Create Thermal Analysis Model

The first step in solving a heat transfer problem is to create a thermal analysis model. This is a container that holds the geometry, thermal material properties, internal heat sources, temperature on the boundaries, heat fluxes through the boundaries, mesh, and initial conditions.

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

Import Geometry

Add the block geometry to the thermal model by using thegeometryFromEdgesfunction. The geometry description file for this problem is calledcrackg.m.

geometryFromEdges(thermalmodel,@crackg);

Plot the geometry, displaying edge labels.

pdegplot(thermalmodel,'EdgeLabels','on') ylim([-1,1]) axisequal

Specify Thermal Properties of Material

Specify the thermal conductivity, mass density, and specific heat of the material.

thermalProperties(thermalmodel,'ThermalConductivity',1,...'MassDensity',1,...'SpecificHeat',1);

Apply Boundary Conditions

Specify the temperature on the left edge as100, and constant heat flow to the exterior through the right edge as-10. The toolbox uses the default insulating boundary condition for all other boundaries.

thermalBC(thermalmodel,'Edge',6,'Temperature',100); thermalBC(thermalmodel,'Edge',1,'HeatFlux',-10);

Set Initial Conditions

Set an initial value of0for the temperature.

thermalIC(thermalmodel,0);

Generate Mesh

Create and plot a mesh.

generateMesh(thermalmodel); figure pdemesh(thermalmodel) title('Mesh with Quadratic Triangular Elements')

Specify Solution Times

Set solution times to be 0 to 5 seconds in steps of 1/2.

tlist = 0:0.5:5;

Calculate Solution

Use thesolvefunction to calculate the solution.

thermalresults = solve(thermalmodel,tlist)

thermalresults = TransientThermalResults with properties: Temperature: [1320x11 double] SolutionTimes: [0 0.5000 1 1.5000 2 2.5000 3 3.5000 4 4.5000 5] XGradients: [1320x11 double] YGradients: [1320x11 double] ZGradients: [] Mesh: [1x1 FEMesh]

Evaluate Heat Flux

Compute the heat flux density.

[qx,qy] = evaluateHeatFlux(thermalresults);

Plot Temperature Distribution and Heat Flux

Plot the solution at the final time step, t = 5.0 seconds, with isothermal lines using a contour plot, and plot the heat flux vector field using arrows.

pdeplot(thermalmodel,'XYData',thermalresults.Temperature(:,end),...'Contour','on',...'FlowData', (qx(:,结束),qy(:,结束),...'ColorMap','hot')