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CHME 333 Workbook
Chapter 3 – Onedimensional, Steady State Conduction
•
Objectives
o
Become very familiar with the HDE in different coordinate systems and how to
integrate it and then apply boundary conditions
o
Understand the concept of
_________________
and how you can use it to simplify
calculations involving composite materials
o
Understand the concept of
_________________
when dealing with composite
materials
o
Understand how to account for
_______________________________
in materials
o
Apply the above concepts to the special case of
______________________
___________________
.
•
Introduction
o
In Chapter 2 we derived the Heat Diffusion equation for the three coordinate
systems and applied it to several applications for the calculation of temperature
profiles and heat transfer rates.
In Chapter 3, we will narrow our focus a bit more
to look at the special cases of onedimensional, steady state conduction.
These
simplifications are very prevalent in heat transfer applications, and the
mathematics of the solution processes are very simple.
The first part of the chapter
will review the general HDE for the three geometries and also introduce the
concept of
thermal resistance
.
The use of
thermal resistance
for systems of
composite materials will greatly simplify the mathematical analysis.
Next, we will
consider how
uniform internal heat generation
affects the HDE solution.
Finally,
we will consider a
major
application of heat transfer – heat transfer from
extended
surfaces (fins)
.
This chapter is one of the longest chapters in the text, and it will
likely take 2 weeks to cover all the material.
Getting a good grasp on this material
is important.
I would rank Chapter 3 as one of the most important chapters of the
text.
•
Review
– solving conduction problems
o
____________________________________
o
____________________________________
o
____________________________________
(Preview – we’re going to do the same thing when we get to mass transfer, only we’ll be
solving for a concentration distribution and applying Fick’s Law)
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p
TTT
T
kkk
q
c
xx
yy
zz
t
ρ
⎛⎞
∂∂
∂
+++
=
⎜⎟
∂
⎝⎠
•
•
Plane Wall between two fluids of different temperature:
o
Assumptions
±
________________________
±
________________________
±
________________________
±
________________________
o
Heat Diffusion Equation
Simplifies to
±
Integrate twice to get general solution:
±
Apply Boundary Conditions
•
±
Specific Solution:
•
Temperature varies ___________
with position
o
Now plug the Temp distribution into ______________
to get the heat transfer rate
±
Heat transfer rate (and flux) is _____________
, independent of x
3
•
Thermal Resistance
– analogous to electrical resistance you learned in Physics
o
Ohms Law:
o
Thermal Resistance to
Conductive
Heat Transfer
±
kA
L
q
T
T
R
x
s
s
cond
t
=
−
=
2
1
,
=
transport
of
rate
Force
Driving
o
Thermal Resistance to
Convective
Heat Transfer
±
=
transport
of
rate
Force
Driving
o
Thermal Resistance to
Radiation
Heat Transfer
±
A
h
q
T
T
R
r
rad
sur
s
rad
t
1
,
=
−
=
(refer to Chapter 1 for
h
r
definition)
o
These equations should be memorized – it will save time during exams
o
What are the units of thermal resistance?
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This note was uploaded on 03/11/2011 for the course CHEME 333 taught by Professor Anthony during the Spring '11 term at UNL.
 Spring '11
 Anthony

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