MATLAB: Radiation in PDE thermal model

pde thermalradiation

Dear community,

I am using the PDE toolkit to build a simple transient thermal model. Radiative heat transfer is a weak, yet present contribution to the phenomenon as the object's temperature is max 10°C over ambient temperature and min -8°C (approximately, due to internal heat generation/absorption), the emissivity is 0.3 and the exposition lasts about 10s per step.

The results I get by considering only convection well match experimental data (see attached picture).

When I introduce the radiant contribution, I get a substantial deviation as if the radiant heat transfer between the object and the ambience would increase the object's temperature rather than decrease it.

This makes no physical sense.

Could you please advice if there is a mistake in my code (see below)?

Tamb=298.15;

emiss=0.3;

hCoeff=30;

ta=Tamb-273.15; %in Celsius

thermalBC(thermalmodel,'Face',[1,2,4,6],'ConvectionCoefficient',hCoeff,'AmbientTemperature',ta);

thermalmodel.StefanBoltzmannConstant = 5.670373E-8;

thermalBC(thermalmodel,'Face',[1,2,4,6],'Emissivity',@(region,state) emiss,'AmbientTemperature',ta)

Thank you,

expl pic.JPG

Best Answer

To activate both radiation and convection on the same boundary, combine them into one assignment as:

thermalBC(thermalmodel,'Face',[1,2,4,6],'ConvectionCoefficient',hCoeff,'Emissivity',@(region,state) emiss, 'AmbientTemperature',ta);

Related Solutions

MATLAB: Unexpected Result for 3-D Thermal Transient Analysis of Heat sink using PDE Solver Toolbox

Here is the correct results using the new STL after fixing two more inconsitencies:

Radiation problem should include temperature in K.
All BCs on a particular set of faces need to be applied at once, otherwise the following assignment would overwrite the preceeding one if they are applied on the same set of faces.

code:

%% Model Setup for Heat Sink
thermalmodel = createpde('thermal','transient');
gm = importGeometry(thermalmodel,'heatsinkv2.stl'); 
pdegplot(thermalmodel,'FaceLabel','on','FaceAlpha',0.5);
axis equal
%% mesh
generateMesh(thermalmodel);
figure;
pdeplot3D(thermalmodel);
%% Boundary Condition,  Aluminium Alloy Properties and Initial Conditions
TCval = @(location,state)139.3 + 0.204*(state.u-273.15); %sets thermal conductivity (W/m/°C) as a function of temperature only approximate equation based on linear trend for table data from ansys engineering alumnium alloy data
MDval = 2770; %density kg/m^3
SHval = 875;  %specific heat (J/kg/°C)
ATval = 25+273.15;   %ambient temperature
CCval = 30;   %convective film coefficient W/m^2
REval = 0.77; %radiation emissivity
thermalmodel.StefanBoltzmannConstant = 5.670373E-8;
faces = [1,3:30];
thermalProperties(thermalmodel,'ThermalConductivity',TCval,'MassDensity',MDval,'SpecificHeat',SHval);
thermalBC(thermalmodel,'Face',faces,'ConvectionCoefficient',@(region,state)CCval,'Emissivity',@(region,state)REval,'AmbientTemperature',ATval);
thermalBC(thermalmodel,'Face',2,'ConvectionCoefficient',5,'Emissivity',0.1,'AmbientTemperature',ATval);
thermalIC(thermalmodel,60+273.15); %sets initial temperature °C problem with this as temp doesnt go down very fast?
%% solve
tlist= [0:10]; %time from 0 to 10seconds
thermalTransientResults = solve(thermalmodel,tlist);
pdeplot3D(thermalmodel,'ColorMapData',thermalTransientResults.Temperature(:,10)-273.15)

Regards,

Ravi

MATLAB: Radiation and convection in thermal models with different ambient and sink temperatures

To pass additional parameter, wrap the functions that actually computes with the ones you specify as inputs. In your example:

...
h = 50;     % Convective heat transfer coefficient [W/m^2 K]
sigma = 5.670367E-8; % Stefann-Boltzmann constant [W/(m^2 K^4)]
Tinf = 25;   % External fluid temperature [°C]
Ts = 15;     % External sink temperature [°C]
emiss = 0.7; % Surface emissivity [-]
mygfunInterface = @(location,state) mygfun(location,state,h,sigma,Tinf,Ts,emiss)
...

Similaraly for q functionction and use

applyBoundaryCondition(Fin,'neumann','edge',[1 3],...
    'q',myqfunInterface,'g',mygfunInterface,'Vectorized','on');

And, updated the actual function to take additinal inputs:

function bcMatrix = mygfun(location,state,h,sigma,Tinf,Ts,emiss)
...
end

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