Temperature Distribution in Heat Sink

This example shows how to create a simple 3-D heat sink geometry and analyze heat transfer on the heat sink. The process has three steps.

1. Create 2-D Geometry in the PDE Modeler App.

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

3. Perform Thermal Analysis.

Create 2-D Geometry in the 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 thermal model for transient analysis.

model = createpde('thermal','transient');

Create a 2-D geometry from decomposed geometry matrix and assign the geometry to the thermal model.

g = geometryFromEdges(model,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);

Assign the modified geometry to the thermal model and plot the geometry.

model.Geometry = g;
figure
pdegplot(g)

Perform Thermal Analysis

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

thermalProperties(model,'ThermalConductivity',400, ...
                        'MassDensity',8960, ...
                        'SpecificHeat',386);

Specify the Stefan-Boltzmann constant.

model.StefanBoltzmannConstant = 5.670367e-8;

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

thermalBC(model,'Face',1:13,'Temperature',1000);

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

thermalBC(model,'Face',14:g.NumFaces, ...
                'ConvectionCoefficient',5, ...
                'AmbientTemperature',300, ...
                'Emissivity',0.8);

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

thermalIC(model,300);

Generate a mesh.

generateMesh(model);

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

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

Plot the temperature distribution for each time step.

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