Boundary constrain leads to internal loop, what happens here and why? - boundary

Question

My Script ceases to work for my easy conduction problem. Could somebody explain to me why the following line of code T.faceValue.constrain(alp/lam*(Tu-T.faceValue),where=mesh.exteriorFaces) # Boundary Condition for Solver results in fipy giving up on me?
Full Code:
cv=900.
lam=5.
alp=300.
T0 = 25.
Tu = 400.
cellSize = 0.05
radius = 1.
mesh = Gmsh2D('''
cellSize = %(cellSize)g;
radius = %(radius)g;
Point(1) = {0, 0, 0, cellSize};
Point(2) = {-radius, 0, 0, cellSize};
Point(3) = {0, radius, 0, cellSize};
Point(4) = {radius, 0, 0, cellSize};
Point(5) = {0, -radius, 0, cellSize};
Circle(6) = {2, 1, 3};
Circle(7) = {3, 1, 4};
Circle(8) = {4, 1, 5};
Circle(9) = {5, 1, 2};
Line Loop(10) = {6, 7, 8, 9};
Plane Surface(11) = {10};
''' % locals()) # doctest: +GMSH
T = CellVariable(name = "HeatingUp",mesh = mesh,value = T0)
viewer = None
if __name__ == '__main__':
try:
viewer = Viewer(vars=T, datamin=T0, datamax=Tu)
viewer.plotMesh()
input("Irregular circular mesh. Press <return> to proceed") # doctest: +GMSH
except:
print("Unable to create a viewer for an irregular mesh (try Matplotlib2DViewer or MayaviViewer)")
# =============================================================================
eq = TransientTerm(coeff=rho*cv)==DiffusionTerm(coeff=lam)
T.faceValue.constrain(alp/lam*(Tu-T.faceValue),where=mesh.exteriorFaces) # Boundary Condition for Solver
timeStepDuration = 0.1
steps = 10
for step in range(steps):
eq.solve(var=T, dt=timeStepDuration) # doctest: +GMSH
if viewer is not None:
viewer.plot() # doctest: +GMSH
``

Answer 1

You've written that T.faceValue depends on T.faceValue, which depends on T.faceValue, which depends on T.faceValue, ... FiPy has dutifully provided you with the infinite loop that you requested.
Just write T.faceValue.constrain(Tu * (alp/lam) / (1 + alp/lam), where=mesh.exteriorFaces).
In the more likely event that you wanted to relate the gradient to the value at the boundary, please see the discussion on Robin conditions.