setupRadiation
Description
fem = setupRadiation( enables
surface-to-surface radiation analysis using the enclosure formed by all faces of the
specified model. An enclosure is a group of surfaces between which heat transfer occurs due
to radiation without conductive media. The function creates a
fem)surfaceToSurfaceSettings object and returns the specified model,
fem, with its ThermalRadiation property set to that
object.
fem = setupRadiation(
specifies additional options using one or more name-value arguments. For example, you can
specify the faces to form enclosures, the enclosure names, and their perfectness.fem,Name=Value)
Examples
Specify radiation parameters for heat transfer between two parallel plates.
Create the geometry representing two parallel plates of the same dimensions. The distance between the plates is 0.4 m.
dist = 0.4; W = 0.05; L = 0.5; H = 0.5; R1 = [3 4 0 W W 0 0 0 L L]; R2 = [3 4 W+dist 2*W+dist 2*W+dist W+dist 0 0 L L]; geom2D = fegeometry(decsg([R1(:) R2(:)], ... 'R1+R2',[char('R1')' char('R2')'])); geom3D = extrude(geom2D,H); pdegplot(geom3D,FaceLabels="on",FaceAlpha=0.3)
Create a finite element model for thermal analysis and include the geometry.
fem = femodel(AnalysisType="thermalSteady",Geometry=geom3D);Generate a mesh.
fem = generateMesh(fem,Hmax=H/4);
Account for surface-to-surface radiation in the enclosure formed by the plates by using the setupRadiation function.
fem = setupRadiation(fem,EnclosureFaces=[5 6]); fem.ThermalRadiation
ans =
surfaceToSurfaceSettings with properties:
ViewFactors: [204×204 double]
ViewFactorMethod: "areaintegral"
Enclosures: dictionary (string ⟼ enclosureDefinition) with 1 entry
ParticipatingEnclosures: "Enclosure_1"
If you do not specify enclosure names, setupRadiation uses the default names, such as "Enclosure_1". The function also sets the enclosure perfectness to true, which means that the solver ignores ambient radiation. To change these settings, use the EnclosureNames and PerfectEnclosure name-value arguments.
fem = setupRadiation(fem,EnclosureFaces=[5 6], ... EnclosureNames="two_plates", ... PerfectEnclosure=false); fem.ThermalRadiation
ans =
surfaceToSurfaceSettings with properties:
ViewFactors: [204×204 double]
ViewFactorMethod: "areaintegral"
Enclosures: dictionary (string ⟼ enclosureDefinition) with 1 entry
ParticipatingEnclosures: "two_plates"
Specify ambient temperature and emissivity for the enclosure formed by the plates.
fem.FaceLoad([5 6]) = faceLoad(AmbientTemperature=0,Emissivity=0.5);
Since R2024a
Find view factors in a cubical cavity using the double area integral method and the Monte Carlo method.
Create and plot a geometry of a sphere with a cubical cavity.
L = 1;
g1 = multisphere(L*1.1);
g2 = multicuboid(L,L,L,Zoffset=-L/2);
g1 = addVoid(g1,g2);
pdegplot(g1,FaceAlpha=0.2,FaceLabels="on")
Create a finite element model for thermal analysis and include the geometry.
fem = femodel(AnalysisType="thermalSteady",Geometry=g1);Generate a mesh.
fem = generateMesh(fem,Hmax=0.1*L);
Account for surface-to-surface radiation in the enclosure represented by the cubical cavity. By default, the setupRadiation function uses the double area integral method to compute view factors.
fem = setupRadiation(fem,EnclosureFaces=2:7);
The toolbox computes view factors based on the finite element mesh. Use the extractGeometricAreaViewFactors helper function to map the computed mesh view factors to the geometric face view factors. To view the code for this function, see Helper Function.
[~,ViewFactors] = extractGeometricAreaViewFactors(fem); ViewFactors
ViewFactors = 6×6
0.0000 0.2020 0.2109 0.2111 0.2106 0.2113
0.2020 0.0000 0.2110 0.2116 0.2114 0.2116
0.2117 0.2117 0.0000 0.2112 0.2019 0.2114
0.2115 0.2111 0.2114 0.0000 0.2112 0.2019
0.2121 0.2113 0.2019 0.2114 0.0000 0.2110
0.2113 0.2111 0.2112 0.2019 0.2115 0.0000
The view factors between each face must be 0.2, which means that all off-diagonal entries in ViewFactors must be very close to 0.2. Now, compute the view factors using the Monte Carlo method and compare the results.
fem = setupRadiation(fem, ... EnclosureFaces=2:7, ... ViewFactorMethod="montecarlo");
The Monte Carlo method improves results for enclosures with a shared edge, but it can take longer to compute view factors.
[~,ViewFactors_MC] = extractGeometricAreaViewFactors(fem); ViewFactors_MC
ViewFactors_MC = 6×6
0 0.2058 0.2015 0.1998 0.1976 0.2008
0.2071 0 0.2051 0.2010 0.2033 0.2005
0.2007 0.2013 0 0.2059 0.2016 0.2034
0.1979 0.2005 0.1988 0 0.2012 0.2053
0.2017 0.2004 0.2002 0.2029 0 0.2005
0.2034 0.2017 0.2030 0.2005 0.2045 0
Helper Function
This code defines the extractGeometricAreaViewFactors helper function, which maps view factors from a mesh to a geometry.
function [A,F] = extractGeometricAreaViewFactors(fem) map = []; for i = 1:length(fem.ThermalRadiation.ParticipatingEnclosures) map = [map, ... fem.ThermalRadiation.Enclosures( ... fem.ThermalRadiation.ParticipatingEnclosures(i) ... ).BoundaryFacetMapping]; end A = zeros(size(map,2),1); F = zeros(size(map,2)); for i = 1:size(map,2) FacetsIDi = map(2:3,i); FacetsIDi = FacetsIDi(1):FacetsIDi(end); FacetsAi = fem.ThermalRadiation.Area(FacetsIDi); Ai = sum(FacetsAi); A(i) = Ai; for j = 1:size(map,2) FacetsIDj = map(2:3,j); FacetsIDj = FacetsIDj(1):FacetsIDj(end); FacetsFij = ... fem.ThermalRadiation.ViewFactors(FacetsIDj, ... FacetsIDi); F(i,j) = sum(FacetsFij*FacetsAi)/sum(FacetsAi); end end end
Input Arguments
Name-Value Arguments
Tips
You must generate a mesh before specifying radiation parameters. Call
generateMeshbefore callingsetupRadiation.When calling
setupRadiation, always usefemas the output argument to assign the resultingsurfaceToSurfaceSettingsobject to theThermalRadiationproperty of the model.
