Hello,
This is my first implementation of a problem using the PDE Toolbox. My 3D time-dependent thermal model is the following : a sphere (radius equals to 1) with radiative flux on the outside surface, with cell at inital temperature . I would like to use a temperature dependent thermal diffusivity where . I have then an analytical expression for it given by : , which I know from documentation for my material.
The parameters used in my simulations are the following :
lambda = @(location,state) 0.46+0.95*exp(-2.3e-3*state.u); % (W/m/K) Thermal conductivity
rho=1000; % (kg/m**3) Density
cp=1000; % (J/kg/K) Specific heat
T0=2000; % (K) Initial temperature
T_out=300; % (K) outer space temperature
eps=1; % Emissivity
dt=20; % (s) time-step
day=3600*24;
tmax=2*day;
tlist = [0:dt:tmax]; % time list
I then implement my model using Matlab PDE Toolbox :
thermalModel = createpde(‘thermal’,’transient’);
gm = multisphere(1);
thermalModel.Geometry=gm;
generateMesh(thermalModel,’Hmax’,0.2,"GeometricOrder","quadratic");
thermalModel.StefanBoltzmannConstant = 5.670373E-8;
thermalProperties(thermalModel,’ThermalConductivity’,lambda,’MassDensity’,rho,’SpecificHeat’,cp);

% Initial Temperature
thermalIC(thermalModel,T0);

% Radiative Flux :
thermalBC(thermalModel,"Face",1,"Emissivity",@(region,state) eps,"AmbientTemperature",T_out, "Vectorized","on");

% Solver
thermalResults = solve(thermalModel,tlist);
Does anyone know whether the implementation is correct ?
Many thanks for any help you can give me !
Regards,
TomHello,
This is my first implementation of a problem using the PDE Toolbox. My 3D time-dependent thermal model is the following : a sphere (radius equals to 1) with radiative flux on the outside surface, with cell at inital temperature . I would like to use a temperature dependent thermal diffusivity where . I have then an analytical expression for it given by : , which I know from documentation for my material.
The parameters used in my simulations are the following :
lambda = @(location,state) 0.46+0.95*exp(-2.3e-3*state.u); % (W/m/K) Thermal conductivity
rho=1000; % (kg/m**3) Density
cp=1000; % (J/kg/K) Specific heat
T0=2000; % (K) Initial temperature
T_out=300; % (K) outer space temperature
eps=1; % Emissivity
dt=20; % (s) time-step
day=3600*24;
tmax=2*day;
tlist = [0:dt:tmax]; % time list
I then implement my model using Matlab PDE Toolbox :
thermalModel = createpde(‘thermal’,’transient’);
gm = multisphere(1);
thermalModel.Geometry=gm;
generateMesh(thermalModel,’Hmax’,0.2,"GeometricOrder","quadratic");
thermalModel.StefanBoltzmannConstant = 5.670373E-8;
thermalProperties(thermalModel,’ThermalConductivity’,lambda,’MassDensity’,rho,’SpecificHeat’,cp);

% Initial Temperature
thermalIC(thermalModel,T0);

% Radiative Flux :
thermalBC(thermalModel,"Face",1,"Emissivity",@(region,state) eps,"AmbientTemperature",T_out, "Vectorized","on");

% Solver
thermalResults = solve(thermalModel,tlist);
Does anyone know whether the implementation is correct ?
Many thanks for any help you can give me !
Regards,
Tom Hello,
This is my first implementation of a problem using the PDE Toolbox. My 3D time-dependent thermal model is the following : a sphere (radius equals to 1) with radiative flux on the outside surface, with cell at inital temperature . I would like to use a temperature dependent thermal diffusivity where . I have then an analytical expression for it given by : , which I know from documentation for my material.
The parameters used in my simulations are the following :
lambda = @(location,state) 0.46+0.95*exp(-2.3e-3*state.u); % (W/m/K) Thermal conductivity
rho=1000; % (kg/m**3) Density
cp=1000; % (J/kg/K) Specific heat
T0=2000; % (K) Initial temperature
T_out=300; % (K) outer space temperature
eps=1; % Emissivity
dt=20; % (s) time-step
day=3600*24;
tmax=2*day;
tlist = [0:dt:tmax]; % time list
I then implement my model using Matlab PDE Toolbox :
thermalModel = createpde(‘thermal’,’transient’);
gm = multisphere(1);
thermalModel.Geometry=gm;
generateMesh(thermalModel,’Hmax’,0.2,"GeometricOrder","quadratic");
thermalModel.StefanBoltzmannConstant = 5.670373E-8;
thermalProperties(thermalModel,’ThermalConductivity’,lambda,’MassDensity’,rho,’SpecificHeat’,cp);

% Initial Temperature
thermalIC(thermalModel,T0);

% Radiative Flux :
thermalBC(thermalModel,"Face",1,"Emissivity",@(region,state) eps,"AmbientTemperature",T_out, "Vectorized","on");

% Solver
thermalResults = solve(thermalModel,tlist);
Does anyone know whether the implementation is correct ?
Many thanks for any help you can give me !
Regards,
Tom pde, diffusivity, toolbox, thermal, temperature, dependent MATLAB Answers — New Questions

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