Create 2-D Geometry in PDE Modeler App

Create a geometry in the PDE Modeler app. First, open the PDE Modeler app with a geometry consisting of a rectangle and 12 circles.

pderect([0 0.01 0 0.008])
for i = 0.002:0.002:0.008
   for j = 0.002:0.002:0.006
       pdecirc(i,j,0.0005)
   end
end

Adjust the axes limits by selecting Options > Axes Limits. Select Auto to use automatic scaling for both axes.

Export the geometry description matrix, set formula, and name-space matrix into the MATLAB^® workspace by selecting Draw > Export Geometry Description, Set Formula, Labels. This data lets you reconstruct the geometry in the workspace.

Extrude 2-D Geometry into 3-D Geometry of Heat Sink

In the MATLAB Command Window, use the decsg function to decompose the exported geometry into minimal regions. Plot the result.

g = decsg(gd,sf,ns);
pdegplot(g,FaceLabels="on")

Create a 2-D geometry from the decomposed geometry matrix.

g = fegeometry(g);

Extrude the 2-D geometry along the z-axis by 0.0005 units.

g = extrude(g,0.0005);

Plot the extruded geometry so that you can see the face labels on the top.

figure
pdegplot(g,FaceLabels="on")
view([0 90])

Extrude the circular faces (faces with IDs from 15 to 26) along the z-axis by 0.005 more units. These faces form the fins of the heat sink.

g = extrude(g,[15:26],0.005);

Plot the geometry.

figure
pdegplot(g)

Perform Thermal Analysis

Create an femodel object for transient thermal analysis and include the geometry.

model = femodel(AnalysisType="thermalTransient", ...
                Geometry = g);

Assuming that the heat sink is made of copper, specify the thermal conductivity, mass density, and specific heat.

model.MaterialProperties = ...
    materialProperties(ThermalConductivity=400, ...
                       MassDensity=8960, ...
                       SpecificHeat=386);

Specify the Stefan-Boltzmann constant.

model.StefanBoltzmann = 5.670367e-8;

Apply the temperature boundary condition on the bottom surface of the heat sink, which consists of 13 faces.

model.FaceBC(1:13) = faceBC(Temperature=1000);

Specify the convection and radiation parameters on all other surfaces of the heat sink.

model.FaceLoad(14:g.NumFaces) = ...
    faceLoad(ConvectionCoefficient=5, ...
             AmbientTemperature=300, ...
             Emissivity=0.8);

Set the initial temperature of all the surfaces to the ambient temperature.

model.CellIC = cellIC(Temperature=300);

Generate a mesh.

model = generateMesh(model);

Solve the transient thermal problem for times between 0 and 0.0075 s with a time step of 0.0025 s.

results = solve(model,0:0.0025:0.0075);

Plot the temperature distribution for each time step.

for i = 1:length(results.SolutionTimes)
  figure
  pdeplot3D(results.Mesh,ColorMapData=results.Temperature(:,i))
  title({['Time = ' num2str(results.SolutionTimes(i)) 's']})
end

You also can plot the same results by using the Visualize PDE Results Live Editor task. First, create a new live script by clicking the New Live Script button in the File section on the Home tab.

On the Live Editor tab, select Task > Visualize PDE Results. This action inserts the task into your script.

To plot the temperature distribution for each time step, follow these steps.