Surface Plot in Matlab (Cylindrical Coordinates)

[phioder]

Hello

Trying to plot in MATLAB the final solution equation u(r,z) of the steady state temperatures in the circular cylinder

u(r,z) is defined in cylindrical coordinates and I'm confused trying to understand also how MATLAB plots a mesh.

After some simplification The final solution looks like:

u(r,z) = u_0 \cdot sinh(\lambda z) \cdot J_0(\lambda r)

and it is defined in

0<r<2

0<z<4

\lambda = constant

The solution of the problem is not defined in \theta and most of 3d plot examples I have found yet on the web define a theta vector.

In MATLAB a one dimensional linspace vector for r, one for z is defined and later evaluated with sinh() and J0(). The resulting vector are multiplied as sinh().*J0(), to get again a one dimensional vector, all vectors are of the same size, so I suppose the vectors are right.

Now the question is, is it possible to display u(x,t) as a surface with Matlab? If yes, could anyone give me some kind of tip, hint on how to implement and understand the plot?

Best Regards and Thank you

 

[Dr Transport]

The solution is indepeendent of \theta, so it doesn't matter, I'd set r = \sqrt{x^2+y^2} and plot in 3-d on that grid. Make x and y on a fine enough grid that you can get a bunch of points for a smooth surface.