Report
The paper is well improved and ready to be published in the journal
Reviewer 2 Report
after revision, the paper can be accepted for publication
Reviewer 3 Report
I accept the paper to be published
Reviewer 4 Report
The article can be published.
