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How do i plot 2D steady state temp in maple?

  1. Nov 9, 2012 #1
    Hi all, I am wondering how I plot the steady state temperature distribution of a square flat sheet in maple. I solved the initial partial differential equation I was given and ended up with a function generalized as

    T(x,y) =(constants)*sum(stuff).

    Which is a Fourier series representing how the temperature flows through my sheet. Only one side of the square sheet is being heated so I have a general idea of how the graph should look, but I'm a maple newbie and wondering if from this explanation if anyone can be a help and provide a template helping me choose the right plot to pick, the commands and calls and how to set up my initial boundary conditions

    T(x,0)= 0
    T(S,y)=0
    T(0,y)=0

    T(x,S)=T_0 <==this is the edge being heated


    If anyone wants more information please let me know! Many thanks
     
  2. jcsd
  3. Nov 9, 2012 #2

    LCKurtz

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    S:=some value; (you can't leave it as a variable to plot it)
    T:=your formula with x and y;
    plot3d(T,x=0..S,y=0..S);

    Whether it will plot your infinite series I don't know. You might have to just plot a large number of terms.
     
    Last edited: Nov 9, 2012
  4. Nov 9, 2012 #3
    Thanks for the help I really appreciate it. Do I need the with(plots) command too ?
     
  5. Nov 9, 2012 #4

    LCKurtz

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    I don't think so. You can put with(plots); in to be safe, it won't hurt.
     
  6. Nov 9, 2012 #5
    Hi,

    This in the picture is what I have so far, any corrections to be noted would be very helpful. I do not know how to get this thing to work !

    [PLAIN]http://postimage.org/image/c5att96xx/ [Broken][/PLAIN]

    changing T(x,y) to just T i also get this:

    [PLAIN]http://postimage.org/image/bby80n0x1/ [Broken][/PLAIN]
     
    Last edited by a moderator: May 6, 2017
  7. Nov 9, 2012 #6
    I also just changed "PI" to the actual symbol to see if that fixed anything, and i get this "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct" still
     
  8. Nov 9, 2012 #7

    LCKurtz

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    It's hard to read those images. But what it displays for your T with all that stuff in the denominator surely can't be correct. You must have some syntax errors in your formula for T. Also I think you want to use Pi, not PI.
     
  9. Nov 9, 2012 #8

    LCKurtz

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    If you want to print your formula here in TeX so I can read it correctly, I can enter it and try it.
     
  10. Nov 9, 2012 #9

    Ray Vickson

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    Change PI to Pi; in Maple, pi is a symbol and PI is the upper-case pi symbol; if you want the usual constant π you need to write Pi. See here:
    evalf([pi,PI,Pi]);
    [pi, PI, 3.141592654]

    (the pi and PI print on screen as π and ∏, but did not copy properly from a Maple worksheet to here).

    RGV
     
  11. Nov 9, 2012 #10
    Thank u , The error in the 2nd picture is the big problem I think ?? If you click the image again it will zoom in so it's easier to read
     
  12. Nov 9, 2012 #11

    LCKurtz

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    Nevermind typing the formula. I think I got it typed in. Here's what I got with S = 1. I don't know what you are doing wrong.

    http://www.public.asu.edu/~kurtz/pictures/picture.jpg [Broken]
     
    Last edited by a moderator: May 6, 2017
  13. Nov 9, 2012 #12
    Cool ! What did was ur input ? Can I see?
     
  14. Nov 9, 2012 #13
    thanks
     
    Last edited: Nov 9, 2012
  15. Nov 9, 2012 #14

    LCKurtz

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    The z values represent the temperature at the points (x,y). You can see it is zero along three edges.

    > T := 40*(sum(sin(n*Pi*x)*sinh(n*Pi*y)/((2*n+1)^2*n*sinh(10*n*Pi)), n = 1 .. 5))/Pi;

    > s := 1;

    > plot3d(T, x = 0 .. s, y = 0 .. s, axes = boxed);
     
  16. Nov 9, 2012 #15
    this look right? i used your code. many thanks!

    [PLAIN]http://postimage.org/image/q6uazt7w1/ [Broken][/PLAIN]

    it makes sense because all 3 sides are 0 while the other side is not. thx so much
     
    Last edited by a moderator: May 6, 2017
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