Process Heat Transfer (Lecture Notes) - Lecture notes, lectures 1 - 9 PDF

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! Process!Heat!Transfer! ! Lecture!Notes! ! ! ! ! ! ! ! Content!:! ! ! 1. Conduction! 2. Convection! 3. Extended!Surface!Fins! 4. Transiet!Heat!Conduction! 5. Analytic!vs!Numerical!Method! 6. Heat!Exchangers! 7. Boiling! 8. Condensation! 9. Radiative!Heat!Transfer! ! ! ! ! ! ! ! ! ! ! ! !

1.#Conduction# Conduction!is!the!transfer!of!heat!from!a!more!energetic!particle!of!a!substance!to!the! adjacent!less!energetic!ones!as!a!reaction!between!the!particles.!! In!simple,!from!hotter!to!a!cooler!part!of!a!body!by!direct!molecular!contact,!without!mixing! occurring!within!the!body.!The!physical!mechanisms!of!heat!conduction!on!the!microscopic! scale!are!complex!and!comprise:!! •!Molecular!collisions!in!gases.! •!Lattice!vibrations!in!solids.! •!Flow!of!free!electrons!in!metals.!! 1.1 Fourier’s#Law# On!the!macroscopic!scale!all!these!processes!are!suitably!described!by!Fourier’s!Law!of!Heat! Conduction.!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! dT!=!T1!–!T2!>0!(Heat!flows!from!hot!to!cold)! dT/dx!is!the!Temperature!Gradient.!! Heat!conduction!is!proportional!to!the!temperature!gradient.!! Heat!is!conducted!in!the!direction!of!decreasing!gradient,!this!is!why!the!gradient!is! negative.!! • q!is!the!Heat!Flux!(Q/A)!(W/m)! •

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1.2 Thermal#Conductivity# • • • • •

Thermal!Conductivity!(k)!is!the!measure!of!a!material’s!ability!to!conduct!heat.! Thermal!Conductivity!is!the!rate!of!heat!transfer!through!a!unit!thickness!per!unit!area! per!unit!temperature!difference.! In!heat!transfer!analysis,!materials!are!normally!assumed!to!be!isotropic!(uniform! properties!in!all!directions)!! Thermal!conductivity!(k)!varies!with!temperature.!! Temperature!dependence!makes!analysis!complex.!Therefore!it!is!common!to!take! k!at!the!average!temperature!and!treat!it!as!a!constant.!!

1.3 Fourier#Law# Flat!Plate!:! !! 1.4 Electrical#Analogy#of#Heat#Transfer# The!heat!transfer!rate!can!be!written!as!:!! ! # ! ! ! ! ! ! ! ! ! ! ! 1.5 Thermal#Contact#Resitance# # # Perfect!Thermal!Contact!:! ! ! ! ! Imperfect!Thermal!Contact!:! ! ! !

1.6 Fourier’s#Law# # # Hollow!Sphere!:!! ! ! ! Cylinder!:! ! ! ! 1.7 Thermal#Insulation# Reasons!for!insulating:! –!Energy!conservation! –!Personal!protection!and!comfort!(!rcrit!always!reduces!the!heat!loss! - For!a!pipe!with!r!!1!indicates!that!fins!are!enhancing(heat!transfer!from!the! surface,!as!they!should.!

3.5#Proper#Fin#Length# • • •

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An!important!step!in!the!design!of!a!fin!is!the!determination!of!the!appropriate!length! of!the!fin!once!the!fin!material!and!the!fin!cross-section!are!specified.! It!is!tempting!to!think!that!the!longer!the!fin,!the!larger!the!surface!area!and!thus!the! higher!the!rate!of!heat!transfer.!! Therefore,!for!maximum!heat!transfer,!the!fin!should!be!infinitely!long.!However,!the! temperature!drops!along!the!fin!exponentially!and!reaches!the!environment! temperature!at!some!length.!The!part!of!the!fin!beyond!this!length!does!not! contribute!to!heat!transfer!since!it!is!at!the!temperature!of!the!environment.! So,!designing!‘extra!long’!fins!is!out!of!the!question!since!it!causes:!! - Material!waste! - Excessive!weight! - Increased!size! - Increased!cost!! In!fact,!such!a!long!fin!will!harm!performance!since!it!will!suppress!fluid!motion!and! thus!reduce!the!convection!heat!transfer!coefficient.!! !

4.#Transient#Heat#Conduction# • • •

Our!analysis!so!far!has!mainly!considered!one!dimensional!steady!state!heat!transfer! which!simplifies!the!analysis!considerably.!i.e.!T(x).!! The!temperature!of!a!body,!in!general,!varies!with!time!as!well!as!position.!i.e.! T(x,y,z,t)!! Certain!bodies!can!be!considered!to!behave!like!a!‘lump’!whose!interior!temperature! remains!effectively!uniform!at!all!times.!i.e.!T(t).!For!such!systems,!lumped!system! analysis!can!be!used!which!significantly!simplifies!the!problem.!!

4.1#Lumped#system#Analysis# Consider!a!body!of!arbitrary!shape!of!mass!m,!volume!V,!surface!area!As,!density!ρ,!and! specific!heat!Cp(initially!at!a!uniform!temperature!Ti(.!At!time!t(=!0,!the!body!is!placed!into!a! medium!at!temperature!T∞,!and!heat!transfer!takes!place!between!the!body!and!its! environment,!with!a!heat!transfer!coefficient!h.(For!the!sake!of!discussion,!we!will!assume! that!T∞!!>!Ti,!but!the!analysis!is!equally!valid!for!the!opposite!case.!We!assume!lumped! system!analysis!to!be!applicable,!so!that!the!temperature!remains!uniform!within!the!body!at! all!times!and!changes!with!time!only,!T(=!T(t).! ! # # If!lumped!system!analysis!is!valid!:! # 4.2#Criteria#for#lumped#system#analysis# •

The!first!step!in!establishing!a!criterion!for!the!applicability!of!the!lumped!system! analysis!is!to!define!a!characteristic#length#as!:!

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and!Biot#number!as!:!

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When!a!body!is!being!heated!by!a!hotter!fluid!(such!as!a!potato!being!baked!in!an! oven),!heat!is!first!convected!to!the!body!and!then!conducted!within!the!body.!! Biot!number!is!the!ratio!of!internal!resistance!to!heat!conduction!to!its!external! resistance!to!heat!convection.!! Therefore,!a!small!Bi!number!represents!small!resistance!to!heat!conduction,!and! small!temperature!gradients!exist!within!the!body.!! Lumped!system!analysis!assumes!a!uniform(temperature!distribution!throughout!the!

body,!which!will!be!the!case!only!when!the!thermal!resistance!of!the!body!to!heat! conduction!(the!conduction(resistance)!is!zero.!Thus,!lumped!system!analysis!is!exact( when!Bi!=!0!and!approximate(when!Bi!>!0.!Of!course,!the!smaller!the!Bi!number,!the! more!accurate!the!lumped!system!analysis.! • •

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It!is!generally!accepted!that!lumped!system!analysis!is!applicable!if:! Bi! saturation temperature.! Characteristic!:!rapid!formation!of!bubbles!at!the!interface!that!detach!from!the!solid! surface.!!

7.1#Types#of#boiling# • • •

Boiling!is!classified!as!pool(boiling(or!flow(boiling,(depending!on!the!presence!of!bulk! fluid!motion.! Boiling!is!called!pool!boiling!in!the!absence!of!bulk!fluid!flow!and!flow!boiling!(or! forced(convection(boiling)!in!the!presence!of!it.! In!flow!boiling,!the!fluid!is!forced!to!move!in!a!heated!pipe!or!over!a!surface!by! external!means!such!as!a!pump.!There-!fore,!flow!boiling!is!always!accompanied!by! other!convection!effects.!

7.2#Regimes#of#Boiling# Wall!temperature!increase!! • •

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In!pool!boiling!the!heat!flux!depends!on!the!temperature!difference!between!wall!and! liquid!saturation!temperature!(?).!! When!the!temperature!of!the!heater!is!increased!monotonically!(this!can!be!the!case! when!the!heater!is!a!stream!of!fluid!pre-treated!in!the!required!temperature)!then!the! following!regimes!of!pool!boiling!appear:!!

Heat!Flux!Increase! • •

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If!an!electric!heater!(conductive!wire)!is!used,!power!runs!through!it,!and!the!heat!flux! can!be!controlled,!a!different!pool-boiling!curve!is!obtained.!! As!the!heat!flux!reaches!its!maximum,!the!temperature!of!the!wire!increases!abruptly! to!a!point!associated!with!the!film!boiling!part!of!the!curve.!This!temperature!is!above! the!melting!temperature!of!the!wire,!and!the!wire!would!burn!out!(burnout!point).!! Decrease!in!heat!flux!:!a!minimum!close!to!qmin!is!reached.! Isolated!bubbles!form!and!temperature!falls!to!a!value!associated!to!the!nucleate! boiling!regime.!! In!flux-controlled!boiling,!the!transition!boiling!regime!is!inaccessible.!Also,!the!boiling! curve!shows!hysteresis.!!

Problem:!find!the!combined!heat!transfer!coefficient,!h,!or!the!wall!temperature,!Tw,!for! known!heat!flux,!mass!flowrate!and!quality! The!following!method!is!suggested:!! 1)!Calculate!the!parameter!X.!! 2)!Evaluate!coefficient!Fc!from!graphs! 3)!Calculate!two!phase!Reynolds!number! 4)!Calculate!hc.! 5)!Evaluate!coefficient!Sc!from!graphs.! 6)!Calculate!hB!from!equation.! 7)!Calculate!h.! ! ! ! ! ! ! ! ! ! ! ! !

8.#Condensation# Condensation!occurs!when!a!vapour!contacts!a!surface!(solid,!liquid…)!which!is!at!a! temperature!below!saturation!temperature!of!the!vapour.! 8.1#Modes#of#condensation# •

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Film#condensation:!Vapour!condenses!out!to!form!continuous!films!on!cold!surfaces! and!slides!down!due!to!gravity.!Thickness!of!the!liquid!film!increases!in!the!direction!of! flow!as!more!condensation!takes!place.!! Dropwise#condensation:!Condensation!occurs!on!a!cold!surface!but!the!condensate! forms!countless!droplets!instead!of!a!continuous!film.!! Homogeneous#condensation:!The!vapour!condenses!out!as!droplets!suspended!in!the! gas!phase,!forming!a!fog.!! Direct#contact#condensation:!It!occurs!when!a!vapour!is!brought!directly!into!contact! with!a!cold!liquid.!The!condensate!forms!on!the!surface!of!the!liquid.!!

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Film!Condensation!

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Dropwise! Condensation!

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Homogeneous! Condensation!

Direct!Contact! Condensation!

Film!condensation:!high!thermal!resistance!due!to!a!liquid!wall!between!solid!and! vapor.!! Dropwise!condensation:!low!thermal!resistance!because!droplets!slide!down!to!clean! the!solid!surface!and!expose!it!to!vapor.!! However,!dropwise!condensation!will!develop!to!film!condensation,!therefore!it!is! common!practice!to!assume!film!condensation!in!design!of!HEX.!

8.2#Real#Condensation# Real!condensation!differs!from!Nusselt!analysis:!! • The!film!is!almost!never!smooth!(ripples).!! • Shear!force!exerted!by!the!flowing!vapour!on!the!liquid!film.!! • Film!may!become!turbulent.!! • Multi-component!effects!(e.g.!effect!of!“incondensable”!gas!on!the!condensation!of! steam)!! 8.3#Dropwise#Condensation# •

When!condensation!starts,!initially!drops!of!condensate!will!form!on!the!condenser! surface.!With!time!more!and!more!drops!will!form!on!the!surface,!which!will!coalesce! with!the!others!and!form!a!continuous!film!(filmwise!condensation).!On!the!other! hand,!in!dropwise!condensation,!the!drops!which!form!will!roll!off!the!surface!before!a! continuous!film!has!a!chance!to!form.!!

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Dropwise!condensation!can!occur!when!steam!condenses!on!a!polished!copper! surface.!However,!on!oxidised!copper!surfaces!or!other!surfaces,!normally!used!in! condensers,!some!special!treatment!is!required!to!produce!dropwise!condensation! (e.g!coating!the!surface!with!plastic!or!gold!plating!it).!! The!transient!nature!of!the!process!(drops!forming,!growing,!rolling!off!the!surface)! and!the!continuous!clearing!of!the!condensate!from!the!surface!to!give!bear!metal,! gives!rise!to!high!heat!transfer!coefficients.!These!can!be!as!high!as!ten!times!those! achieved!by!filmwise!condensation.!! Despite!the!high!heat!transfer!coefficients!dropwise!condensation!has!little!practical! application!due!to!a!number!of!reasons,!e.g.!! -!Because!of!fouling!it!is!difficult!to!maintain!the!surface!properties!favourable!to! dropwise!condensation!!

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9.#Radiation#Heat#Transfer# 9.1#General#Features# • • • • • • • • • • • •

Does!not!require!a!medium.!! The!only!heat!transfer!mechanism!possible!under!! high!vacuum!conditions.!! Heat!is!emitted!through!electromagnetic!radiation!! by!any!body!at!a!temperature!greater!than!0!K.!! Fastest!form!of!heat!transfer!(speed!of!light).!! Heat!can!flow!from!a!hotter!body!to!a!colder!body!through!a!medium!which!may!be!at! a!third!temperature!that!is!higher!or!lower!than!that!of!the!other!two.!! High!temperature!processes!or!for!safety!calculations!it!has!! to!be!taken!into!account.!! It!depends!on!the!properties!of!materials!and!surfaces!and!these!are!also!temperature! dependent.!! Surfaces!that!emit!more!radiation,!tend!to!absorb!more!radiation.!! The!treatment!of!radiation!heat!transfer!is!based!on!the!idealised!blackbody.!!

# 9.2#Fundamental#Concept# •

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All!forms!of!matter!emit!radiation.!The!mechanism!of!emission!is!related!to!energy! released!as!a!result!of!oscillations!or!transitions!of!the!many!electrons!that!constitute! matter.!The!oscillations!are!sustained!by!the!internal!energy,!and!therefore!the! temperature!of!the!matter.!! For!gases!and!semi-transparent!solids,!emission!is!a!volumetric!phenomenon.!! In!most!solids!and!liquids,!radiation!from!interior!molecules!is!absorbed!by!internal! molecules.!Consequently,!radiation!is!emitted!from!molecules!~!1μm!from!the!surface.!! Here,!we!will!consider!radiation!to!be!an!exclusively!surface!phenomenon.!!

9.2#Electromagnetic#Spectrum# • • • • • • •

Electromagnetic!radiation!in!vacuum!travels!at!the!speed!of! light!with!an!energy!inversely!proportional!to!the!wavelength.!! Different!frequency!(energy)!radiation!has!different!properties.!! Thermal!radiation!is!produced!as!a!result!of!energy!transitions! of!molecules,!atoms!and!electrons.!! Temperature!is!a!measure!of!the!strength!of!these!activities!at! the!microscopic!level.!! The!rate!of!thermal!radiation!emission!increases!with!increasing! temperature.!! Thermal!radiation!is!emitted!by!all!matter!that!is!>!0!K.!! Thermal!radiation!spans!0.1!to!100!μm!(including!visible!and! infrared!region!as!well!as!some!of!the!ultra!violet!region.!!

9.3#Blackbody# •

Ideal!emitter.!!

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– All!energy!is!emitted!! – Evenly!in!all!directions!(diffuse!emitter)!! Ideal!absorber.!! – All!the!energy!is!absorbed!(regardless!of!wavelength)!! – From!all!directions!! – No!reflection!! – No!transmission!! Properties!of!real!surfaces!are!defined!relative!to!the!blackbody.!! Most!surfaces!that!appear!black!behave!roughly!as!blackbodies.!!

9.4#The#Isothermal#Cavity# • • • •

After!multiple!reflections,!virtually!all! radiation!entering!the!cavity!is!absorbed.!! Emission!from!the!aperture!is!the! maximum!possible!emission!achievable!for!! the!temperature!associated!with!the! cavity!and!is!diffuse.!! The!cumulative!effect!of!radiation! emission!from!and!reflection!off!the!cavity! wall!is!to!provide!diffuse!irradiation!corresponding!to!theemission!from!blackbody.!

! 9.5#Tables#of#Important#Definitions# ! The!process!of!converting!radiation!intercepted!by!matter!to!internal!thermal! Absorption!! energy.!! AbsorptivityThe!fraction!of!the!incident!radiation!absorbed!by!matter!α.!! Blackbody!! The!ideal!emitter!and!absorber.!Denoted!by!subscript!b.!! Modifier!referring!to!directional!independence!of!the!intensity!associated!with! Diffuse!! emitted,!reflected!or!incident!radiation.!! Directional!! Modifier!referring!to!a!particular!direction.!Denoted!by!subscript!θ.!! The!process!of!radiation!production!by!matter!at!a!finite!temperature.!! Emission!! Modifiers:!diffuse,!blackbody,!spectral.!! ! Kirchhoff’s! Radiation!between!emission!and!absorption!properties!for!surfaces!irradiated! Law!! by!a!blackbody!at!the!same!temperature.!! Plank’s!Law!! Spectral!distribution!of!emission!from!a!blackbody.!! Radiosity!! Reflection!!

Rate!at!which!radiation!leaves!a!surface!due!to!emission!and!reflection!in!all! directions!per!unit!area!of!the!surface.!! Process!of!redirection!of!radiation!on!a!surface.!Modifiers:!diffuse,!specular.!!

Fraction!of!incident!radiation!reflected!by!matter,!ρ.!Modifiers:!directional,! hemispherical,!spectral,!total.!! Region!subtended!by!an!element!of!area!on!the!surface!of!a!sphere!with! Solid!angle!! respect!to!the!centre!of!the!sphere,!ω!(sr).!! Reflectivity!!

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