How to have multiple Robin boundary conditions?

[CalebDmArcher]

I am wondering if this is the correct way to write the equation if I have more than 1 Robin boundary condition:
I have a thermal simulation with different convention coefficients on 2 different surfaces of the structure.

# Define free air convection coefficient [W/(m^2*K)]
h1 = 5000.
h2 = 10.

free_air_surfaces = mesh.facesFront | mesh.facesBack  # Only top and bottom
convection_surfaces_front = mesh.facesFront  # This is the bottom of the structure, use h2
convection_surfaces_back = mesh.facesBack  # This is the top of the structure, use h1

Gamma = D * ~free_air_surfaces

dPf = FaceVariable(mesh=mesh,
                   value=mesh._faceToCellDistanceRatio * mesh.cellDistanceVectors)

n = mesh.faceNormals
b = D

convection_surfaces_front = mesh.facesFront  # from in mesh is the bottom of the structure, use h2
convection_surfaces_back = mesh.facesBack  # back in mesh is the top of the structure, use h1

a_front = FaceVariable(mesh=mesh, value=h2 * n, rank=1)
a_back = FaceVariable(mesh=mesh, value=h1 * n, rank=1)

g_front = FaceVariable(mesh=mesh, value=h2 * T_ambient, rank=0)
g_back = FaceVariable(mesh=mesh, value=h1 * T_ambient, rank=0)

RobinCoeff_front = convection_surfaces_front * D * n / (dPf.dot(a_front) + b)
RobinCoeff_back = convection_surfaces_back * D * n / (dPf.dot(a_back) + b)

RobinTerm_front = (RobinCoeff_front * a_front.dot(mesh.faceNormals))
RobinTerm_back = (RobinCoeff_back * a_back.dot(mesh.faceNormals))

eq = (DiffusionTerm(coeff=Gamma) +
      source +
      (RobinCoeff_front * g_front).divergence +  # Apply front convection condition
      (RobinCoeff_back * g_back).divergence -    # Apply back convection condition
      ImplicitSourceTerm(coeff=RobinTerm_front.divergence + RobinTerm_back.divergence))

So basically it is just adding two different Robin boundary terms.
May I know if this is the correct way to do so?

[guyer]

Yes, I think that should work.

Alternatively:

convection_surfaces = convection_surfaces_front | convection_surfaces_back

n = FaceVariable(mesh=mesh, value=mesh.faceNormals)

h = (h2 * convection_surfaces_front + h1 * convection_surfaces_back)
a = h * n
g = h * T_ambient

RobinCoeff = convection_surfaces * D * n / (dPf.dot(a) + b)
RobinTerm = RobinCoeff * a.dot(n)

eq = (DiffusionTerm(coeff=Gamma) +
      source +
      (RobinCoeff * g).divergence -
      ImplicitSourceTerm(coeff=RobinTerm.divergence))