setupRadiation

Specify radiation parameters for surface-to-surface heat transfer

Since R2023b

Syntax

fem = setupRadiation(fem)

fem = setupRadiation(fem,Name=Value)

Description

fem = setupRadiation(fem) 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 surfaceToSurfaceSettings object and returns the specified model, fem, with its ThermalRadiation property set to that object.

fem = setupRadiation(fem,Name=Value) 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.

Examples

Specify Radiation Parameters

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: [204x204 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: [204x204 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);

Compute View Factors

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    0.2114    0.2116    0.2110    0.2116
    0.2020    0.0000    0.2106    0.2112    0.2109    0.2113
    0.2113    0.2121    0.0000    0.2112    0.2019    0.2114
    0.2111    0.2115    0.2114    0.0000    0.2112    0.2019
    0.2117    0.2117    0.2019    0.2114    0.0000    0.2110
    0.2110    0.2113    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    0.2023    0.2030    0.1988    0.2022    0.1980
    0.2037         0    0.2029    0.2036    0.2020    0.2014
    0.2009    0.2007         0    0.2028    0.2041    0.2012
    0.2021    0.2035    0.1975         0    0.1993    0.2045
    0.1974    0.1986    0.2012    0.2009         0    0.2047
    0.2052    0.2063    0.2035    0.2036    0.2013         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

fem — Finite element model

femodel object

Finite element model, specified as an femodel object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: fem = setupRadiation(fem,EnclosureFaces=[5 6],EnclosureNames="two_plates")

EnclosureFaces — Faces to form enclosures

vector of positive integers | cell array of vectors of positive integers

Faces to form enclosures, specified as a vector of positive integers for one enclosure in the model or a cell array of vectors of positive integers for multiple enclosures in the model.

Example: EnclosureFaces={[1 2 50],[68 97]}

EnclosureNames — Names of enclosures

"Enclosure_1","Enclosure_2",... (default) | string | character vector | vector of strings | cell array of character vectors

Names of enclosures, specified as a string or a character vector for a single enclosure or a vector of strings or cell array of character vectors for multiple enclosures.

Example: EnclosureNames=["groupA" "groupB"]

Data Types: string | char

PerfectEnclosure — Enclosure perfectness

true (default) | false | logical vector

Enclosure perfectness, specified as true or false for a single enclosure or a vector of these values for multiple enclosures. Setting perfectness to true ignores ambient radiation.

Example: PerfectEnclosure=[true false]

Data Types: logical

ViewFactorMethod — Method for computing view factors

"areaintegral" (default) | "montecarlo"

Since R2024a

Method for computing view factors, specified as "areaintegral" or montecarlo". By default, the method uses the double area integral method to compute view factors. The Monte Carlo method improves results for enclosures with a shared edge, such as two orthogonal faces of a box, but it can take longer to compute view factors.

Example: ViewFactorMethod="montecarlo"

Data Types: string

Tips

• You must generate a mesh before specifying radiation parameters. Call generateMesh before calling setupRadiation.

• When calling setupRadiation, always use fem as the output argument to assign the resulting surfaceToSurfaceSettings object to the ThermalRadiation property of the model.

Version History

Introduced in R2023b

R2024a: Compute view factors using Monte Carlo method

In addition to the default double area integral method for computing view factors, the toolbox now supports the Monte Carlo method. You can specify the view factor computation method by using the ViewFactorMethod name-value argument.