Dear all,
again I have a problem with a simple convection boundary condition in a heat
transfer problem. The problem will get more complicated later, but for
verification I set up a 2 D Mesh set to a fixed T at the bottom and having
convection boundary conditions at the top. The equation is just the steady
state conduction equation.
0= k (d^2T/dx^2+d^2T/dy^2)
the convection boundary condition should lead to:
dT/dy=h/k(Tinf-T)
(Tinf is a constant fluid Temperature, h the convection coeff. and k the
thermal conductivity)
The calculated surface temperature in my script depends on the value I
assign initially to T (T_bot -53 in the script). The simple analytical
result is calculated at the end, but I never get the correct result.
What am I doing wrong? (I first tried solve() before trying sweep()...)
Thanks for your help!
Burak
--------------
from fipy import *
#
L=0.02
H=0.005
dx=0.00025
dy = dx
nx = int(L/dx)
ny = int(H/dy)
L = dx * nx
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
#
T_bot = 500.
Tinf=300.
alph=100. #convection coefficient
D=1.5 #thermal conductivity
#
X, Y = mesh.faceCenters
#facesTopLeft = ( mesh.facesTop )#& (X < L *.1))
facesBottomLeft = ( mesh.facesBottom)# & (X <=2*dx))
T = CellVariable(name = "solution variable",
mesh = mesh,value=T_bot-53, hasOld=1)
#
#One heated position at the bottom (later, at the moment all is heated)
T.constrain(T_bot, facesBottomLeft)
#cooling on the top due to convection
T.faceGrad.constrain((alph/D*(Tinf-T.faceValue.value)*
mesh.faceNormals),where=mesh.facesTop)
eq = DiffusionTerm(coeff=D)
#
viewer=Viewer(T)
#
res=1e10
co=0
while co<1e1:
res=eq.sweep(var=T,dt=1e5)
co+=1
print res,co#eq.solve(var=T)
#
ma,mi=max(T.faceValue),min(T.faceValue)
print "Max,Min",ma,mi,ma-mi
viewer.plot()
Bi=alph*H/D
Ts=(T_bot+Tinf*Bi)/(1+Bi)
print Ts,"expected surface value",T_bot-Ts,Ts-Tinf,Bi
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