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

[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


If anyone wants more information please let me know! Many thanks

 

[LCKurtz]

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

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.

 

[bossman007]

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

 

[LCKurtz]

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

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

 

[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/ [/PLAIN]

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

[PLAIN]http://postimage.org/image/bby80n0x1/ [/PLAIN]

 

[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

 

[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.

 

[LCKurtz]

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

 

[Ray Vickson]

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

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

 

[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

 

[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

 

[bossman007]

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

 

[bossman007]

thanks

 

[LCKurtz]

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

The graph you got is confusing because its supposed to be a flat sheet

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);

 

[bossman007]

this look right? i used your code. many thanks!

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

it makes sense because all 3 sides are 0 while the other side is not. thanks so much