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Surface Plot in Matlab (Cylindrical Coordinates)

  1. Dec 19, 2007 #1
    Hello

    Trying to plot in matlab the final solution equation [tex]u(r,z)[/tex] of the steady state temperatures in the circular cylinder

    [tex]u(r,z)[/tex] 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:

    [tex]u(r,z) = u_0 \cdot sinh(\lambda z) \cdot J_0(\lambda r)[/tex]

    and it is defined in

    [tex]0<r<2[/tex]

    [tex]0<z<4[/tex]

    [tex]\lambda = constant[/tex]

    The solution of the problem is not defined in [tex]\theta[/tex] 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 [tex]u(x,t)[/tex] 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
     
    Last edited: Dec 19, 2007
  2. jcsd
  3. Dec 19, 2007 #2

    Dr Transport

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    Science Advisor
    Gold Member

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