Treatment of source term on the boundary: FEA and Comsol

[madani]

TL;DR Summary

Treatment of source term on the boundary: Finite Element Analysis using Comsol Multiphysics

I would like to solve a coupled system of two PDEs using Comsol for the following geometry:

Equation 1 (valid for 0⩽Z⩽bm):

The initial and boundary conditions are:
Tm(r,t→0)=20
Tm(r→rw,t)=70
Tm(r→∞,t)=20

However, for bm⩽Z⩽bm+b2, the equation to solve is:

With the following initial and boundary conditions:
T2(r,t→0)=19
T2(z→bm,t)=Tm(r,t)
T2(z→bm+b2,t)=19Now, to solve the above PDEs, the coefficient form PDE in Comsol can be used. Two adjacent domains can be drawn, with each of which representing each equation mentioned above. However, my question is how to define the source term at the interface between two layers (at z=bm) for the region representing Equation 1. In Comsol, we can add flux/source term to the PDE, which has the following formulation:

However, the source term $\[{\left. {{\lambda _2}\frac{{\partial {T_2}}}{{\partial z}}} \right|_{z = {b_m}}}\]$ is not in the form provided as in the above picture. I have also tried to add a constraint and add Equation 1 on the interface (z=bm), however, I couldn't see any changes (Please see below pic):

Does anyone know how to add the source term such as this in Comsol?

Thanks in advance!

 

[Achy47]

I understand your question and would be happy to help you solve this coupled system of PDEs using Comsol. First, let's break down the problem and see how we can define the source term at the interface between the two layers.

In Comsol, the source term is defined as a function of the dependent variables and their derivatives. In your case, the source term at the interface (z=bm) would be a function of Tm and its derivative with respect to z. This can be written as:

##\[{\left. {{\lambda _2}\frac{{\partial {T_2}}}{{\partial z}}} \right|_{z = {b_m}}} = {\lambda _2}\frac{{\partial {T_m}}}{{\partial z}}\]

To add this source term in Comsol, you can follow these steps:

1. In the "Expression" window, click on "Define Expression" and give it a name (e.g. "Source Term").
2. In the "Variables" tab, add the dependent variable Tm and its derivative with respect to z (dTm/dz). You can find these variables under the "Dependent Variables" section.
3. In the "Expression" tab, write the expression for the source term as shown above.
4. Click on "OK" to save the expression.

Now, to add this source term to your PDE, you can follow these steps:

1. In the "Physics" window, select the PDE that represents Equation 1 (valid for 0⩽Z⩽bm).
2. In the "Source Term" tab, click on "Add" and select "Expression" from the drop-down menu.
3. In the "Expression" window, select the expression that you defined earlier (e.g. "Source Term").
4. Click on "OK" to add the source term to your PDE.

This will add the source term to your PDE at the interface (z=bm). You can repeat these steps for the second PDE representing the equation for bm⩽Z⩽bm+b2.

I hope this helps you solve your problem. If you have any further questions, please feel free to ask.