Homework Set #9:
Problem #1:
Read the statement of Problem 10.B.4 in BSL, but do NOT answer questions (a) and (b) in the
text. Answer the followings:
(a) Use shell energy balance to derive a differential equation for temperature T.
(b) Show that the diffe

Homework Set #10:
Problem # 1:
The crude oil with temperature-independent physical properties is in fully developed laminar
flow between two flat surfaces placed a distance 2B apart. For z < 0 the fluid is uniform at T =
T1. For z > 0 heat is added at a c

Homework Set #8:
Problem #1:
A large, rectangular solid, of thickness L in the y direction and infinite in the x and z directions,
is perfectly insulated on one surface (y = 0), and the opposite face (y = L) is maintained at
temperature T0. There is no el

Shell Energy Balance
Energy conservation for homogeneous media
Energy influxes (inward arrows)
y
P(x,y,z)
P(x y z)
z
x
Heat source
Energy outfluxes (outward arrows)
Energy balance for an unsteady-state system
Rate of
energy in
Rate of work
by forces
Rate

Shell Momentum Balance for Steady Laminar Flow
Definitions of momentum fluxes
Molecular momentum transfer
Fluid at rest: static pressure p is due to momentum transfer among
molecules in random motion.
Fluid in motion: viscous stress is due to molecular

An Introduction to Rheology
Basic concepts and definitions
Rheology: defined as the science of deformation and flow
Rheometry: concerned with measurements of stress and strain of materials in
simple or complex deformation/flow geometry
Simple deformation

Equations of Change for Isothermal Systems
The equation of continuity (or mass balance equation)
Mass influx
(inward arrows)
Mass balance over a fixed control volume
y
x y z
x z
ux
x
uy
x y
z
x
t
t
z
uz
z
y
.u
For incompressible fluids:
z
y
uy
ux
x
t
y
uz

PGE 322K
TRANSPORT P ENOMEN IN
NSPO
PHENOMENA N
GEOSYSTEMS ENGINEERING
Dr. Quoc. P. Nguyen
The University of Texas at Austin
Cockrell School of Engineering
Department of Petroleum Engineering and Geosystems
Shell
1
Funded Research Program
Enhanced Oil Rec

Mechanisms of Energy Transfer
Mechanisms of energy transfer
Energy transfer by work
p
xx
xy
p
yx
zx
xz
yy
yz
p
zy
zz
Energy influxes (inward arrows)
y
P(x,y,z)
z
x
Heat sources
Energy outfluxes (outward arrows)
Mechanisms of Energy Transfer
Mechanisms of

Homework Set #4:
Problem #1:
A. A non-Newtonian power-law fluid is contained between infinite, parallel, horizontal flat
plates separated by a distance . The top plate is moving in the x direction with velocity V.
The bottom plate is fixed in place.
0 x
t

Problem #2:
An incompressible solution flows with rectilinear flow in the x direction;
y
x
(Z direction perpendicular to page)
for this system, identify the correct answer(s) below
Answer:
b. vy = 0
c. vz = 0
d. vxvx|x=0 = vxvx|x=L
e. vyvy|y=0 = vyvy|y=
f

Non-isothermal Equations of change
Energy conservation for homogeneous media
Total energy balance
t
(EK
U)
U )u
.( E K
. pu
.q
. .u
u.g
S
: u
u.g
Kinetic energy balance
EK
t
. uEK
. pu
p
.u
. .u
Internal energy balance
t
( U)
.( U u )
.q
p
.u
:
S
u
Non-is