internalHeatSource

Specify internal heat source for a thermal model

Description

example

internalHeatSource(thermalmodel,heatSourceValue) specifies an internal heat source for the thermal model. This syntax declares that the entire geometry is a heat source.

Note

Use internalHeatSource for specifying internal heat generators, that is, for specifying heat sources that belong to the geometry of the model. To specify a heat influx from an external source, use the thermalBC function with the HeatFlux parameter.

example

internalHeatSource(thermalmodel,heatSourceValue,RegionType,RegionID) specifies geometry regions of type RegionType with ID numbers in RegionID as heat sources. Always specify heatSourceValue first, then specify RegionType and RegionID.

heatSource = internalHeatSource(___) returns the heat source object.

Examples

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Create a transient thermal model.

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

Import the geometry.

gm = importGeometry(thermalmodel,'SquareBeam.STL');

Set thermal conductivity to 0.2, mass density to 2700e-9, and specific heat to 920.

thermalProperties(thermalmodel,'ThermalConductivity',0.2, ...
                               'MassDensity',2700e-9, ...
                               'SpecificHeat',920)
ans = 
  ThermalMaterialAssignment with properties:

             RegionType: 'cell'
               RegionID: 1
    ThermalConductivity: 0.2000
            MassDensity: 2.7000e-06
           SpecificHeat: 920

Specify that the entire geometry generates heat at the rate 2e-4.

internalHeatSource(thermalmodel,2e-4)
ans = 
  HeatSourceAssignment with properties:

    RegionType: 'cell'
      RegionID: 1
    HeatSource: 2.0000e-04

Create a steady-state thermal model.

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

Create the geometry.

SQ1 = [3; 4; 0; 3; 3; 0; 0; 0; 3; 3];
D1 = [2; 4; 0.5; 1.5; 2.5; 1.5; 1.5; 0.5; 1.5; 2.5];
gd = [SQ1 D1];
sf = 'SQ1+D1';
ns = char('SQ1','D1');
ns = ns';
dl = decsg(gd,sf,ns);

geometryFromEdges(thermalModel,dl);

Set thermal conductivity to 50, mass density to 2500, and specific heat to 600.

thermalProperties(thermalModel,'ThermalConductivity',50, ...
                               'MassDensity',2500, ...
                               'SpecificHeat',600);

Specify that face 1 generates heat at 25.

internalHeatSource(thermalModel,25,'Face',1)
ans = 
  HeatSourceAssignment with properties:

    RegionType: 'face'
      RegionID: 1
    HeatSource: 25

Use a function handle to specify an internal heat source that depends on coordinates.

Create a thermal model for transient analysis and include the geometry. The geometry is a rod with a circular cross section. The 2-D model is a rectangular strip whose y-dimension extends from the axis of symmetry to the outer surface, and whose x-dimension extends over the actual length of the rod.

thermalmodel = createpde('thermal','transient');
g = decsg([3 4 -1.5 1.5 1.5 -1.5 0 0 .2 .2]');
geometryFromEdges(thermalmodel,g);

The heat is generated within the rod due to the radioactive decay. Therefore, the entire geometry is an internal nonlinear heat source and can be represented by a function of the y-coordinate, for example, q=2000y.

q = @(location,state)2000*location.y;

Specify the internal heat source for the transient model.

internalHeatSource(thermalmodel,q)
ans = 
  HeatSourceAssignment with properties:

    RegionType: 'face'
      RegionID: 1
    HeatSource: @(location,state)2000*location.y

Use a function handle to specify an internal heat source that depends on time.

Create a thermal model for transient analysis and include the geometry. The geometry is a rectangular strip.

thermalmodel = createpde('thermal','transient');
g = decsg([3 4 -1.5 1.5 1.5 -1.5 0 0 .2 .2]');
geometryFromEdges(thermalmodel,g);

Specify the thermal properties of the rod.

thermalProperties(thermalmodel,'ThermalConductivity',40,...
                               'MassDensity',7800,...
                               'SpecificHeat',500);

Specify the boundary conditions and initial temperature.

thermalBC(thermalmodel,'Edge',2,'Temperature',100);
thermalBC(thermalmodel,'Edge',3,...
                       'ConvectionCoefficient',50,...
                       'AmbientTemperature',100);
thermalIC(thermalmodel,0);

Specify that the entire geometry generates heat at the rate 20000t during the first 500 seconds, and then the heat source turns off. For details, see Time-Dependent Heat Source Function.

internalHeatSource(thermalmodel,@heatSource);

Generate the mesh, solve the model using the solution times from 0 to 50000 seconds, and plot the results.

generateMesh(thermalmodel);

tfinal = 50000;
tlist = 0:100:tfinal;
result = solve(thermalmodel,tlist);
T = result.Temperature;

figure 
subplot(2,1,1)
pdeplot(thermalmodel,'XYData',T(:,6),'Contour','on')
axis equal
title(sprintf('Temperature at %g s',tlist(6)))
subplot(2,1,2)
pdeplot(thermalmodel,'XYData',T(:,end),'Contour','on')
axis equal
title(sprintf('Temperature at %g s',tfinal))

Always ensure that your function returns a matrix of NaN of the correct size when state.time is NaN. The solver properly recognizes a time-dependent problem by passing NaN state values and looking for returned NaN values. Without this condition, the solver might fail or return incorrect results.

internalHeatSource(thermalmodel,@heatSourceInvalid);

result = solve(thermalmodel,tlist);
T = result.Temperature;

figure 
subplot(2,1,1)
pdeplot(thermalmodel,'XYData',T(:,6),'Contour','on')
axis equal
title(sprintf('Temperature at %g s',tlist(6)))
subplot(2,1,2)
pdeplot(thermalmodel,'XYData',T(:,end),'Contour','on')
axis equal
title(sprintf('Temperature at %g s',tfinal))

Time-Dependent Heat Source Function

function Q = heatSource(location,state)
  Q = zeros(1,numel(location.x));
if(isnan(state.time))
% Returning a NaN when time=NaN tells the solver that the heat source is a function of time.
  Q(1,:) = NaN;
  return
end
if state.time < 500
  Q(1,:) = 20000*state.time;
end
end

function Q = heatSourceInvalid(location,state) % No checks for NaN
  Q = zeros(1,numel(location.x));
if state.time < 500
  Q(1,:) = 20000*state.time;
end
end

Input Arguments

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Thermal model, specified as a ThermalModel object. The model contains the geometry, mesh, thermal properties of the material, internal heat source, boundary conditions, and initial conditions.

Example: thermalmodel = createpde('thermal','steadystate')

Geometric region type, specified as 'Face' for a 2-D model or 'Cell' for a 3-D model.

Example: internalHeatSource(thermalmodel,25,'Cell',1)

Data Types: char | string

Geometric region ID, specified as a vector of positive integers. Find the region IDs by using pdegplot.

Example: internalHeatSource(thermalmodel,25,'Cell',1:3)

Data Types: double

Heat source value, specified as a number or a function handle. Use a function handle to specify the internal heat source that depends on space, time, or temperature. For details, see More About.

Example: internalHeatSource(thermalmodel,25)

Data Types: double | function_handle

Output Arguments

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Handle to heat source, returned as an object. heatSourceValue associates the heat source value with the geometric region.

More About

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Specifying Nonconstant Parameters of a Thermal Model

Use a function handle to specify these thermal parameters when they depend on space, temperature, and time:

  • Thermal conductivity of the material

  • Mass density of the material

  • Specific heat of the material

  • Internal heat source

  • Temperature on the boundary

  • Heat flux through the boundary

  • Convection coefficient on the boundary

  • Radiation emissivity coefficient on the boundary

  • Initial temperature

For example, use function handles to specify the thermal conductivity, internal heat source, convection coefficient, and initial temperature for this model.

thermalProperties(model,'ThermalConductivity',@myfun)
internalHeatSource(model,'Face',2,@myfun)
thermalBC(model,'Edge',[3,4], ...
                'ConvectionCoefficient',@myfun, ...
                'AmbientTemperature',27)
thermalIC(model,@myfun)

The function must be of the form:

function thermalVal = myfun(location,state)

The solver passes the location and state data to your function:

  • location — A structure containing these fields:

    • location.x — The x-coordinate of the point or points

    • location.y — The y-coordinate of the point or points

    • location.z — For a 3-D or an axisymmetric geometry, the z-coordinate of the point or points

    • location.r — For an axisymmetric geometry, the r-coordinate of the point or points

    Furthermore, for boundary conditions, the solver passes these data in the location structure:

    • location.nxx-component of the normal vector at the evaluation point or points

    • location.nyy-component of the normal vector at the evaluation point or points

    • location.nz — For a 3-D or an axisymmetric geometry, z-component of the normal vector at the evaluation point or points

    • location.nz — For an axisymmetric geometry, z-component of the normal vector at the evaluation point or points

  • state — A structure containing these fields for transient or nonlinear problems:

    • state.u — Temperatures at the corresponding points of the location structure

    • state.ux — Estimates of the x-component of temperature gradients at the corresponding points of the location structure

    • state.uy — Estimates of the y-component of temperature gradients at the corresponding points of the location structure

    • state.uz — For a 3-D or an axisymmetric geometry, estimates of the z-component of temperature gradients at the corresponding points of the location structure

    • state.ur — For an axisymmetric geometry, estimates of the r-component of temperature gradients at the corresponding points of the location structure

    • state.time — Time at evaluation points

Thermal material properties (thermal conductivity, mass density, and specific heat) and internal heat source get these data from the solver:

  • location.x, location.y, location.z, location.r

  • Subdomain ID

  • state.u, state.ux, state.uy, state.uz, state.r, state.time

Boundary conditions (temperature on the boundary, heat flux, convection coefficient, and radiation emissivity coefficient) get these data from the solver:

  • location.x, location.y, location.z, location.r

  • location.nx, location.ny, location.nz, location.nr

  • state.u, state.time

Initial temperature gets the following data from the solver:

  • location.x, location.y, location.z, location.r

  • Subdomain ID

For all thermal parameters, except for thermal conductivity, your function must return a row vector thermalVal with the number of columns equal to the number of evaluation points, for example, M = length(location.y).

For thermal conductivity, your function must return a matrix thermalVal with number of rows equal to 1, Ndim, Ndim*(Ndim+1)/2, or Ndim*Ndim, where Ndim is 2 for 2-D problems and 3 for 3-D problems. The number of columns must equal the number of evaluation points, for example, M = length(location.y). For details about dimensions of the matrix, see c Coefficient for specifyCoefficients.

If properties depend on the time or temperature, ensure that your function returns a matrix of NaN of the correct size when state.u or state.time are NaN. Solvers check whether a problem is time dependent by passing NaN state values and looking for returned NaN values.

Introduced in R2017a