Solidification Heat Transfer Model using PDE Toolbox
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Hello,
I would like to model the solidifcation of a material at initial temperature that is cooled down in outer space up to by radiation transfer on the surface. Due to the range of temperature, a phase change happens inside my domain. The material I use is basalt and I know from documentation those values :
- Specific heat of solid basalt:
- Latent heat of crystallization of basaltic magma:
- Crystallization temperature of basalt: ,
I have already implemented the following Finite Element Model but would now like to take into account the phase change.
%% Parameters
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=200; % (s) time-step
day=3600*24;
tmax=6*day;
tlist = [0:dt:tmax];
lambda = @(location,state) (0.46+0.95*exp(-2.3e-3*state.u));
%% Model
thermalModel = createpde('thermal','transient');
gm = multisphere(1);
thermalModel.Geometry=gm;
generateMesh(thermalModel,'Hmax',0.2,"GeometricOrder","quadratic");
thermalModel.StefanBoltzmannConstant = 5.670373E-8;
thermalIC(thermalModel,T0);
thermalProperties(thermalModel,'ThermalConductivity',lambda,'MassDensity',rho,'SpecificHeat',cp);
thermalBC(thermalModel,"Face",1,"Emissivity",@(region,state) eps,"AmbientTemperature",T_out, "Vectorized","on");
thermalResults = solve(thermalModel,tlist);
Does anyone happen to know how to model the solidifcation inside the domain when it's cooled down over time ? Knowing that this phenomenon would start to occur at crystallization temperature of basalt. I thought about the internalHeatSource function but can't figure how to properly implement it.
Many thanks for any help you can give me !
Regards,
Tom
5 个评论
Yifeng Tang
2024-6-20
If the material stays in place (doesn't flow away when in liquid phase) and the density change is neglible (so volume stays the same and you don't have to remap the coordinates), I feel like a cp function is sufficient to model the thermal aspects of the melting/solidification. You may be able to consider other properties, like conductivity, as functions of temperature, if you believe they do change significantly over the temperature range in question. I don't have specific domain knowledge here to recommend one way or the other.
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