Coupling problem of heat transfer and diffusion

General
1

I am a beginner and I want to calculate The coupling problem of heat transfer and diffusion, where the diffusion coefficient is a function of temperature, by learning The FEniCS Tutorial II, I have written the following program, but there seem to be some problems, I think the program must have more than one problem, but I want to solve step by step, my program is as follows:

from fenics import *
import numpy as np
import matplotlib.pyplot as plt

# 定义已知表达式
kB = Constant(8.6e-5)  
r = Constant(0.3)  
Sext = Constant(0.0) 
fai = Constant(1e24) 
c_ini = Constant(0) 
c_evi = Constant(1)  

t_total = 10  
num_steps = 500   
dt = t_total / num_steps   

def D(T):   
    return 4.17e-7*exp(-0.39/(kB*T))

def KrW(T):    
    return 3.2e-15*exp(-1.16/(kB*T))

def KrCuCrZr(T):   
    return 2.9e-14*exp(-1.92/(kB*T))

mesh = Mesh('10_10_10s_slab/mesh.xml.gz')

W = FunctionSpace(mesh, 'P', 1)
V = FunctionSpace(mesh, 'P', 1)

class BoundaryX0(SubDomain):    
    def inside(self, x, on_boundary):
        return on_boundary and abs(x[0]-0.00)<DOLFIN_EPS

class BoundaryX1(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and abs(x[0]-0.01)<DOLFIN_EPS
    
class BoundaryY0(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and abs(x[1]-0.00)<DOLFIN_EPS

class BoundaryY1(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and abs(x[1]-0.01)<DOLFIN_EPS

bx0 = BoundaryX0()   
bx1 = BoundaryX1()
by0 = BoundaryY0()
by1 = BoundaryY1()

boundary_markers = MeshFunction('size_t', mesh, mesh.topology().dim()-1)  

#boundary_markers.set_all(9999)  
bx0.mark(boundary_markers, 0)   
bx1.mark(boundary_markers, 1)
by0.mark(boundary_markers, 2)
by1.mark(boundary_markers, 3)

ds = Measure('ds', domain=mesh, subdomain_data=boundary_markers)
        
T = Function(W)
c = Function(V)
c_n = Function(V)    # initial
v = TestFunction(V)

F = c*v*dx + dt*D(T)*dot(grad(c),grad(v))*dx - c_n*v*dx - dt*Sext*v*dx - dt*((1-r)*fai-KrW(T)*c**2)*ds(3) - dt*(KrCuCrZr(T)*c**2)*ds(2)
        
xdmffile_c = XDMFFile('10_10_10s_slab/diffusion.xdmf')

xdmffile_c.parameters["flush_output"] = True
xdmffile_c.parameters["functions_share_mesh"] = True
    
timeseries_T = TimeSeries('10_10_10s_slab/temperature_series')

progress = Progress('Time-stepping', num_steps)
t = 0

for n in range(num_steps):
    t += dt
    
    timeseries_T.retrieve(T.vector(), t)
    
    solve(F == 0, c)
    plot(c)
    
    xdmffile_c.write(c, t)
   
    c_n.assign(c)
    
    set_log_level(LogLevel.PROGRESS)
    progress += 1
    set_log_level(LogLevel.ERROR)

When I run the above program, I get the following error:

ArityMismatch: Integrand arguments () differ from form arguments (Argument(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 353), FiniteElement('Lagrange', triangle, 1)), 0, None),).
2

These terms do not have a v in them, which they should

3

Thank you for your answer, I was too careless, the program can actually run normally now, I will run it first to see the result, thank you again!