Heat and Mass Transfer

515 Pages·080.83 MB·English

by  S. Senthil

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I _
[ ANNA UNIVERSITYSYLLABUS
ME1351:HEATAND MASS TRANSFER _ CONTENTS
:201l4f
hanical Engineering -(R'egulation
ForB.E.VISemester Mec -- --- ,
CHAPTER 1: CONDUCTION
~H;at
l.CO~OU,~TlONt_ Mechanism of Heat Transfer - Conduction Transfer 1.1
ConvBaeScItCio.nCoanncdep!)Rad-iation - General ..Di.f.f.erential equatiodnC 0I'f H.eat' . 1.1.1. Modes of Heat Transfer _ I.I
ConduUciCillon- FOllrl'er Law of Conduction - Cartesian an y m.dncal 1.1.2. Fourier Law of Conduction ...1.2
Coord·lilates - One Dimensional Steady State Heat .Conduction - 1.1.3. General Heat Conduction Equation in
Conduction through Plane Wall, Cylinders and Spherical Systems _ Cartesian Co-ordinates . 1.2
Composite Systems - Conduction with Internal Heat Generation _ 1.1.4. General Heat Conduction Equation in
Cylindrical Co-ordinates 1.9
Extended Surfaces - Unsteady Heat Conduction - Lumped Analysis _
1.1.5. Conduction of Heat through aSlab or Plane Wall.. .1.14
Useof Heislers Chart.
1.1.6. Conduction of Heat through a Hollow Cylinder 1.16
2.CONVECTION
1.1.7. Conduction of Heat through a Hollow Sphere 1.17
Basic Concepts - Convective Heat Transfer Coefficients - Boundary
1.1.8. Newton's Law ofCooling........................ . 1.19
Layer Concept - Types of Convection - Forced Convection _
1.1.9. Heat Transfer through aComposite Plane Wall
Dimensional Analysis - External Flow - Flow over Plates, Cylinders and
with inside and Outside Convection 1.19
Spheres - Internal Flow - Laminar and Turbulent Flow - Combined
1.1.10. Heat Transfer through Composite Pipes (or) Cylinders
Laminar and Turbulent - Flow over Bank of tubes - Free Convection _
with Inside and Outside Convection 1.22
Dimensional Analysis - Flow over vertical plate, Horizontal plate,
Inclined plate, Cylinders and Spheres. 1.1.11. Solved Problems 0" Slabs 1.25
3. PHASE CHANGE HEAT TRANSFER AND HEAT 1.1.12. Soilled University Problems 011Slabs 1.74
EXCHANGERS 1.1.13. Solved Problems 011 Cylinders 1.111
Nusselts theory of condensation - Pool boiling, flow boiling, 1.1.14. Solved University Problems 011 Cylinders 1.144
correlations in boiling and condensation. Types of Heat Exchangers _ 1.1.15. SO/liedProblems 011 Hollow Sphere 1.160
1.2. Critical Radius of Insulation 1.167
LMTD Method of Heat Exchanger Analysis -- Effectiveness _ NTU
I? I Critical Radius of Insulation for aCylinder 1.167
method of Heat Exchanger Analysis - Overall Heat Transfer Coefficient _ 1:2:2:
Fouling Factors. Solved Problems 1.169
4.RADIATION 1.3. Heat Conduction with Heat Generation 1.179
1.3.1. Plane Wall with Internal Heat Generation 1.179
Basic Concepts, Laws of Radiation - Stefan Boltzman Law, Kirchoff
1.3.2. Cylinder with Internal Heat Generation 1.183
Law - Black Body Radiation - Grey Body Radiation Shape Factor
1.3.3. Internal Heat Generation - Formulae Used 1.185
Algebra - Electrical Analogy - Radiation Shields - Introduction to Gas
Radiation. 1.3.4. Solved Problems 011 Plane Willi with Internal
5.MASS TRANSFER Heat Generation 1.187
1.3.5. Solved Problems 011 Cylinder with
Basic Concepts - Diffusion Mass Transfer - Fick's law of diffusion _
Internal Heat Generation 1.196
Steady State Molecular Diffusion - Convective Mass Transfer _
1.3.6. Solved Problems OilSphere with
Momentum, Heat and Mass Transfer Analogy _ Convective Mass
Transfer Correlations. lnternul Heat Generation 1.202
T;~~·~·~t~·Fi;~..:~::·::·:.:::·:.:·:.::·::·.::::.::.::=::::::::':::::::::~::~~
Note :.(Use of Standard Heat and Mass Transfer Data Book is 1.4. ~.i:SI.
pernulled 117the University Examination).
1.4.2. Temperature Distribution and Heat
Dissipation in Fin . 1.206
1.4.3. Application......... . 1.21
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1.4.'-l. Fill Ftliciellc)' ··. ..1.217 ('onteuts (.3
1.~.5. Fin rfkcriVt'ness. " ..1.217
1.~.6. Ftll"lllllllicUsed..... . 1.2IS 2.4.3. Free (or) Natural Convection . 2.9
IA.7. So/I't!d Proh/ellH" 1.219 2.4.4. Forced Convection .. ..2.10
1.4.8. SII/I'd U"itl(!f.5i~I' Prublctn« 1.245 2.5. The Local and Average Heat Transfer Coefricients for
1.4.9. Pr()hkllll/Or Practice ················ ..· 1.263 Flat Plate - Laminar Flow 2.10
15. Transient Heat Condul~tioll (or) Unsteady State 2.6. The Local and Average Heat. Transfer Coefficients for
Conduction 1.264 Flat Plate-Turhulcnt Flow 2.13
2.6.1. lleat Transfer ocificient for Combination of
1.5.I. l3ior Number . . 1.264
1.5.:? Lumped Heat Anal)' is . 1.266 Laminar and Turbulent Flow... .. 2.15
2.7. Boundary Layer Thickness, Shear Stress and Skin Friction
1.5.3. Solved Problems -1_llIlIped lleatAII(I~I/JiJ ....•.........•. 1.269
Coefficient for Turbulent Flow 2.IR
'.5.4. Solllcd University Prohlelll.,·-Llllllped
tteot AII(I~I'jiJ ........•..........•..•......••....•...•..•.........•.•...••. 1.288 2.8. Heat Transfer 1'1'0111 Flat Surfaces - Formulae Used 2.23
I. -.S Heat Flow in Semi-lnfiutie Solids 1.306 2.8.1. Problems 011 Flat Surfaces - Forced Convection 2.26
2.8.2. Solved University Problems 011 Flat Surfaces -
1.5.6. SO/lied Problems - Semi-illfillite Solids 1.30R
Forced Convection 2.83
1.5.7. Transient Heat Flow in an Infillite Plate ...1.329 2.9. How over Cylinders and Spheres 2.115
1.5.8. Solved Problems - lufintie Slllitl,· 1.332 2.9.1. Formulae Usedfer Flow Over Cylinders
I.S.9. SO/lied University Problem" - Infinite Solids 1.351 and Spheres 2.116
1.6. 1'11'0Mark QlleJtiOlIl & AII.'"II'en 1.374 2.9.2. Solved Problems - Flow Over Cylinders 2.117
2.10. Flow over 'lalli, ofTubes 2.122
CHAPTER II:CONVECTIVE HEAT TRANSFER 2.10.1. Formulue Usedlor Flow Over Balik of Tubes 2.123
2.1. I)i111(~niosnaIAIIalysis -..-..-..-..-..-..--..-..-..-..-..-..- :~~ 2.10.2. Solved Problem 2.124
2.1.1. Dimensions ...2.1 2.11. Flow through it Cylinder -Internal Flow 2.126
2.11.1. Formulae usedfor Flow titrough
2 1.2. Buckingham 1I Theorem. ... . 2.2
2.1.3. Advantages cf Dimensional Analysis . 2.3 Cylinders (lnternul flow) 2.127
2.11.2. S;)lved Problems - Flow through Cylinders
2.14. Limitations of Dimensional Analysis 2.3
2.2. (lnteruat Flow) 2.129
Dimensionless Numbers and their Physical Significance 2.4
2.11.3. Solved University Problems - Internal Flow 2.150
2.2.1. Reynolds Number (Re) 2.4
2.12. Free Convection 2.162
2.2.2. Prandrl Number (Pr) 2.4
2.12.1. Formulae Used/or Free Convection 2.162
~2.2;.3~. ~Nustse~lt N:u:mtbe~r ((~N~u)r~~•?,•~.•~.••:•:•;••••••••••.••;2.•5;••••••••.••2•.1•2•.2•. ••So•lv.e•d.•Pr•ob•le•m.s•.0•11 Free Convection (or)
Natural Convection 2.165
2.12.3. Solved University Problems - Free Convection 2.194
2.2.6. ~e\Vlonion and Non-Newtollioll Fluids 2.6 2.13. Problems for Practice 2.217
EL;;;~~~:~~::;~p·:~:.::::·::.:.::.::::~~~::: 2.14. TII'oMurk Questions {lilt! Allswers 2.219
:::::::::::::::::::~~::::::::::::::~:7;
2.3.
L~;~;~·:::············································";'8 CHAPTER III: PHASE CHANGE HEAT TRANSFER AND HEAT
2~ I. Types of Boundary
EXCHANGERS
2.:.~. !iydrodynalllic Boundary 1.~··~·r:·· ·· ······· ..······· ..····2·9
2.).). r~lenn;]IUoUfldarylayer y ..· ····· 2·9 3.1. Boiling and Condensation ~.I
2.4. 3.1.1. Introduction . ).1
'l'~~'"rC'..···..·..: ,..:::::::::::::::::::::::::::::::::
i~lIlve~~~:lt~;;:~ 2:9 3.1.2. Boiling . ....3.1
-u.
2 Types ofC~nveoc!i onveC!rOfl 2.9 3.1.3. Condensation 3.1
. . .3.1
011.... . 2.9 3.1.4. Applications .
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C.4 Heat and Mass Tram/a Contents C.5
3.1.5. Boilll1gHeat Transfer Phenomena 3.2 4.3. Emissive Power 4.1
3.1.6. Flow Boiling... ········ ..· · 3.4 4.4. Monochromatic Emissive Power 4.2
3.1.7. Boiling Correlations J.) 4.5. Absorption, Reflection and Transmission 4.2
3.1.8. Solved Prohlellls 3.7 4.6. Concept of Black Body 4.3
3.1.9. Solved A11IUIUniversity Problems 3.23 4.7. Planck's Distribution Law 4.4
3.1 10. Condensation. . 3.29
4.8. Wien's Displacement Law 4.4
3.1.11. Modes ofCondensation · 3.29
4.9. Stefan-Boltzmann Law · 4.5
3.1.12. Filmwise Condensation 3.29
4.10. Maximum Emissive Power 4.5
3.1.13. Dropwise Condensation ..· 3.30
4.11. Emissivity 4.6
3.1.14. Nusselt's Theory for Film Condensation 3.30
4.12. Gray Body 4.6
3.1.15. Correlation for Filmwise Condensation Process 3.30
4.13. Kirchoff's Law of Radiation 4.6
3.1.16. Solved Problems Oil Laminar Flow,
4.14. Intensity of Radiation 4.6
Vertical Surfaces 3.32
4.15. Lambert's Cosine Law 4.7
3.1.17. SolvedProblems Oil Laminar Flow,
4.16. Formulae Used 4.7
Horizontal Surfaces 3.54
4.17. Solved Problems 4.8
3.1.18. Solved Anna University Problems 3.61
4.18. Solved University Problems 4.25
3.1.19. Problems for Practice 3.65
3.2. Heat Exchangers 3.66 4.19. Radiation Exchange Between Surfaces 4.31
3.2.1. Introduction 3.66 4.20. Radiation Exchange Between Two Black Surfaces separated
3.2.2. Type of Heat Exchangers 3.66 by a Non-absorbing Medium 4.31
3.2.3. Logarithmic Mean Temperature Difference (LMTD) 3.73 4.21. Sha pe Factor 4.36
3.2.4. Assumptions 3.73 4.22. Shape Factor Algebra 4.36
3.2.5. Logarithmic Mean Temperature Difference for 4.23. Heat Exchange Between Two Non-Black (Gray)
Parallel Flow 3.73 Parallel Planes 4.37
3.2.6. Logarithmic Mean Temperature Difference for 4.24. Heat Exchange Between Two Large Cocnentric Cylinders or
Counter Flow 3.77 Spheres 4.41
3.2.7. Fouling Factors 3.81 4.25. Radia tion Shield 4.45
3.2.8. Effectiveness by Using Number of 4.26. Solved Problems 4.49
Transfer Units (NTU) 3.82 4.27. Solved Problems 011 Radiation Shield 4.60
3.2.9. Problems on Parallel Flow and Counter 4.28. Solved University Problems 4.79
Flow Heat £\:cllangers , 3.82 4.29. Electrical Network Analogy for Thermal Radiation Systems
3.2.10.Problems 011 Cross Flow Heal Exchangers (or) by Using Radiosity and Irradiation 4.IOO
32I Shell and Tube Heal Exchangers 3.109 4.30. Radiation of Heat Exchange for Three Gray Surfaces 4.104
3'2'1~' Solved Anna UI1iversity Problems 3.117 4.31. Solved Problems 4.105
3'2'13' Smo1lved Problems Oil NT(! Method 3.J24 4.32. University Solved Problems 4.129
3'2'14' ; b"1University Solved Problems 3.138
" . ro emsfor Practice 4.33. Radiation from Gases and Vapours 4.153
3.2.15. TwoM k . ..·..·..· · 3.145 4.34. Mean Bea m Length 4.154
ur Questions and AI1swers 3.146
4.35. Solved Problems ·4.155
CHAPTER IV:RADIAnON 4.36. Problems for Practice 4.166
4.1. Introduction .. 4.37. Two Mark. Qlte.5tiOl1!iand Al1swers 4.168
4.2. Emission Properties 4.1
· · · · · 4.1
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5.1. Jntroductlo.n · 5.1
5.2. ModesofMass Transfer ·..· · · ·..· S.1
5.3. Diffusion Mass Transfer ..· ·..· ·· · · · S.1
5.4. Molecu~ar~iffusion ·..· · · ·..·..· · 5.2
5.5. Eddy Dlffuslon 5.2
5.6. Convection Mass Transfer ·..· · 5.1
5.7. Cocentrations ·· · ·..·· ·· ·..··..·· 5.2
5.8. Fick'~ Law of Diffusion ·..·..·..· 5.3
5.9. Steady State Diffusion through a Plane Membrane 5.4
~.I O. So/J'edProblems Oil Concentrations 5.6 Chapter 1:Conduction
~.II. Solved Problems OilMembrane 5.17
5.12. Solved Univeristy Problems on Membrane 5.21
cr Basic Concepts
5.13. Steady State Equimolar Counter Diffusion 5.23
5.14. Solved Problems OilEquimolar Counter Diffusion 5.26
5.15. Solved University Problems 011 Equimolar CF General Differential
Counter Diffusion 5.31 Equation
5.I6. Isothermal Evaporation ofWater into Air 5.34
5.17. Solved Problems on Isothermal Evaporation 0" Fourier Law of Conduction
of WaterintoAir 5.35
5.J8. Solved University Problems OilIsothermal Evaporation C7 Internal Heat Generation
of Waterinto Air 5.44
5.19. Convective Mass Transfer S.54 c:r Extended Surfaces
5.20. Types ofConvective Mass Transfer 5.54
5.21. Free Convective Mass Transfer 5.54 c- Unsteady Heat Conduction
5.22. Forced Convective Mass Transfer 5.S4
5.23. Significance of Dimensionless Groups 5.54
cr Solved Problems
5.24. Formulae Usedfor Flat Plate Problem.') 5.56
5.25. Solved Problems on Flat Plate 5.57
5.26. Anna University Solved Problems 011 Flat Plate 5.65 (7' Solved University Problems
5.27. Formulue Usedfor Internal Flow Problems 5.68
5.28. Solved Problems on Intemal Flow 5.69
5.29. UniversitySolved Problems 5.72
5.30. Problemsfor Practice 5.75
5.31. TwoMark Questions and Answers 5.76
ANNA UNIVERSITY SOLVED QUESTION PAPERS........S.1- S.71
DO
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CHAPTER-I
1.CONDUCTION
1.1HEAT TRANSFER
Heat transfer can be defined as the transmission of energy
from one region to another region due to temperature difference.
1.1.1Modes of Heat Transfer
*
Conduction
*
Convection
* Radiation
Conduction
Heat conduction isamechanism of heat transfer from aregion
of high temperature toaregion of low temperature within amedium
(solid, liquid orgases) or between different medium indirect physical
contact.
Inconduction, energy exchange takes place by the kinematic
motion ordirect impact of molecules. Pure conduction isfound only
insolids.
Convection
Convection isaprocess of heat transfer that will occur between
a solid surface and a fluid medium when they are at different
temperatures.
Convection ispossible only inthe presence offluid medium.
Radiation
The heat transfer from one body to another without any
transmitting medium isknown as radiation. It isan electromagnetic
wave phenomenon.
'2
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I.': Heat tnd Transfer
HII.\.\'
1.1.2 Fourier tal" or Conduction Conduction 1.3
Rate of heal conduction is proponional 10 the area mea lIred O.
1101'111:11 tothe iirection of heat OO\V and io the temperature gradient
inthat direction.
Q
O. °C.·Ch)
Element volume
\ here
A- Area in 111-
dT _ Temperature gradient in k/m
dr
Fig. 1.1.
k- Thermal nducti iry in W/m"-
Net heat conducted into element from all the coordinate
Thermal conducti it)' is defined a the abilit fa ub tan e
directions.
toconduct heat.
Let qx be the heat flux in a direction of face ABO and
[The negative sign indicates that the h at 0 w in a dire ti n
along which there isadecrease in temperature] q¥ dx be the heat flux in adirection f face EF H.
The rate f heat' fl 'n"ine. t th eIernent .In x diirection through
1.1.3 General heat conduction equation in the face AB 0 i
cartesian coordinates
I I
Consider a small rectangular element fide dx, d and Q, dz ... (1.2
I
d: as shown in Fig.I.I.
where k hermal nducti ity, W/mK
The energ balance of this rectangular element i btain d
from first law of thermodynam ics. ernperature gradient
1
Net heat The rate heat fl \ ut f tJre eIernent I.nx directi n thr ugh
l
conducted into Heat Heat the fa e EFGH i
=> element from generated t st red
all the coordinate \\ithin the = in rhe Q +dx Q ax )dx
l
directions element j elern nt../ aT
-k -d d:
x I
... 1.1
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Conduction 1.5
/4 Heata~_ .. ~
Subtracting (1.2)- (1.3) . Net heat conducted into element from all the coordinate
directions
=-k aT dydz _Il-.k .~.QIdydz=
Ox- ox M
Q(I'+dxl x AX ![
~[ :.[ kx:] + ky :] + k, :] ] dx dy dz
~ax [kx aaxT Jdx dy dZ]
... (1.7)
er of
=·-k. -ax dydz +kx -8x dydz + HeatStoredintheelement
.t
We know that,
He~t stored} Mass Of} { SpeCifiC} { Rise in }
mthe = the x heat of the x temperature
or] { {
=> Q _Q = .a1x_ [kx ax dx dy dz ... (1.4) element element element of element
.I' (.I' +dx) aT
at
m x Cp?<
Similarly !
,. aT
[k dy at
Q)'.-Q(y+(M = ~ y :;] dx dz .•. (1.5) p x dx dy dz x Cp x
[v Mass =Density x Volume]
••• (1.6)
er
Heat stored in}
{ the element = p Cpatdx dy dz ... (1.8)
Adding (1.4) + (1.5) +(1.6)
Heatgenerated within theelement
g:
[k'l: Jdt
Net heat conducted = a~ dy dz + Heat generated within the element isgiven by
q
Q = dx dy dz ... (1.9)
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1.6 Heal ami Mass Tran.~ler
Conduction I.?
Substituting eqllation (1.7), (1.8) and (1.9) in equation {I.I)
I;_ Case (i):No heat sources
[k\ ~ 1 c [k,. c~] a~ [k: ~ J]
(\'1) ~ .. ,\ +0..'.. 0· + 0_ dx L~l'dz In the absence of internal heat generation, equation (1.10)
reduces to
02r 02r 02r
or
+q dxdy dz PCp oart dx dydz ax2 +-0+,2- az2 oc at ..• (1.11 )
This equation is known as diffusion equation (or) Fourier's
equation.
Case (ii):Steady state conditions
Considering the material is isotropic. So, In steady state condition, the temperature does not change
k, =ky= k, = k = constant. with time. So, aotr' = O. The heat ~onduction equation (1.10)
reduces to
&r &r -~r] or
-a+x2-+-k0~+q=c:pz2C- P at +-iJ+2r- 02r +q- =0 ... (1.12)
0'2 o:z2 k
Divided by k,
(or)
iJ1r in q pCp or
+-0,+1-+&-2 k·' =--k at V-)T +-q = 0
k
or This equation is known as Poisson's equation.
... (1.10)
at
a:
In the absence of internal heat generation, equation (1.12)
becomes :,
It is a general three dimensional heat conduction equation
... (1.13)
in cartesian coordinates
k
where, a: =;: Thermal diffusivity = -- - m2/s (or)
. . .. pCp .
Thermal diffusivity is nothing but how fast heat is diffused
through a material during changes of temperature with time. This equation is known as Laplace equation.
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I.8 Heal and Ma.H' Transfer
Out! (iii): Onedimensional steady state "e(lf condllcliOll--- Conduction J, 9
Ifthe temperature varies only inthex direction the e . 1.1.4 General Heat Conduction Equation in Cylindrical
, ,quatloll
(1.10) reduces to Co-ordinates
The general heat conduction equation in cartesian
o2T q
-a--x-'; 1 I.; z-0 •.• (1.14) coordinates derived inthe previous section isused for solids with
rectangular boundaries like squares, cubes, slabs etc. But, the
Inthe absence of interns Iheat generation, equation (1.14) cartesian coordinate system is not applicable for the solids like
becomes: cylinders, cones, spheres etc. For cylindrical solids, acylindrical
coordinate system is used.
'" (1.15) Consider asmall cylindrical element of sides dr, dcj> and dz
as shown in fig.I.2.
Case(iv): Twodimensional steady slate "eat conductio"
Ifthe temperature varies only in the x and y directions, the
equation (I. 10)becomes:
... (1.16)
In the absence of internal heat generation, equation (I. 16) I
:dr
redcues to
I
J~_(r,4J,z
Elemental volume
atYxT2 -j---oi-fy1l =0 ... (I. 17) /// '
dz Q(r+dr)
Case(,~: Unsteady state, one dimensional, without internal
healgeneration :
, oi
n un~teady state, the temperature changes with time,
-a,
i.e., :t:O.So, the general conduction equation (I. J0) reduces to
Fig.J.2
()
... (1.18) The volume of the element dv = rd~ drdz .
o: ("'"
Let us assume that thermal conductivity k, Specific heat e
I p
and density p are constant.
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