How to plot temperature along a defined line within a 2D temperature field

I can obtain 2D temperature field solutions such as the steady state example below. I would like to be able to plot the temperature along a defined line within this domain. For example, how can I produce a plot of T as a function of x for Y= 0 from X= -15 to X= 0 or for X= -12 from Y= -15 to Y= +15? I would also like to be able to do this at a defined time for a transient problem. I am aware of the slice command but I just want a simple T vs X or Y plot. Thanks

thermalmodel = createpde("thermal","steadystate");

R2= [3,4,-15,15,15,-15,-15,-15,15,15]';

geom=[R2]

g=decsg(geom)

model= createpde

geometryFromEdges(thermalmodel,g);

pdegplot(thermalmodel,"EdgeLabels","on")

xlim([-20 20])

axis equal

thermalProperties(thermalmodel,"ThermalConductivity",1);

thermalBC(thermalmodel,"Edge",1,"Temperature",100);

thermalBC(thermalmodel,"Edge",2,"Temperature",100);

thermalBC(thermalmodel,"Edge",3,"Temperature",100);

thermalBC(thermalmodel,"Edge",4,"Temperature",400);

generateMesh(thermalmodel);

figure

pdemesh(thermalmodel)

title("Mesh with Quadratic Triangular Elements")

thermalresults = solve(thermalmodel)

pdeplot(thermalresults.Mesh,XYData=thermalresults.Temperature,ColorMap="jet")

title("Temperature In The Plate, Steady State Solution")

xlabel("X-coordinate, meters")

ylabel("Y-coordinate, meters")

axis equal

Answer 1

[Torsten]

Does this help ?

https://uk.mathworks.com/matlabcentral/answers/52403-plot-solution-of-pde-toolbox-on-a-line-or-submanifold

[John McGrath]

Hi Torsten

I'm a relative novice with Matlab so I'll have to figure out what the point matrix, p, and the solution vector, u, are for my problem. I think the solution vector is the temperature

T= thermalresults.TemperatureNot so sure about the point matrix vector

thanks

john

[Torsten]

thermalmodel = createpde("thermal","steadystate");

R2= [3,4,-15,15,15,-15,-15,-15,15,15]';
geom=[R2];
g=decsg(geom);
model= createpde;
geometryFromEdges(thermalmodel,g);
pdegplot(thermalmodel,"EdgeLabels","on");
xlim([-20 20])
axis equal

thermalProperties(thermalmodel,"ThermalConductivity",1);

thermalBC(thermalmodel,"Edge",1,"Temperature",100);
thermalBC(thermalmodel,"Edge",2,"Temperature",100);
thermalBC(thermalmodel,"Edge",3,"Temperature",100);
thermalBC(thermalmodel,"Edge",4,"Temperature",400);

mesh = generateMesh(thermalmodel);
figure
pdemesh(thermalmodel);
title("Mesh with Quadratic Triangular Elements")

thermalresults = solve(thermalmodel);

pdeplot(thermalresults.Mesh,XYData=thermalresults.Temperature,ColorMap="jet")

title("Temperature In The Plate, Steady State Solution")
xlabel("X-coordinate, meters")
ylabel("Y-coordinate, meters")
axis equal

plotAlongLine(mesh.Nodes, thermalresults.Temperature, [-15,0], [0,0], 25);

plotAlongLine(mesh.Nodes, thermalresults.Temperature, [-12,-15], [-12,15], 25);

function plotAlongLine(p, u, xy1, xy2, numpts)
  x = linspace(xy1(1),xy2(1),numpts);
  y = linspace(xy1(2),xy2(2),numpts);
  F = TriScatteredInterp(p(1,:)', p(2,:)', u);
  uxy = F(x,y);
  figure; 
  if xy1(1)==xy2(1)
    plot(y, uxy);
  else
    plot(x, uxy)
  end
  grid on
end

[John McGrath]

Thorsten

This is fantastic! Thanks so much for your help.

Is there an easy way to export the T vs x or T vs Y data as a file?

john

[Torsten]

Define x, y and uxy as output arguments of the function "plotAlongLine" and write them to file.

Usually, "fprintf" is used for this:

https://uk.mathworks.com/help/matlab/ref/fprintf.html

If you don't know how to proceed, I recommend MATLAB Onramp, an introductory course free-of-costs to learn the basics of the language:

https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

Answer 2

[Image Analyst]

I know you already got an answer that you've accepted but I just thought I'd mention improfile. It can give you a profile of values in a matrix from any point to any other point.

[John McGrath]

Thank you very much!