MATLAB: Specify boundary conditions for a thermal model (PDE)

Hello everyone,

I need to simulate the heat transfer on a surface by using the PDE Toolbox. I have defined the geometry, the mesh, thermal properties of the material, the internal heat source, but I don't know how to define the following boundary conditions:

Surface boundary condition (z=0): where S is the heat flux proportional to the incidence angle (i), sigma is the Stefan-Boltzmann constant, epsilon is the emissivity, k the thermal conductivity.
Bottom boundary condition (z=D): where Q is the heat production of the body

Does anyone have any ideas?

Thanks for any help!

Pamela

thermalmodel = createpde('thermal','transient');
%% Geometry
gm = multicuboid(1,1,[0.1 1.9],'ZOffset',[0 0.1]);
thermalmodel.Geometry = gm;
gm2 = rotate(gm,180,[0 0 0],[0 1 0]);
thermalmodel.Geometry = gm2;
%pdegplot(thermalmodel,'CellLabels','on','FaceAlpha',0.5)
%% Generate a mesh for the geometry 
msh = generateMesh(thermalmodel,'Hmax', 5);
%% Specify thermal properties of the material 
%--------------------------------------------------------------------------
%DENSITY (rho)
rhob = 1000;
rho = @(location,state)rhob*((location.z + 0.122)/(location.z + 0.18));
%SPECIFIC HEAT (cp)
ca=1;
cb=3;
cc=5;
cd=0.4;
ce=9;
cp = @(location,state)ca+cb*state.u+cc*(state.u)^2+cd*(state.u)^3+ce*(state.u)^4;
%THERMAL CONDUCTIVITY (k)
kb = 0.8;
ks = 0.7;
rhos = 2100;
sigma = 8.67e-08;
epsilon = 0.95;
l = 5.5e-05;
beta = 4*sigma*epsilon*l;
kc = @(location,state)kb-(kb-ks)*((rhob-(rho(location,state))))/(rhob-rhos);
k = @(location,state)beta*(state.u)^3+(kc(location,state));
thermalProperties(thermalmodel,'ThermalConductivity',k, 'MassDensity',rho,'SpecificHeat',cp)
%% Internal heat source [W m^-2]
Q = 0.020
internalHeatSource(thermalmodel,Q)

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