Stackoverflow answer, https://stackoverflow.com/questions/57937418/how-to-write-equation-terms-with-independent-variable-in-fipy

tmp.py

from fipy import Variable,FaceVariable,CellVariable,Grid1D,ImplicitSourceTerm,TransientTerm,DiffusionTerm,Viewer,ConvectionTerm
from fipy.tools import numerix

import math

D = 1
c0 = 1
ka = 1
r0 = 1

nx = 100
dx = 2*math.pi/100
mesh = Grid1D(nx=nx, dx=dx)
conc = CellVariable(name="concentration", mesh=mesh, value=0., hasOld=True) # This is the "phi" in the docs
valueLeft = c0
valueRight = 0
conc.constrain(valueRight, mesh.facesRight)
conc.constrain(valueLeft, mesh.facesLeft)
timeStepDuration = 0.9 * dx**2 / (2 * D)
steps = 100
show_per_steps = 50

A = 1 / (r0**2 * numerix.sin(mesh.x)[0])
dA = -(numerix.cos(mesh.x)[0])/(r0**2 * numerix.sin(mesh.x)[0]**2)
dsindA = (numerix.cos(mesh.x)[0])**3/(numerix.sin(mesh.x)[0])**2
eqX = TransientTerm() + ImplicitSourceTerm(ka) == DiffusionTerm(D*A*numerix.sin(mesh.x)) - ConvectionTerm(D*dA*numerix.cos(mesh.cellCenters))+ D*conc*dsindA

sweeps = 3

from builtins import range
for step in range(steps):
    conc.updateOld()
    for sweep in range(sweeps):
        res = eqX.sweep(var=conc, dt=timeStepDuration)
        print(res)
    if __name__ == '__main__' and step % show_per_steps == 0:
        viewer = Viewer(vars=(conc), datamin=0., datamax=c0)
        viewer.plot()