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 m
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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 so
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 s
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 f
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. Becaus
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, a
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.
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