This preview shows pages 1–2. Sign up to view the full content.
10.34 – Fall 2006
Homework #8
Due Date: Wednesday, November 1
st
, 2006 – 9 AM
Problem 1:
Solve 6.B.1 in Beers’ (pg. 432) by GMRES, using sparse representation of the large
matrix. Note that you may have to restart GMRES after a few iterations, and also things
may work better if you precondition the matrix. Your Matlab program should take T
0
,T
1
,
lambda, rho, C
P
, Re, mu, and R as inputs.
Please run your program for the case (you do
not need to answer specific questions ask in Beers’ book, only the ones asked here):
T
0
= 300 K
T
1
= 400 K
λ
= 0.6 W/mK
ρ
= 1 g/cm
3
C
P
= 4 J/gK
Re = 100
μ
= 0.5 cP = 0.5 x 10
3
Ns/m
2
R = 5 cm
Generate following plots (over a range that shows all dynamics):

A 3D surface plot and 2D contour/pcolor plot of the velocity field

A plot showing the T(z) for r = 0, 1, 2, 3, 4 cm (all on the same figure)
Hints and notes:
The flow in the problem and the ambiguous boundary conditions in the z
direction create a problem: how can we define the axial boundary conditions?
This is a place
where the scaling analysis you have learned in transport can be important.
We know that at 
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '04
 ClarkColton

Click to edit the document details