Hi,
i would like to reproduce the analytical solution for Couette flow with temperature-dependent viscosity and i am getting a wrong result...
The setup is described in Turcotte and Schubert: Geodynamics, page 313. It is a steady flow between two boundaries, the left boundary moves with velocity v0 and has temperature T0, right boundary is fixed and has temperature T1. There are no heat sources, so the temperature profile is linear. Viscosity is C*exp(E/RT), where C,E and R are constants.
The solution should be
v/v0 (x)=(exp( (-E*(T1-T0))/(R * T0**2)*(1-x/h) )-1) / (exp( (-E*(T1-T0))/(R * T0**2) ) -1)
where h is the distance between the boundaries, 0<x<h.
I use
h=1,C=1, T0=1, T1=1.5, E=10, R=1, v0=1 (see attached sif-file). The result is quite different from the analytical solution (more like for E=6), but i don't know why... Any suggestions?
Thanks
Petra
Couette flow with temperature-dependent viscosity
Couette flow with temperature-dependent viscosity
- Attachments
-
- mesh.grd
- grd-file
- (595 Bytes) Downloaded 225 times
Re: Couette flow with temperature-dependent viscosity
Hi Petra,
using Maple to solve
d(exp(10/(1+x/2)*dv/dx)/dx=0
i get
v:=a+b*((2+x)*exp(-20/(2+x))-20*Ei(1,20/(2+x)))
with v(0)=1,v(1)=0 we have
a ~ 1.017288049, b ~ -2256.783772
evaluating this with x=[0,1] seems to agree with ElmerSolver results. Am i missing something?
-Juha
using Maple to solve
d(exp(10/(1+x/2)*dv/dx)/dx=0
i get
v:=a+b*((2+x)*exp(-20/(2+x))-20*Ei(1,20/(2+x)))
with v(0)=1,v(1)=0 we have
a ~ 1.017288049, b ~ -2256.783772
evaluating this with x=[0,1] seems to agree with ElmerSolver results. Am i missing something?
-Juha
Re: Couette flow with temperature-dependent viscosity
Hello Juha,
thank you very much for your answer. As always, you are right. The analytical solution is only approximate and (although shown in the book with these parameters) it is quite far from the correct solution in this case.
Thanks a lot again,
Petra
thank you very much for your answer. As always, you are right. The analytical solution is only approximate and (although shown in the book with these parameters) it is quite far from the correct solution in this case.
Thanks a lot again,
Petra