How to impose a variable temperature distribution for one edge of a rectangular plate while keeping the temperatures of other three edges same and constant?

Hi all,

I was trying to plot heat flux lines for a heat transfer problem. The problem specifies a 0.3m by 0.1m rectangular plate. Its right, left and bottom edges are kept at 273.15K and the top edge has a temperature distribution:

with thermal conductivity, k=2.5 W/mK. I've tried the following to solve this problem:

load('gd');
load('ns');
load('sf');


g=decsg(gd,sf,ns);
thermalmodel = createpde('thermal');
geometryFromEdges(thermalmodel,g);
pdegplot(thermalmodel,'EdgeLabels','on')
xlim([0 .3])
ylim([0 .15])
axis equal
dx=.0001;
x=0:dx:.3;
thermalProperties(thermalmodel,'ThermalConductivity',2.5,'Face',1);
thermalBC(thermalmodel,'Edge',1,'Temperature',273.15);
thermalBC(thermalmodel,'Edge',2,'Temperature',273.15);
thermalBC(thermalmodel,'Edge',4,'Temperature',273.15);
thermalBC(thermalmodel,'Edge',3,'Temperature',30.*sin(pi.*x/.3));
generateMesh(thermalmodel);
results = solve(thermalmodel)

I'm getting the following error: Error using pde.ThermalBC/set.Temperature (line 136)

Temperature for all specified edges or faces must be a scalar value or a single function handle. Could someone suggest how I can impose the variable temperature distribution?

Answer 1

[Ravi Kumar]

Hi Anik,

Define a function to model variation of temperature and use it in BC specification:

tFunc = @(region,state) 30.*sin(pi.*region.x/3)

thermalBC(thermalmodel,'Edge',3,'Temperature',@tFunc);

Regards,

Ravi

[Anik Faisal]

Hi Ravi,

Thanks for your suggestion! do I need to define the region and state to use the 'tFunc'? cause I've included the two lines of code you kindly provided here and getting the following error:

Error: File: prob1.m Line: 20 Column: 48

"tFunc" was previously used as a variable, conflicting with its use here as the name of a function or command.

See "How MATLAB Recognizes Command Syntax" in the MATLAB documentation for details.

load('gd');
load('ns');
load('sf');


g=decsg(gd,sf,ns);
thermalmodel = createpde('thermal');
geometryFromEdges(thermalmodel,g);
pdegplot(thermalmodel,'EdgeLabels','on')
xlim([0 .3])
ylim([0 .15])
axis equal
dx=.0001;
x=0:dx:.3;
thermalProperties(thermalmodel,'ThermalConductivity',2.5,'Face',1);
thermalBC(thermalmodel,'Edge',1,'Temperature',273.15);
thermalBC(thermalmodel,'Edge',2,'Temperature',273.15);
thermalBC(thermalmodel,'Edge',4,'Temperature',273.15);
tFunc = @(region,state) 30.*sin(pi.*region.x/3)
thermalBC(thermalmodel,'Edge',3,'Temperature',@tFunc);
generateMesh(thermalmodel);
results = solve(thermalmodel)

[Ravi Kumar]

I made a mistake in my original post, you don't need "@" in front of tFunc as it is already a function handle. Use:

tFunc = @(region,state) 30.*sin(pi.*region.x/3)

thermalBC(thermalmodel,'Edge',3,'Temperature',tFunc);

[Anik Faisal]

Thanks, Ravi! much appreciated

[Anik Faisal]

Any suggestions regarding plotting the isotherms for this problem?

[Ravi Kumar]

You can try contour, countour3, contourf, etc using the results.Temperature data.

Also, refer to the plots at the end of thermal model example:

https://www.mathworks.com/help/pde/ug/heat-conduction-in-multidomain-geometry-with-nonuniform-heat-flux.html

[Anik Faisal]

Thanks again! Much obliged.