@AHSAN 

When I incorporate your suggestions regarding display, the main graph disappers and only enlarge legends appear on my side.
Can you upload the worksheet, I don't understand what you are saying. 

@AHSAN 

"Sir, I tried many times to download your file, but I couldn’t because of an error"
When I simply click on file  video_2.pdf the video automatically launches.
I don't know why it doesn't work with you,maybe because I realized this video on my Mac using Quick Media Player (mov file) and the Mac OS uses this latter by default when I click on the link.
Probably some video converter exists to enable watching it on Windows or Linux but I really don't have time, nor the computer, to fix this issue.

So I can't help you on this point.

"I tried something in which the legends are now appearing above the graph axes, but I am trying to shift them to the bottom so they don’t mix with the axes, but I am not able to do it"
If you use the DocumentTools, DocumentTools:-Layout packages, like in my procedure, to place legends below the graph I can tell you three things:

1. The result will not be that good that iit is (for me) with right legends.
2. If the legend does not appear correctly on the right, putting them below likely won't change anything.
3. Last by not least: be extremely carreful using these two packages for they really don't support syntax errors or wrong Layout constructions (at least with my 2015 version, but these issues may have been fixed on more recent versions): locking of the worksheet forcing to quit Maple and unreaparable corruption of the file.

So, here again, I can't help you.

By the way, I asked you in this COMMENT to do a little modification in my code and post the plot which contains the legends: I'm still waiting...

"In addition, is it possible to automatically add the numeric values on top of each bar so that the correct values appear above every bar?"
If you plot groups of bars with respect to Br and We, each of these groups contain 4 bars.
In order to give a visual impression of groups, the bars within each group are organized in some way. Writting on top of them the value of Nu_cube(Br, M, We) is of course possible but will result in an image extremely confused, whatever the rotation you do.

So I really think this would be a very bad idea to do that.

Some reflections...
Your last question raises a main point: Do you really know what bar-graphs (bar charts) are used for?
Bar Chart  are mainly used to quickly understand visually how a quantity (Nu in your case) depends on several categorical data (Br, M, We). Categorical means these data have a finite number of values (they could be "red", "green" and "blue" or 1, 2, 3 after coding)..
So, using bar-graphs to represent the variation of a quantity which continuously depends on some others is already a debatable choice.

When i say  to quickly understand visually this also mean that the detailed dependcies of, in your case Nu wrt Br, M, We, is of no matter: what you (should) want is to get a rough idea of what happens or of the underlying phenomena at play. So the values of Nu in themselves are of no importance: only their relative variations should matter when you decide using bar-graphs or alike.

Asking for the values of Nu for each bar suggests at the contrary that those same values matter for you.
If it so, a bar-graph might not be the best representation to use (observe that it is already quite delicate to understand what the dependencies of Nu to Br, M, We are by looking to the "3D clustered bar-charts" I construct.

So I advice you to think twice to the informations you really want to display and to the reasons you think these "3D clustered bar-charts" are the best representation for them.
Here are 3 links you could get some idea from:  R(1), R(2), (3).

"The internationally recognized symbol % (per cent) may be used with the SI.

When it is used, a space separates the number and the symbol %. The symbol % should be used rather than the name “per cent”. In written text, however, the symbol % generally takes the meaning of “parts per hundred”. Phrases such as “percentage by mass”, “percentage by volume”, or “percentage by amount of substance” shall not be used; the extra information on the quantity should instead be conveyed in the description and symbol for the quantity."

BIPM The International System of Units, 9th edition 2019 p 151.

So "per cent", is not a unit 1, and % has never been its symbol, it is just an "internationally adopted writting convention" (so there is noreason to introduce something like pu).

You write "It would be nice if Maple Flow could recognize units that are numerically 1".
I don't use Maple Flow but I guess it can handle angles and solid angles, which are the only two quantities with unit 1: the radian (rad) and the steradian (sr), ibid. § 2.3.3, p 137.
If it is so, Maple Flow  "recognize units that are numerically 1".

@AHSAN 

Because Mapleprimes doesn't accept the uploading of mov files I changed the extension to pdf.
Simply click on the link below to watch the video, or download the file, change pdf to mov and open it with your prefered video player.
 video_2.pdf

@AHSAN 

Click on EACH CELL (one contains the plot, the other the legend).

Besides, the legends do not seem to be aligned vertically:  add the red line at this position in procedure bars and post me new plot you get

  print(display(Legends));

  C1 := Cell( InlinePlot(All), columnspan=7 ):
  C2 := Cell( InlinePlot(Legends) ):
  TC := Table(seq(Column(), k=1..8), widthmode=percentage, width=60, interior=none,
          Row(C1, C2)
        ):

@AHSAN 

The last line 

InsertContent(Worksheet(Group(Input( TC )))):

of procedure bars must be replaced, for Maple versions >= 2018, by the line 

InsertContent(Worksheet( TC )):

Try this and let me know, sorry

@AHSAN 

Finally I hade a 10 minutes delay, here is the code Bar_view_help_sand15(bis).mw

@AHSAN 

You write "I run your command but receive an error."
You seem surprised?
Didin't you understant I asked you to do this to see if you Maple version accepted or not legends for 3D plot?

I'm going to complete my code and send it to you in a few hours (I have other constraints right now).

@AHSAN 

I know how to  use legends, but just try to use them for a 3D plot, for instance

plot3d(x*y, x=0..1, y=0..1, legend="abc")

and tell me if you get an error.

If you still get one with your Maple version you will have something like in my updated COMMENT.

Yet another posibilities:

@AHSAN 

Does your Maple version accept legends for 3D plots?

Mine (2015) does not and we need to use some tricks to display a legend, sort of.
For instance would wou be satisfied by something like this?


If plot3d ot PLOT3D accepts legends I can't help you. If not let me know.

@AHSAN 

Reply to your COMMENT.

You wrote "How do we obtain these values? Are these values dummy or generated from my problem? ":
Answer: my data are just illustrative and produced by LinearAlgebra:-RandomMatrix (read carefuly my worksheet)

Remark: You provided several images where bars are placed at the nodes of plane regular grid (the first on is in your initial question). There is no group here: the data can be represented by a numeric matrix and what my procedure F (worksheet Bars.mw) does is nothing by representing graphically this matrix in order that the image is close to the one you provide in your QUESTION and in this COMMENT. Note that you also produce a similar image in THIS COMMENT

But your problem does not correspond to these images because the quantity to plot as bars does not depend on 2 variables but on 3 variables.
In fact you lured me from the beginning by providing images that have no sense here.

As I said above my procedure F is aimed at displaying data of Matrix type.
Yours correspond to a  3d-array (Array(1..4, 1..3, 1..3)) meaning F cannot handle them.

A possibility could be, for instance to apply F to a 2D subarray, for instance Array(1, .., ..).

@AHSAN

Here is a procedure named bars which enables a bargraoh representation of Nu_cube either as

1. groups of 3 bars in the [M, Br] plane
2. groups of 3 bars in the [M, We] plane
3. groups of 4 bars in the [Brn We] plane

Given what I saw in you last file you seem perfectly capable, using optional parameter, to modify the rendering in order to get the image ou desire.

I also solved (at least for the data you use) the 

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

issue.

Bar_view_help_sand15.mw


.

@Suryakanth 

begin uploading yourworksheet using the bid greenarrow in the menubar

@AHSAN 

If it is a matter of values: compare the data matrix in my worksheet with yours, maybe the initial random seed different.

If it is a matter of display: click on the image, enlarge it, use the '+' button on the plot menu bar (sorry I use Maple 2015 and things might be different with your version) to zoom in.

@dharr 

(at least for your example, but I'm sure you were already aware of that, see pursuit3_from_Dharr.mw)

One question is "Does it exist starting points such that the Wolf can eat the Goat?"

Another one is, "How would an AI answer this problem "Let a Goat moving at constant speed along the unit circle and a Wolf located ourside the unit disk. What strategy should the Wolf, moving at the same speed than the Goat, adopt to catch the Goat?"

I guess an AI knowing about this problem could propose the "chase in the direction od the goat" strategy...
But this not a correct one because the Wolf will never (I'm pretty sure about that) catch the Goat.
Does a RIAI (Really intelligent AI) will propose a strategy like the one I evoke at the end of the attached file? (Not that I am Really Intelligent but I use to observe my cants and their potential preys).

A funny thing is that if the Wolf is slower than the Goat it will end eating the Goat (in fact I believe that the Goat will hurt its back).