How to solve Phase Change Stefan problem with the PDEtool?
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Elisa Revello
am 14 Jan. 2023
Beantwortet: Torsten
am 15 Jan. 2023
I am trying to solve the Heat transfer Stefan problem with the pdetool in Matlab (governing equations are reported in "PDE governing equations".png, without convection), with the initial and boundary conditions attached.
I don't understand how to specify the required conditions for the 2 different geometries (represented in the "1D melting process".png) and how to build them in the PDE Modeler. The attached file .m only refers to the first geometry (liquid) and the input data are the following:
Thanks in advance for the help.
rho = 1370; % density [kg/m^3]
k_s = 0.830; % thermal conductivity solid phase [W/(m K)]
k_l = 0.660; % thermal conductivity liquid phase[W/(m K)]
cp_s = 1.69; % specific heat capacity solid phase [kJ/(kg K)]
cp_l = 1.96; % specific heat capacity liquid phase [kJ/(kg K)]
L = 227; % latent heat of the phase change [kJ/kg]
T_melt = 115+273; % melting temperature of the PCM [K]
alpha_s = k_s/(rho*cp_s); % thermal diffusivity solid phase [m^2/s]
alpha_l = k_l/(rho*cp_l); % thermal diffusivity liquid phase [m^2/s]
T_0 = -10+273; % initial temperature of the PCM [K]
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Torsten
am 15 Jan. 2023
There is no chance to solve the problem with a standard tool to solve partial differential equations (like the PDE Toolbox).
I suggest to non-dimensionalize the spatial coordinate as described in
and use ODE15S to solve the resulting system of ordinary differential equations for the temperature.
Look up "method-of-lines" for more details.
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