3
Laminar Internal Flow
Exercises
1. Consider laminar ow between two parallel plates. The ow is incompressible, has constant properties,
and is fully developed.
(a) Derive the velocity prole and the mean velocity.
(b) Derive the Nusselt number for the con
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3
Numerical Methods for Convection
The topic of computational uid dynamics (CFD) could easily occupy an entire semester indeed, we have
such courses in our catalog. The objective here is to examine some of the basic features of solving, via
numerical mean
2
A Mathematica Primer
2.1
Basics
Mathematica is a very powerful package for performing symbolic and numerical mathematics. It has a fairly
steep learning curve, and takes some patience and involves some frustration to become adept at using it.
My experie
5
Laminar Internal Flow
5.1
Governing Equations
These notes will cover the general topic of heat transfer to a laminar ow of uid that is moving through an
enclosed channel. This channel can take the form of a simple circular pipe, or more complicated geom
5
Laminar External Flow
5.1
The boundary layer
A boundary layer is an easy physical concept to grasp; it is the result of the noslip boundary condition
as uid ows over the surface of an object. Because of viscosity, the uid directly adjacent to the object
Thanksgiving break problem
This problem will be part of the nal exam, so you are instructed to work the problem entirely on your own.
I will assign the rest of the nal exam problems after the break, and they will be due the last day of nals
week.
The situ
mech7220-hw3-solns.nb
1
In[239]:= Remove@"Global`"D
In[240]:= Off@General:"spell1", General:"spell"D
sp@x_ D := Simplify@PowerExpand@xDD
con@x_ D := x . Complex@0, n_ D Complex@0, nD
fs@x_ D := FullSimplify@xD
fs@x_, b_ D := FullSimplify@x, bD
Here are th
1
Conservation Equations
Exercises
1. Fill in the details in the derivation of Eq. (12) from Eq. (11).
( u) +
t
(u u) =
u
+u
t
+
t
(u) + (u
)u =
Du
Dt
=0
2. Derive Eq. 14 beginning with Eq. 13.
Apply the divergence theorem to Eq. (13):
t
u2
2
e+
u
+
MECH 7220/26 Convection heat transfer: Fall 2010
Instructor:
Daniel W. Mackowski
344 Ross, 844-3334, mackodw@auburn.edu
oce hours MWF 2:003:00, TH 1:00-3:00
Text:
Convective Heat Transfer, Adrian Bejan,
Supplemental notes and reading assignments will be a
1
1.1
Conservation Equations
Conservation of mass
Mass conservation states that the net rate of change of the mass of a control volume (CV) is equal to the
net rate of transport across the boundary of the CV. In vector form,
d
dt
n u dA = 0
dV +
V
(1)
A