Scanned by CamScanner 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 Scanned by CamScanner r.: 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 . Scanned by CamScanner 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 Scanned by CamScanner ~C~.6~~R~ea~t~a~n~d~~~a~s~s~r.~ra~n~sfi~e_r - =C-H-AP-T-E-R-V-:~M7.A~S~S~T~RA~NS~F~E~R~------------------ ------ 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 Scanned by CamScanner 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 Scanned by CamScanner 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 Scanned by CamScanner 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) Scanned by CamScanner 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. Scanned by CamScanner - 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. Scanned by CamScanner