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.