Need help plotting T(x,y,z,t) at different times?!

Sorry, I think I accepted an answer so my thread closed. I'm new here.

I want to plot the first few terms of this triple sum I solved for (should be a good approximation) I was thinking about showing the initial temperature distribution (t=0), and then T(x,y,z,t=100000) or something to show how it disipated over time. Im not sure how to go about it. Here is the sum I have.

http://gyazo.com/0d5b37819ddd88eedb4f3a0587e74567

Ill also post the code I came up with, essentially I have a function, with 4 variables, T(x,y,z,t). I hope this is clear. Here is what I've tried. Id appreciate any help. I just want to plot that function at different values of t :(

clc; clear all; close all

k=46; %conductivity 
rho=3970; %material density
cp=765; %specific heat

alpha=k/(rho*cp);

x=0:pi;  
y=0:pi; 
z=0:pi;
t=0:10;

T=@(x,y,z,t) (1.376*sin(x).*sin(y).*cos(0.5*z).*exp((-2.25*alpha*t))+(0.153*sin(3*x).*sin(3*y).*cos(0.5*z).*exp((-18.25*alpha*t)-(0.055*sin(5*x).*sin(5*y).*cos(0.5*z).*exp((-50.25*alpha*t))-(0.827*sin(x).*sin(y).*co(1.5*z).*exp((-4.25*alpha*t)-(0.092*sin(3*x).*sin(3*y).*cos(1.5*z).*exp((-20.25*alpha*t)-(0.33*sin(5*x).*sin(5*y).*cos(1.5*z).*exp((-52.25*alpha*t));

x=0:pi;  
y=0:pi; 
z=0:pi;
t=0:10;

surf(T)

Answer 1

[Walter Roberson]

[X, Y, Z] = ndgrid(x, y, z);

T0 = T(X, Y, Z, 0);
subplot(2,1,1);
surf(T0);

subplot(2,1,2);
T10000 = T(X, Y, Z, 10000);
surf(T10000);

But I suggest you double-check what the result is of

x=0:pi;

Answer 2

[Jonathan]

Hey, thanks for your response! I'm getting an error that I cant seem to reconcile.

Undefined function 'co' for input arguments of type 'double'.

Error in @(x,y,z,t)(1.376.*sin(x).*sin(y).*cos(0.5*z).*exp((-2.25*alpha*t))+(0.153*sin(3*x).*sin(3*y).*cos(0.5*z).*exp((-18.25*alpha*t)-(0.055*sin(5*x).*sin(5*y).*cos(0.5*z).*exp((-50.25*alpha*t))-(0.827*sin(x).*sin(y).*co(1.5*z).*exp((-4.25*alpha*t)-(0.092*sin(3*x).*sin(3*y).*cos(1.5*z).*exp((-20.25*alpha*t)-(0.33*sin(5*x).*sin(5*y).*cos(1.5*z).*exp((-52.25*alpha*t)))))))))))

Error in Untitled (line 19) T0 = T(X, Y, Z, 0);

[Matt Kindig]

The error is because there is no function 'co' on your path. The error appears to be in the "co(1.5*z)" expression-- should it be "cos(1.5*z)"?

[Jonathan]

Haha thanks :). I'm still getting an error. Here is my code:

clc; clear all; close all

k=46; %conductivity rho=3970; %material density cp=765; %specific heat

alpha=k/(rho*cp);

T=@(x,y,z,t) (1.376.*sin(x).*sin(y).*cos(0.5*z).*exp((-2.25*alpha*t))+(0.153*sin(3*x).*sin(3*y).*cos(0.5*z).*exp((-18.25*alpha*t)-(0.055*sin(5*x).*sin(5*y).*cos(0.5*z).*exp((-50.25*alpha*t))-(0.827*sin(x).*sin(y).*cos(1.5*z).*exp((-4.25*alpha*t)-(0.092*sin(3*x).*sin(3*y).*cos(1.5*z).*exp((-20.25*alpha*t)-(0.33*sin(5*x).*sin(5*y).*cos(1.5*z).*exp((-52.25*alpha*t)))))))))));

x=0:pi; y=0:pi; z=0:pi; t=0:10;

[X, Y, Z] = ndgrid(x, y, z);

T0 = T(X, Y, Z, 0); subplot(2,1,1); surf(T0);

subplot(2,1,2); T10000 = T(X, Y, Z, 10000); surf(T10000);

Here is my error:

CData must be an M-by-N matrix or M-by-N-by-3 array

Error in graph3d.surfaceplot>localConstructor (line 136) h = graph3d.surfaceplot(argin{:});

Error in graph3d.surfaceplot (line 7) h = localConstructor(varargin{:});

Error in surf (line 98) hh = double(graph3d.surfaceplot(args{:},'parent',parax));

Error in Untitled2 (line 15) surf(T0);

Is CData color stuff? Thanks guys, I appreciate it :)

[Walter Roberson]

Ah, the problem is that I suggested that you surf() a 3D matrix of information, which is not possible.

How were you hoping to represent the 4D plot T(x range, y range, z range, fixed temperature) in a 2.5D graphics system ?