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.

 

[tacman]

Hello,

Thank you for reaching out with your question about plotting a surface in MATLAB using cylindrical coordinates. It is definitely possible to display u(r,z) as a surface in MATLAB. Here are some tips and hints to help you understand and implement the plot:

1. First, make sure you have defined your r and z vectors correctly. As you mentioned, the vectors should be one-dimensional and of the same size.

2. Next, you can use the "meshgrid" function in MATLAB to create a grid of points for r and z. This will help you to evaluate the solution at each point on the grid.

3. Once you have your grid, you can use the "surf" function in MATLAB to plot the surface. The syntax for this function is "surf(X,Y,Z)", where X and Y are the grid matrices created using meshgrid, and Z is the evaluated solution u(r,z).

4. You can also use the "shading" option in the "surf" function to control the appearance of the surface. For example, you can use "shading interp" to create a smooth surface or "shading flat" for a flat surface.

5. If you want to add labels and a colorbar to your plot, you can use the "xlabel", "ylabel", and "colorbar" functions in MATLAB.

I hope these tips help you to plot your solution u(r,z) as a surface in MATLAB. If you have any further questions, please don't hesitate to ask. Good luck with your project!