Course Materials. • Course Text: Fundamentals of Heat and Mass Transfer. –
Bergman, Levine, Incropera and DeWif, 7th Edi(on. – 6th Edi(on is also OK, but ...
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Heat Transfer I ENGR 6901 Fall, 2014 Dr. Y.S. Muzychka ER 4021
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
What is Heat Transfer?
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• 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 Q ˙ 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˙ .
Three Modes of Heat Transfer ConducSon
ConvecSon
T2
T1
RadiaSon
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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 Fourier’s Law
Newton’s Law
#T − T & q'' = −k% 2 1 ( $ L '
q'' = h (Ts − T∞ )
Stefan-‐Boltzmann Eqn. q''1 = σT14 , q''2 = σT24
q''12 = σ(T14 − T24 )
€
€
€
€
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ConducSon Heat Transfer • Fourier’s Law q'' = −k
€
$T − T ' dT ≈ −k& 2 1 ) % L ( dx
#T − T & #T − T & q = −kA% 2 1 ( = kA% 1 2 ( $ L ' $ €L '
"W % 2 #$ m &'
[W ]
• k is the thermal conducSvity and € depends o n t he t ype 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
ConducSon Heat Transfer
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ConvecSon Heat Transfer • Newton’s Law of Cooling
q'' = h (Ts − T∞ )
"W % $# m 2 '&
q = hA(Ts − T∞ )
[W ]
€
• h is the convecSon heat transfer coefficient and € € depends on many things: €
– Process – Fluid ProperSes – Geometry – LocaSon
ConvecSon Heat Transfer • Convec6on Heat Transfer is controlled by a thin hydrodynamic fluid layer at the heat transfer surface. • A thermal boundary layer is also present and can be smaller, larger or equal in thickness to the hydrodynamic boundary layer. • ConvecSon Heat Transfer coefficients are someSmes called “film coefficients” as a result. • ConvecSon Heat Transfer is classified according to: – Single Phase versus Two Phase (boiling/condensaSon) – External Flow versus Internal Flow – Forced Flow (pressure driven flow) versus Natural Flow (density driven flow)
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€
• • • •
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RadiaSon Heat Transfer
Stefan-‐Boltzmann EquaSon q''rad = σ(Ts4 − Tsur4 ) "$#W m %'& σ = 5.67 × 10 −8 [ W /m 2 K 4 ] is the Stefan-‐Boltzmann constant More generally, we write: q''rad = σε (Ts4 − Tsur4 ) "$#W m %'& 2
€
€
4 qrad = σεA(Ts4 − Tsur )
2
[W ]
ε is the surface emissivity (a property). We will examine € € When ε = 1 we this later in more detail. have a “black body” € € • T must be in Kelvin [K]
RadiaSon Heat Transfer • A “black body” emits thermal radiaSon according to: E b = σTs4
or
E = εE b = εσTs4
• A body also receives or absorbs thermal radiaSon according to (α is the absorpSvity): 4 € = αG = ασTsur Gabs
€
• For a simple engineering surface where (ε = α) or a “grey surface” as it is called, we have: €
q''rad = εE b − αG
or
4 q''rad = εσ(Ts4 − Tsur )
• Radiant exchange is generally more complex as we α ≠ ε . shall s ee l ater. T here a re s urfaces w here € €
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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”.
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RadiaSon Heat Transfer
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RadiaSon Heat Transfer
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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
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ConservaSon of Energy • Rate Balance
" net rateof energy % "time rateof change % " net rateof energy % $ ' transfer int o the $ ' $ ' "net rateof energy % $ ' $of energy contained ' = $ transferred in ' − $transferred out ' + $control volume ' ' $within thecontrol ' $ as heat transfer ' $ $ ' $ ' $ ' $#as work at time t '&W˙ $ accompanying mass ' #volume at time t &CV # at time t &Q˙ $# flow through ports '&
• ConservaSon of energy is also frequently used in the € following form using enthalpy h: dECV = Q˙ − W˙ + ∑ m˙ $& h + Vi2 + gz ') − ∑ m˙ $& h + Ve2 + gz ') CV CV i i i e e e dt 2 2 % ( % ( inlets exits • Closed System €
dE CV = Q˙ CV − W˙ CV dt
or
E = KE + PE + U €
€
ΔE CV = QCV − WCV
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Surface Balances • We frequently rely on surface balances in calculaSons:
E˙ in = E˙ out q''cond = q''conv + q''rad
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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: – q [W] is heat transfer rate [W = J/s]. – q' [W/m] is heat transfer per unit length. – q'' [W/m2] is heat flux. € – q˙ [W/m3] is heat transfer per unit volume. € I someSmes (occasionally or frequently) use Q [W] and q [W/m2] along with Note:
€
€
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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