If you want to apply an internal boundary condition on edge E3 (the interface between Face 1 and Face 2) in MATLAB’s "PDE Toolbox", specifically a condition that involves the temperature on both sides of the edge (let’s say ( T_1 ) on Face 1 and ( T_2 ) on Face 2)—here’s what you need to know:
1. For most internal boundary conditions (like thermal contact or interface conditions), you need to model each region with its own PDE.
So, set N=2 when you create your model:
N = 2;
modello = createpde(N);
2. After defining your geometry and identifying the edge number of E3 (use pdegplot to check), you can apply a mixed (Robin-type) boundary condition that couples the two regions.
For example, if you want the flux across E3 to be proportional to the temperature difference (( q = h(T_1 - T_2) )), use:
h = 100; % Example heat transfer coefficient
applyBoundaryCondition(modello, ...
'mixed', ...
'Edge', E3, ...
'EquationIndex', [1 2], ...
'q', [h -h; -h h], ...
'g', [0; 0]);
This enforces the relationship between the temperatures on both sides of the edge.
3. If you only have a single PDE (N=1), you can only set standard boundary conditions (Dirichlet, Neumann, Robin) on edges, not interface conditions involving both sides.
In summary:
- For interface conditions between regions, use a system with N=2 and a 'mixed' boundary condition with 'EquationIndex'.
- For simple flux or temperature conditions, use 'neumann' or 'dirichlet' as usual.
For more information, Please refer the following MathWorks documentation link:
Hope this helps!
