Heat Transfer I ENGR 6901 Fall, Dr. Y.S. Muzychka ER 4021

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1 1 Heat Transfer I ENGR 6901 Fall, 2014 Dr. Y.S. Muzychka ER 4021

2 Course Materials 2 Course Text: Fundamentals of Heat and Mass Transfer Bergman, Levine, Incropera and DeWiQ, 7 th EdiSon 6 th EdiSon is also OK, but some new problems added. Text went through a major revision for the 6 th. Text went through a minor revision for the 7 th. 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 2-4 PM Outside of this Sme, by appointment only. y.s.muzychka@mun.ca TA s: To be announced. Thermodynamics and Fluids texts are also helpful for addisonal material on fundamentals related to this course

3 Important Dates 3 Classes Begin: September, 3 rd, 2014 Midterm Break: October 13/14, 2014 October 16th, 2014 (Tuesday Schedule) Quizzes: October 17 th / November 12 th, 2014 Last Day of Classes: December 3 rd, 2014 Exams Begin: December 8 th, 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.

4 Course Grading 4 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%

5 Text SecSons for this Course Chapter 1 IntroducSon: Chapter 2 ConducSon: Chapter 3 1- D Steady ConducSon: Chapter 4 2- D Steady ConducSon: 4.3 Chapter 5 Transient ConducSon: Chapter 6 ConvecSon: Chapter 7 External Flow: Chapter 8 Internal Flow: Chapter 9 Natural ConvecSon: Chapter 12 RadiaSon: Chapter 13 RadiaSon Exchange: of 14 chapters, approximately 55% of text by secson topics, and by pages to read (?). 5

6 6 Heat Transfer I IntroducSon

7 What is Heat Transfer? 7 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.

8 Three Modes of Heat Transfer 8 ConducSon ConvecSon T 2 T 1 RadiaSon

9 Three Modes of Heat Transfer 9 Systems with ConducSon, ConvecSon, and RadiaSon We will examine individual mode problems and muls- mode problems.

10 Three Modes of Heat Transfer 10 Fourier s Law Newton s Law Stefan- Boltzmann Eqn. # q''= k T T q'' & 1 = σt 4 4 1, q'' 2 = σt % ( q''= h( T $ L ' s T ) q'' 12 = σ T 4 4 ( 1 T 2 )

11 ConducSon Heat Transfer 11 Fourier s Law q''= k dt dx k $ T T ' 2 1 & ) % L ( " W % m 2 # $ &' # q = ka T T & # 2 1 % ( = ka T T & 1 2 % ( $ L ' $ L ' k is the thermal conducsvity and depends on the type of material separasng the two surfaces: Metals ~ W/mK Non- Metals ~ W/mK Liquids ~ W/mK Gases ~ W/mK [ W ]

12 ConducSon Heat Transfer 12

13 ConvecSon Heat Transfer 13 Newton s Law of Cooling q''= h( T s T ) " W % m 2 # $ &' q = ha( T s T ) [ W ] h is the convecson heat transfer coefficient and depends on many things: Process Fluid ProperSes Geometry LocaSon

14 ConvecSon Heat Transfer Convec6on Heat Transfer is controlled by a thin hydrodynamic fluid layer at the heat transfer surface. 14 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)

15 RadiaSon Heat Transfer ( ) Stefan- Boltzmann EquaSon q'' rad = σ T 4 4 s T " sur W % m 2 # $ &' σ = is the Stefan- Boltzmann constant 8 [ W /m 2 K 4 ] " % More generally, we write: ( ) # $ ( ) W q'' rad = σε T 4 4 s T sur q rad = σεa T 4 4 s T sur W m 2& ' 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] [ ] 15

16 RadiaSon Heat Transfer A black body emits thermal radiason according to: E b = σt s 4 or A body also receives or absorbs thermal radiason according to (α is the absorpsvity): 4 G abs = αg = ασt sur E = εe b = εσt s 4 For a simple engineering surface where (ε = α) or a grey surface as it is called, we have: 16 q'' rad = εe b αg or q'' rad = εσ( T 4 4 s T ) sur Radiant exchange is generally more complex as we shall see later. There are surfaces where α ε.

17 RadiaSon Heat Transfer Radia6on Heat Transfer is the most complex mode of heat transfer. 17 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.

18 RadiaSon Heat Transfer 18

19 RadiaSon Heat Transfer 19

20 ConservaSon of Energy Since we are dealing with the transfer of energy, we will be uslizing the First Law of Thermodynamics extensively. 20 Closed System Open System

21 Rate Balance " time rateof change % $ ' $ of energy contained ' $ within thecontrol ' $ ' # volume at time t & ConservaSon of energy is also frequently used in the following form using enthalpy h: de CV dt ConservaSon of Energy CV = Q CV W CV + " net rateof energy% $ ' transferred in = $ ' $ as heat transfer ' $ ' # at time t & inlets m i Q " net rateof energy% $ ' $ transferred out ' # $ aswork at time t & ' W $ h i + V 2 i 2 + gz ' & i) % ( " net rateof energy % $ ' $ transferint othe ' + $ control volume ' $ ' $ accompanying mass ' # $ flow through ports &' exits m e $ h e + V 2 e 2 + gz ' & e) % ( 21 Closed System de CV dt = Q CV W CV or ΔE CV = Q CV W CV E = KE + PE +U

22 Surface Balances 22 We frequently rely on surface balances in calculasons: '' q cond E in = E out '' = q conv '' + q rad

23 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. 23 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/m 2 ] is heat flux. q [W/m 3 ] is heat transfer per unit volume. Note: I somesmes (occasionally or frequently) use Q [W] and q [W/m 2 ] 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.

24 Example 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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