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

1. Nov 9, 2012

bossman007

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

2. Nov 9, 2012

LCKurtz

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
3. Nov 9, 2012

bossman007

Thanks for the help I really appreciate it. Do I need the with(plots) command too ?

4. Nov 9, 2012

LCKurtz

I don't think so. You can put with(plots); in to be safe, it won't hurt.

5. Nov 9, 2012

bossman007

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
6. Nov 9, 2012

bossman007

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

7. Nov 9, 2012

LCKurtz

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.

8. Nov 9, 2012

LCKurtz

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

9. Nov 9, 2012

Ray Vickson

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

10. Nov 9, 2012

bossman007

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

11. Nov 9, 2012

LCKurtz

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
12. Nov 9, 2012

bossman007

Cool ! What did was ur input ? Can I see?

13. Nov 9, 2012

bossman007

thanks

Last edited: Nov 9, 2012
14. Nov 9, 2012

LCKurtz

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);

15. Nov 9, 2012

bossman007

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