Mesh/Contour Plot of Temperature Distribution

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Jeremiah 2013-11-11

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评论： Jeremiah 2013-11-11

I am attempting to solve the following problem:

x,y spacing=.2
Create a surface and contour plot of temperature distribution from the given data.
Given equations describe heat dist. in a flat square metal plate:
T(x,y)=(T2-T1)*w(x,y)+T1 
where w(x,y)=(2pi) * (summation(n is odd, to infinity)((2/n) * sin((n*pi*x)/L)) * (sinh((n*pi*y/L)) / (sinh((n*pi*W)/L))
T1=3 sides held at constant of 70 degrees
T2=4th side held at constant of 200 degrees
W=L=2ft.

This is my current code and dilemma, with my current code the dimensions of x,y,T(temperature) have dimensions that are not compatible to graph using functions such as surf(x,y,t). Any insight or direction is greatly appreciated.

clc;
clear all;
T1=70;T2=200;L=2;W=2;i=0; %givens defined
for x=0:.2:2%for loop for W defined as x
      i=i+1;%i increment of growth defined
      j=0;%j initial defined
         for y=0:.2:2 %for loop for L defined as y
             j=j+1;%j increment of growth defined
             error=100; Initial error defined
             term=10*eps; Initial term defined(attempted to simulation term going to infinity)
             n=1;% n initial defined
             while abs(error)>.01%while loop defined as absolute value of error >1 percent
             termnext=term+(2*pi)*(2/n)*(sin(n*pi*x)/L)*((sinh((n*pi*y)/L))/(sinh((n*pi*W)/L)));%Next term defined from previous term + the given equation.
             if abs(error)~=0 %conditional statement revising error value when error ~=0
             error=((termnext-term)/term)*100;
             n=n+2; %n increment of growth defined as odd by adding 2 each cycle
             end
             end
         end
  end
  t(x,y)=(T2-T1)*termnext+T1;%Given equation of t defined with substitution of (w(x,y)
  surfc(x,y,t)% unsuccessful attempt at plotting x vs y vs t.

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Answer 1

Walter Roberson 2013-11-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105619-mesh-contour-plot-of-temperature-distribution#answer_114800

在 MATLAB Online 中打开

surfc(0:.2:2, 0:.2:2, t)

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Walter Roberson 2013-11-11

在 MATLAB Online 中打开

When x or y are not integers, you cannot store into t(x,y).

xvals = 0 : 0.2 : 2;
yvals = 0 : 0.2 : 2;
for xidx = 1 : length(xvals)
  x = xvals(xidx);
  for yidx = 1 : length(yvals)
    y = yvals(yidx);
    ......
    w(xidx, yidx) = ....
  end
end
T = (T2-T1) * w + T1;
surfc(xvals, yvals, T)

Jeremiah 2013-11-11

Tricky Tricky, thank you so much for your insight, I did not know the integers limitations. It explains why I would get unexpected sizes when viewing my workspace for the variable. This is a pretty strong/cool code!

Thank you!

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