error "Inner matrix dimensiion must Agree"

Please I'm trying to plot graphs and varying parameter Gr and t which is temperature. But i keep getting an error "Inner matrix dimensiion must Agree"

>> Gr = [5:5:25];

>> t = [0.2:0.2:1];

>> H = 1;

>> n = 1;

>> N = 5;

>> Pr = 0.72;

>> S = 0.2;

% This is my code

>> U = -Gr*(t.^2/2 + Pr*(N-n)*(t.^4/24 - t.^2/4) + (Pr*(N-n))^2*(t.^6/720 - t.^4/48 + 5*t.^2)...

+ (Pr*(N-n))^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) + (Pr*(N-n))^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 -61*t.^4/17280 + 1385*t.^2/806400)...

- 1/2 + Pr*(N-n)*5/24 - (Pr*(N-n))^2*61/720 + (Pr*(N-n))^3*277/8064 - (Pr*(N-n)^4*(0.014))...

-(S + H - n)*Gr*(t.^4/24 * Pr*(N-n)*(t.^6/720 - t.^4/48) + (Pr*(N - n))^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...

+ (Pr*(N-n))^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 + 61*t.^4/17280) + (Pr*(N-n))^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680)...

- t.^2/4 + Pr*(N-n)*5*t.^2/48 - (Pr*(N-n))^2*61*t.^2/1440 + (Pr*(N-n))^3*277*t.^2/16128 - (Pr*(N-n))^4*(7*t.^2/1000))...

-(1/24 + Pr*(N-n)*(1/720 -1/48) + (Pr*(N-n))^2*(1/40320 - 1/1440 + 5/576) + (Pr*(N-n))^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + (Pr*(N-n))^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)

-1/4 + Pr*(N-n)*5/48 - (Pr*(N-n))^2*61/1440 + (Pr*(N-n))^3*277/16128-(Pr*(N-n))^4*(7/100)))

Error using *

Inner matrix dimensions must agree.

>>

>>

Answer 1

[DGM]

You're trying to do matrix multiplication with arrays of incompatible size. You probably mean to do .* elementwise multiplication.

Also, those exponentiations are probably all wrong as well. For example:

1^2/3

ans = 0.3333

1^(2/3)

ans = 1

EDIT: also, this improperly-continued line means that the trailing ) isn't being used. Since the parentheses are balanced, that means that another parentheses is either added or missing somewhere. It's impossible to know where.

+ A^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + A^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)

[Maduka]

Please what will I do to make the code work, it’s too lengthy and keep giving error, the image below is the formular I want to write

[DGM]

Try this. I make no guarantees that I haven't missed something. EDIT: I've gone back and checked this against the paper as given. I found a few more mistakes, but the expression as printed is still ambiguous.

Gr = 5:5:25; % vectors are orthogonal, allowing implicit expansion to 2D
t = (0.2:0.2:1).';
H = 1;
n = 1;
N = 5;
Pr = 0.72;
S = 0.2;

% pull out common terms
B = Pr*(N-n);

% pull out term blocks
% note that the terms of TB1 begin with an imbalanced (Pr*(N-n)^k, so it's unclear what that means
% i'm going to assume that means (Pr*(N-n))^k, not Pr*(N-n)^k
TB1 = t.^2/2 ...
    + B*(t.^4/24 - t.^2/4) ... 
    + B^2*(t.^6/720 - t.^4/48 + 5*t.^2/48)... % 5*t^2/48
    + B^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) ...
    + B^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 - 61*t.^4/17280 + 1385*t.^2/806400) - 1/2 ...
    + B*5/24 ...
    - B^2*61/720 ...
    + B^3*277/8064 ...
    - B^4*(0.014);

TB2 = t.^4/24 ... % + not *
    + B.*(t.^6/720 - t.^4/48) ... 
    + B^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...
    + B^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 - 61*t.^4/17280) ...
    + B^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680) - t.^2/4 ...
    + B*5*t.^2/48 ...
    - B^2*61*t.^2/1440 ...
    + B^3*277*t.^2/16128 ...
    - B^4*(7*t.^2/1000);

TB3 = 1/24 ...
    + B*(1/720 - 1/48) ...
    + B^2*(1/40320 - 1/1440 + 5/576) ...
    + B^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) ...
    + B^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680) - 1/4 ...
    + B*5/48 ...
    - B^2*61/1440 ...
    + B^3*277/16128 ...
    - B^4*7/100;

U = -Gr.*TB1 - (S + H - n)*Gr.*(TB2 - TB3); % elementwise multiply

% plot everything
figure
contourf(Gr,t,U)
colorbar

figure;
hp = plot(t,U,'-d');
lstr = cell(numel(Gr),1);
for k = 1:numel(Gr)
    lstr{k} = sprintf('Gr = %d',Gr(k));
end
legend(hp,lstr,'location','southwest')

Obviously that doesn't look like the given plot, but I don't know what else to say. This is how I marked out the expression as I transcribed it:

Each blue term is a product of the form (Pr*(N-n))^p*(subexpression). I'm assuming that this pattern extends to the terms in TB1. Outside the three major terms marked in yellow, the expression is plainly U = -Gr.*TB1 - (S + H - n)*Gr.*(TB2 - TB3);

If I've missed more transcription errors, I don't know where they'd be. If the printed formula is incorrect, I wouldn't know.

[Maduka]

I sincerely appreciate your effort,

But My major concern is replicating the graph. Is it possible to use the table value and replicate the exact graph in Matlab?

[Torsten]

Obviously, there are mistakes in the formula for U (e.g. missing or misplaced brackets).

So if you give us the correct U, we can replicate your graph.

[DGM]

I guess you can just plot it if that's the correct data.

Gr = 5:5:25; % vectors are orthogonal, allowing implicit expansion to 2D
t = (0:0.2:1).';

U = [0 0 0 0 0;
    -0.1015 -0.203 -0.3045 -0.406 -0.5075;
    -0.4167 -0.8334 -1.2501 -1.6667 -2.0834;
    -0.9861 -1.9722 -2.9583 -3.9444 -4.9305;
    -1.8796 -3.7592 -5.6388 -7.5184 -9.398;
    -3.2068 -6.4137 -9.6205 -12.8274 -16.0342];

hp = plot(t,U,'-d');
lstr = cell(numel(Gr),1);
for k = 1:numel(Gr)
    lstr{k} = sprintf('Gr = %d',Gr(k));
end
legend(hp,lstr,'location','southwest')

[Maduka]

DGM how do I remove those dots representing the points on the graph?

I want to remove it

[DGM]

You can remove the markers in the call to plot()

hp = plot(t,U,'-d') % solid line with diamond markers
hp = plot(t,U,'-') % solid line with no markers

[Maduka]

Thanks, this really helped

[Maduka]

@DGM

N = [5:5:10 20:30:80];

t = (0:0.2:1).';

U = [0 0 0 0 0;

-0.203 -0.2045 -0.2094 -0.2248 -0.2411;

-0.8334 -0.8742 -0.9593 -1.2573 -1.6266;

-1.9722 -2.1899 -2.6840 -4.737 -7.9306;

-3.7592 -4.51 -6.3789 -16.1119 -35.5583;

-6.4136 -8.4597 -14.1636 -52.4222 -148.671];

hp = plot(t,U,'-');

lstr = cell(numel(N),1);

title('Effect of Radiation on Velocity')

for k = 1:numel(N)

lstr{k} = sprintf('N = %d',N(k));

end

legend(hp,lstr,'location','southwest')

On this plot, how do I convert those lines to curves, so the sharp points won't be noticed

[DGM]

If you just want to smooth the curve and still have it go through the original points, you can do some sort of spline interpolation.

N = [5:5:10 20:30:80]; 
torig = (0:0.2:1).'; % original t

U = [0 0 0 0 0;
    -0.203 -0.2045 -0.2094 -0.2248 -0.2411;
    -0.8334 -0.8742 -0.9593 -1.2573 -1.6266;
    -1.9722 -2.1899 -2.6840 -4.737 -7.9306;
    -3.7592 -4.51 -6.3789 -16.1119 -35.5583;
    -6.4136 -8.4597 -14.1636 -52.4222 -148.671];

% interpolate U using a finer t
t = (0:0.05:1).';
U = interp1(torig,U,t,'spline'); % use spline interpolation to smooth the curve

hp = plot(t,U,'-');

lstr = cell(numel(N),1);
title('Effect of Radiation on Velocity')
for k = 1:numel(N)
    lstr{k} = sprintf('N = %d',N(k));
end
legend(hp,lstr,'location','southwest')

Answer 2

[Torsten]

GR = [5:5:25];
T = [0.2:0.2:1];
H = 1;
n = 1;
N = 5;
Pr = 0.72;
S = 0.2;
for i = 1:numel(GR)
  Gr = GR(i);
  for j = 1: numel(T)
    t = T(j);
    U(i,j) = -Gr*(t.^2/2 + Pr*(N-n)*(t.^4/24 - t.^2/4) + (Pr*(N-n))^2*(t.^6/720 - t.^4/48 + 5*t.^2)...
              + (Pr*(N-n))^3*(t.^8/40320 - t.^6/1440 + 5*t.^4/576 - 61*t.^2/1440) + (Pr*(N-n))^4*(t.^10/36288000 - t.^8/80640 + 5*t.^6/17280 -61*t.^4/17280 + 1385*t.^2/806400)...
              - 1/2 + Pr*(N-n)*5/24 - (Pr*(N-n))^2*61/720 + (Pr*(N-n))^3*277/8064 - (Pr*(N-n)^4*(0.014))...
              -(S + H - n)*Gr*(t.^4/24 * Pr*(N-n)*(t.^6/720 - t.^4/48) + (Pr*(N - n))^2*(t.^8/40320 - t.^6/1440 + 5*t.^4/576)...
              + (Pr*(N-n))^3*(t.^10/32688000 - t.^8/80640 + 5*t.^6/17280 + 61*t.^4/17280) + (Pr*(N-n))^4*(t.^12/479001600 - t.^10/7257600 + 5*t.^8/967680 - 61*t.^6/518400 + 1385*t.^4/967680)...
              - t.^2/4 + Pr*(N-n)*5*t.^2/48 - (Pr*(N-n))^2*61*t.^2/1440 + (Pr*(N-n))^3*277*t.^2/16128 - (Pr*(N-n))^4*(7*t.^2/1000))...
              -(1/24 + Pr*(N-n)*(1/720 -1/48) + (Pr*(N-n))^2*(1/40320 - 1/1440 + 5/576) + (Pr*(N-n))^3*(1/36288000 - 1/80640 + 5/17280 - 61/17280) + (Pr*(N-n))^4*(1/479001600 - 1/7257600 + 5/967680 - 61/518400 + 1385/967680)...)
              -1/4 + Pr*(N-n)*5/48 - (Pr*(N-n))^2*61/1440 + (Pr*(N-n))^3*277/16128-(Pr*(N-n))^4*(7/100)));
  end
end
contourf(GR,T,U)
colorbar

[DGM]

- (Pr*(N-n))^4*(0.014)

instead of

- (Pr*(N-n)^4*(0.014))

The printed formula is full of imbalanced parentheses, so that's just the way I read it.

EDIT: also, the way U is addressed is transposed with respect to how it's plotted. It's easy to miss since the vectors have the same length.

[Maduka]

Please can you help me structure it better?

[Maduka]

@DGM please can you help structure the code, this is the nature of graph I’m expecting