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Heat Transfer I ENGR 6901 Fall, 2014
Dr. Y.S. Muzychka ER 4021
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Course Materials • Course Text: Fundamentals of Heat and Mass Transfer – Bergman, Levine, Incropera and DeWiQ, 7th EdiSon – 6th EdiSon is also OK, but some new problems added. – Text went through a major revision for the 6th. – Text went through a minor revision for the 7th. – Most content is covered the same in earlier ediSons.
• Course Notes and Handouts • Most Course Material to be posted on Webpage • Power Point will posted every week or two • Office Hours: Wednesday’s @ 2-‐4 PM
– Outside of this Sme, by appointment only. • Email: [email protected] • TA’s: To be announced. • Thermodynamics and Fluids texts are also helpful for
addiSonal material on fundamentals related to this course
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Important Dates • Classes Begin: September, 3rd, 2014 • Midterm Break: October 13/14, 2014 • October 16th, 2014 (Tuesday Schedule) • Quizzes: October 17th / November 12th , 2014 • Last Day of Classes: December 3rd, 2014 • Exams Begin: December 8th, 2014 • Tuesday’s: Tutorial is a must! – There is slightly more material to cover in this one core course offering of Heat Transfer, therefore we must rely on tutorials for extra problems.
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Course Grading • Quizzes (2): 40% • Final Exam: 60% • Grade will be based on this scheme or a redistribuSon of my choosing provided that: – 40%/60% < Final Grade < 30%/70%
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Text SecSons for this Course • Chapter 1 – IntroducSon: 1.1-‐1.5 • Chapter 2 – ConducSon: 2.1-‐2.4 • Chapter 3 – 1-‐D Steady ConducSon: 3.1-‐3.6 • Chapter 4 – 2-‐D Steady ConducSon: 4.3 • Chapter 5 – Transient ConducSon: 5.1-‐5.7 • Chapter 6 – ConvecSon: 6.1-‐6.7 • Chapter 7 – External Flow: 7.1-‐7.5 • Chapter 8 – Internal Flow: 8.1-‐8.5 • Chapter 9 – Natural ConvecSon: 9.1-‐9.6 • Chapter 12 – RadiaSon: 12.1-‐12.8 • Chapter 13 – RadiaSon Exchange: 13.1-‐13.3
– 10 of 14 chapters, approximately 55% of text by secSon topics, and by pages to read (?).
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Heat Transfer I IntroducSon
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What is Heat Transfer? • Heat Transfer is the study of how energy is transferred through a temperature difference.
• Heat transfer is classified according to three fundamental modes: Conduc6on, Convec6on, and Radia6on.
• In Thermodynamics we always worked with a heat transfer given, but in this course we learn how to calculate it.
• In Thermodynamics we worked with macro-‐ energy balances. In this course we will uSlize micro-‐ (differen6al) energy balances, to obtain relaSonships to obtain .
€
˙ Q
€
˙ Q
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Three Modes of Heat Transfer ConducSon ConvecSon
RadiaSon
T2
T1
8
Three Modes of Heat Transfer Systems with ConducSon, ConvecSon, and RadiaSon
• We will examine individual mode problems and mulS-‐mode problems.
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Three Modes of Heat Transfer
€
q' '= −k T2 −T1L
#
$ %
&
' (
€
q' '= h Ts −T∞( )
€
q' '1 =σT14, q' '2 =σT2
4Fourier’s Law Newton’s Law Stefan-‐Boltzmann Eqn.
€
q' '12 =σ T14 −T2
4( )
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ConducSon Heat Transfer • Fourier’s Law
• k is the thermal conducSvity and depends on the type of material separaSng the two surfaces: – Metals ~ 10 – 400 W/mK – Non-‐Metals ~ 0.1 – 500 W/mK – Liquids ~ 0.1 – 10 W/mK – Gases ~ 0.01 – 0.1 W/mK
€
q' '= −k dTdx
≈ −kT2 −T1L
$
% &
'
( )
€
q = −kA T2 −T1L
#
$ %
&
' ( = kA
T1 −T2L
#
$ %
&
' (
€
Wm2
" # $
% & '
€
W[ ]
11
ConducSon Heat Transfer 12
ConvecSon Heat Transfer • Newton’s Law of Cooling
• h is the convecSon heat transfer coefficient and depends on many things: – Process – Fluid ProperSes – Geometry – LocaSon
€
q' '= h Ts −T∞( )
€
q = hA Ts −T∞( )€
Wm2
" # $
% & '
€
W[ ]
13
ConvecSon Heat Transfer • Convec6on Heat Transfer is controlled by a thin hydrodynamic fluid layer at the heat transfer surface.
• A thermal boundary layer is also present and can be smaller, larger or equal in thickness to the hydrodynamic boundary layer.
• ConvecSon Heat Transfer coefficients are someSmes called “film coefficients” as a result.
• ConvecSon Heat Transfer is classified according to: – Single Phase versus Two Phase (boiling/condensaSon) – External Flow versus Internal Flow – Forced Flow (pressure driven flow) versus Natural Flow (density driven flow)
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RadiaSon Heat Transfer • Stefan-‐Boltzmann EquaSon • is the Stefan-‐Boltzmann constant • More generally, we write: • ε is the surface emissivity (a property). We will examine
this later in more detail. When ε = 1 we have a “black body”
• T must be in Kelvin [K]
€
q' 'rad =σ Ts4 −Tsur
4( )
€
σ = 5.67 ×10−8 W /m2K 4[ ]
€
q' 'rad =σε Ts4 −Tsur
4( )€
Wm2
" # $
% & '
€
Wm2
" # $
% & '
€
qrad =σεA Ts4 −Tsur
4( )
€
W[ ]
15
• A “black body” emits thermal radiaSon according to:
• A body also receives or absorbs thermal radiaSon according to (α is the absorpSvity):
• For a simple engineering surface where (ε = α) or a “grey surface” as it is called, we have:
• Radiant exchange is generally more complex as we shall see later. There are surfaces where .
RadiaSon Heat Transfer
€
Eb =σTs4
€
Gabs = αG = ασTsur4
€
q' 'rad = εσ Ts4 −Tsur
4( )
€
E = εEb = εσTs4
or
€
q' 'rad = εEb −αG or
€
α ≠ ε
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RadiaSon Heat Transfer • Radia6on Heat Transfer is the most complex mode of heat transfer.
• Thermal radiaSon can be absorbed, reflected, and transmiQed by a body.
• Thermal radiaSon is an electromagneSc wave phenomena similar to light.
• Surface properSes depend on spectral (wave length) and direcSonality (specular or diffuse) characterisScs.
• Radiant exchange between surfaces can be quite complicated.
• Thermal radiaSon is a “line of sight” transfer process and requires “view factors”.
17
RadiaSon Heat Transfer 18
RadiaSon Heat Transfer 19
ConservaSon of Energy • Since we are dealing with the transfer of energy, we will be uSlizing the First Law of Thermodynamics extensively.
Closed System
Open System
20
• Rate Balance
• ConservaSon of energy is also frequently used in the following form using enthalpy h:
• Closed System
€
dECV
dt= ˙ Q CV − ˙ W CV + ˙ m i
inlets∑ hi +
Vi2
2+ gzi
$
% &
'
( ) − ˙ m e
exits∑ he +
Ve2
2+ gze
$
% &
'
( )
€
dECV
dt= ˙ Q CV − ˙ W CV
€
ΔECV =QCV −WCVor
€
E = KE + PE +U
€
time rateof changeof energy containedwithin thecontrolvolume at time t
"
#
$ $ $ $
%
&
' ' ' '
CV
=
net rateof energytransferred inasheat transferat time t
"
#
$ $ $ $
%
&
' ' ' '
˙ Q
−
net rateof energytransferredoutaswork at time t
"
#
$ $ $
%
&
' ' ' ˙ W
+
net rateof energytransfer int o thecontrol volumeaccompanyingmassflow through ports
"
#
$ $ $ $ $ $
%
&
' ' ' ' ' '
ConservaSon of Energy 21
Surface Balances
€
˙ E in = ˙ E out
qcond'' = qconv
'' + qrad''
• We frequently rely on surface balances in calculaSons:
22
Units and NotaSon • Review the secSon on units carefully. We will use SI units in this course. Also be familiar with the various prefixes: micro, milli, nano, pico, etc.
• Finally, the text has adopted the following notaSon for heat transfer rates: – [W] is heat transfer rate [W = J/s]. – [W/m] is heat transfer per unit length. – [W/m2] is heat flux. – [W/m3] is heat transfer per unit volume.
€
˙ q
€
q' '
€
q'
€
q
Note: I someSmes (occasionally or frequently) use Q [W] and q [W/m2] along with Q/L [W/m]. Its old school and I’m older (than you)! Just check the equaSons for the presence of the area A or lack thereof.
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Example -‐ 1 • Consider the three modes of heat transfer: conducSon, convecSon, and radiaSon, from the perspecSve of the basic laws. Let’s examine: – i) convecSon/conducSon balance for a boundary layer, and
– Ii) the concept of an equivalent radia6on heat transfer coefficient, and
– iii) how the radiaSon heat transfer coefficient varies under ideal condiSons.
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