hand out kuliah boiler heat transfer

8/13/2019 Hand Out Kuliah Boiler Heat Transfer

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Boiler Heat Transfer.

Basic concepts of heat transfer

There are three modes of heat transfer: conduction, convection and radiation. One or

more of these modes controls the amount of heat transfer in all applications.

Conduction

Temperature is a property that indicates the kinetic energy possessed by the molecules of

a substance; the higher the temperature the greater the kinetic energy or molecular

activity of the substance. Molecular conduction of heat is simply the transfer of energy

due to a temperature difference between adjacent molecules in a solid, liuid or gas.!onduction heat transfer is evaluated using "ourier#s law:

q kA dT dx c $ % (1)

The flow of heat, qc, is positive when the temperature gradient, dT&dx, is negative. Thisresult, consistent with the second law of thermodynamics, indicates that heat flows in thedirection of decreasing temperature. The heat flow, qc, is in a direction normal 'or

perpendicular( to an area,A, and the gradient, dT&dx, is the change of temperature in the

direction of heat flow. The thermal conductivity, k, a property of the material, uantifies

its ability to conduct heat. ) range of thermal conductivities is listed in Table *. Thediscrete form of the conduction law is written:

Q kA L T T $ % ' ( * + (2)

"ig. * illustrates positive heat flow described by this euation and shows the effect of

variable thermal conductivity on the temperature distribution. The grouping kA/L isknown as the thermal conductance,Kc; the inverseL/kA is known as the thermal

resistance,Rc andKc = *&Rc. ) special case of conduction is the thermal contact

resistance across a joint between solid materials. )t the interface of two solid materials

the surface to surface contact is imperfect from the gap that prevails due to surfaceroughness. n nuclear applications with fuel pellets and fuel cladding, surface contact

resistance can have a major impact on heat transfer. f one dimensional steady heat flow

is assumed, the heat transfer across a gap is defined by:

q T T Rct $ % * + (3)

where the uantityRct is called the thermal contact resistance, *&hct), and hct is calledthe contact coefficient. T* and T+ are the average surface temperatures on each side of

the gap. Tabulated values of the contact coefficient are presented in -eferences * and +.


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/amples include 011 2tu&h ft+ " '*.3 k4&m+ 5( between two sections of ground 016

stainless steel in air and +7,111 2tu&h ft+ " '*6+ k4&m+ 5( between two sections ofground copper in air. The factors are usually unknown for specific applications and

estimates need to be made. There are two principal contributions across the gap 8 solid to

solid conduction at the points of contact and thermal conduction through the entrappedgases in the void spaces.

Convection

!onvection heat transfer within a fluid 'gas or liuid( occurs by a combination of

molecular conduction and macroscopic fluid motion. !onvection occurs adjacent to

heated surfaces as a result of fluid motion past the surface as shown in "ig. +. 9atural

convection occurs when the fluid motion is due to buoyancy effects caused by localdensity differences. n the top portion of "ig. +, the fluid motion is due to heat flow from

the surface to the fluid; the fluid density decreases causing the lighter fluid to rise and be

replaced by cooler fluid. "orced convection results when mechanical forces from devicessuch as fans give motion to the fluids. The rate of heat transfer by convection, qcv, is

defined:

q hAT T cv s f $ % ' ( (4)

where h is the local heat transfer coefficient,A is the surface area, Ts is the surfacetemperature and T is the fluid temperature.

uation 6 is known as 9ewton#s aw of !ooling and the term hAs is the convection

conductance,Kcv. The heat transfer coefficient, h, is also termed the unit conductance,because it is defined as the conductance per unit area. )verage heat transfer coefficients

over a surface are used in most engineering applications. This convective heat transfer

coefficient is a function of the thermal and fluid dynamic properties and the surfacegeometry. )ppro/imate ranges are shown in Table +.

Radiation


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-adiation is the transfer of energy between bodies by electromagnetic waves. This

transfer, unlike conduction or convection, reuires no intervening medium. The

electromagnetic radiation, in the wavelength range of 1.* to *11 micrometers, isproduced solely by the temperature of a body. nergy at the body#s surface is converted

into electromagnetic waves that emanate from the surface and strike another body. , and absorptivity ?. The sum of thesefractions euals one:

Fig. 29atural and forced convection. )bove, boundary layer on a vertical flat plate.2elow, velocity profiles for laminar and turbulent boundary layers in flow over a flat

plate. '@ertical scale enlarged for clarity.(

= > ? A A $* (5)


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Therefore, a can be eliminated from uation H, and emissivity is all that is needed to

describe the radiation properties of the surface. Table 0 shows some representative values

of emissivity. f all surfaces are assumed to be gray, a simpler treatment of radiation ispossible.

"or two surface enclosures, this treatment involves introducing a total e/change factor,F*+, which depends on the configuration 'geometry(, the emissivities and the surface

areas.0 f the emissivity depends on wavelength, the surface is termed a selective or nonC

gray radiator. )ccording to 5irchhoff#s law, spectral emissivity and spectral absorptivity

are always euivalent, JK $ ?K, for nongray surfaces. Total emissivity is the integratedaverage of JK over the spectrum of emitted radiation, and total absorptivity is the

integrated average of ?K over the spectrum of incident radiation. The terms e!ss!v!ty and

e!tta"ce 'and corresponding terms absor#t!v!ty and absor#ta"ce( are commonlyinterchanged in the literature. "or convenience, the term e!tta"ce is used here for total

e!ss!v!ty and absor#ta"ce is used for total absor#t!v!ty, of nonCgray surfaces. "or nonC

gray surfaces, the emittance can be e/pressed as a function of the surface temperature J'Ts(, and absorptance as a function of the incident radiation or flame temperature, ? 'Tf(.

2ased on 5irchhoff #s law, plots of J vs Ts may be interpreted as plots of ? vs Tf if the

physical state of the surface is unchanged. )n analysis of nonCgray conditions reuirestemperature dependent emittance and absorptance, or spectral property calculations

which are more complicated. )n e/ample of nonCgray radiators in a boiler are the ashdeposits on waterwall heating surfaces. The net radiation heat transfer between twoblackbody surfaces which are separated by a vacuum or nonparticipating gas is written:

q AF T T *+ * *+ * 6 + 6 $ % ' ( D (11)

A* is the surface area;F*+ is the geometric shape factor and represents the fraction of

radiant energy leaving surface * that directly strikes surface +. )s will be discussed later

for radiation between two surfaces,F*+ is the e/change factor for two surfaces based onthe geometric arrangement only, andF*+ is the e/change factor that includes the effects

of emissivity for gray surfaces, and participating media between the surfaces. "or

blackbody surfaces 'J* $ J+ $ *( and nonparticipating media,F*+ $F*+. T* and T+ arethe surface temperatures.


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A F A F * *+ + +* $ (13)

This euation, known as the principle of reciprocity, guarantees conservation of theradiant heat transfer between two surfaces. The following rule applies to the surfaces of

an enclosure:

F!$ $ $ * (14)

stating that the total fraction of energy leaving surface ! to all other '$( surfaces musteual *. Many te/ts include the calculation of geometric shape factors, commonly named

shape factors or configuration factors.*,+ -adiation balances for participating and

nonparticipating media are presented later in the chapter.

Heat transfer properties and correlations

Thermal conductivity, specific heat and density

Thermal conductivity, k, is a material property that is expressed in Btu/h ft F(W/m K) and is dependent on the chemical composition and physicalcharacteristics of the sustance. The relative order of ma!nitude of values forvarious sustances is sho"n in Tale #. Thermal conductivities are !enerallyhi!hest for solids, lo"er for li$uids and lo"er yet for !ases. %nsulatin! materialshavethe lo"est conductivities of solid materials. Thermal conductivities of pure metals!enerally decrease "ith an increase in temperature, "hile alloy conductivitiesmay either increase or decrease. (&eeFi!. #.) 'onductivities of several steels and alloys are sho"n in Tale #. Thermalconductivities of various refractory materials are sho"n in 'hapter , Fi!. *+.

For many heat transfer calculations it is sufficiently accurate to assume aconstant thermal conductivity that corresponds to the avera!e temperature ofthe material. The effective thermal conductivity of ash deposits on "ater "allheatin! surfaces varies "idely dependin! on temperature, composition, heatin!cycle and physical characteristics of the deposits. The lo"er limit is close to thethermal conductivity of air or lo"er (+.+ Btu/h ft F or +.+ W/m K), and theupper limit does not exceed values for refractory materials (*.- Btu/h ft F or .-W/m K). The effective thermal conductivity of a friale particulate layer is nearthe lo"er limit and is fairly independent of temperature elo" *+ to ++F(00 to *+-') at "hich sinterin! usually occurs. 1ove this temperature,particles fuse to!ether and thermal contact et"een particles increases,resultin!

in a sharp increase in thermal conductivity. The hi!hest conductivity is achieved"ith complete meltin!. The physical chan!es caused y fusion and meltin! areirreversile upon coolin!, and thermal conductivity of fused deposits decreases"ith decreasin! temperature.

Thermal conductance of ash deposits (k/x) is less sensitive to chan!in!conditions than thermal conductivity. 1s the deposit !ro"s in thickness (x),thermal conductivity (k) also increases due to fusion and sla!!in!. The net effectis that unit thermal conductance may only vary


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y a factor of four, to *++ Btu/h ft F (*- to W/m '), "hile variations inthermal conductivity are an order of ma!nitude lar!er. The thermal effects ofcoalash deposits are further descried y Wall et al.The thermal conductivity of"ater ran!es from +. Btu/h ft F (+.# W/m K) at room temperature to +.*Btu/h ft F (+. W/m K) near the critical point. Water properties are relativelyinsensitive to pressure, particularly at pressures far from the critical point. 2ost

other nonmetallic li$uid thermal conductivities ran!e from +.+ to +.* Btu/h ft F(+.+0 to +. W/m K). %n addition, thermal conductivities of most li$uids decrease"ith temperature.

The thermal conductivities of !ases increase "ith temperature and areindependent of pressure at normal oiler conditions. These conductivities!enerally decrease "ith increasin! molecular "ei!ht. The relatively hi!hconductivity of hydro!en (a lo" molecular "ei!ht !as) makes it a !ood coolin!medium for electric !enerators. The relatively lo" conductivity of ar!on (a hi!hmolecular "ei!ht !as) makes a !ood insulatin! medium for thermal pane"indo"s.

When calculatin! the conductivity of nonhomo!eneous materials, the desi!nermust use an apparentthermal conductivity to account for the porous or layered construction materials.%n oilers and furnaces "ith refractory "alls, thermal conductivity may vary fromsite to site due to variations in structure, composition, density, or porosity "henthe materials "ere installed.

The thermal conductivities of these materials are stron!ly dependent on theirapparent ulk density(mass per unit volume). For hi!her temperature insulations, the apparentthermal conductivity of firous insulations and insulatin! firerick decreases asulk density increases, ecause the denser material attenuates the radiation.3o"ever, an inflection occurs at some point at "hich a further increase in density

increases the thermal conductivity due to conduction in the solid material.Theory sho"s that specific heats of solids and li$uids are !enerally independentof pressure.

Tale # lists specific heats of various metals, alloys and nonhomo!eneousmaterials at F (+'). These values may e used at other temperatures "ithoutsi!nificant error.

The temperature dependence of the specific heat for !ases is more pronouncedthan for solids and li$uids. %n oiler applications, pressure dependence may!enerally e ne!lected. Tales a and !ive specific heat data for air and other!ases. %n the case of steam and "ater, property variations (specific heat andthermal conductivity) can e si!nificant over the ran!es of temperature andpressure found in oilers. %t is therefore recommended that the properties ascompiled in the 1merican &ociety of 2echanical 4n!ineers (1&24) &team Talese used.

Radiation propertiesBodies that are !ood radiation asorers are e$ually !ood emitters and Kirchhoff5s la" states that, for !ray surfaces at thermal e$uilirium, their emissivities aree$ual to their asorptivities. 1 blackbody is one "hich asors all incident radiant


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ener!y "hile reflectin! or transmittin! none of it. The asorptivity and emissivityof a lackody are, y definition, each e$ual to one. This terminolo!y does notnecessarily mean that the ody appears to e lack. &no", for instance, asorsonly a small portion of the incident visile li!ht, ut to the lon!er "avelen!ths(the ulk of thermal radiation),sno" is almost a lackody. 1t a temperature of +++F (*+0') a lackody

!lo"s ri!htly, ecause a non6ne!li!ile part of its radiation is in the visileran!e. Bodies are never completely lack, ut a hole throu!h the "all of a lar!eenclosure can e used to approximate lackody conditions, ecause radiationenterin! the hole under!oes multiple reflections and asorptions. 1s a result,most of the radiation is retained in the enclosure, and surfaces are treated as!ray.

Fortunately, a numer of commercial surfaces, particularly at hi!h temperatures,have emissivities of+.+ to +.0 and ehave much like lackodies. Typical avera!e emissivityvalues are noted in Tale 0. 1lthou!h emissivity depends on the surfacecomposition and rou!hness and "avelen!th of radiation, the "avelen!thdependence is often ne!lected in practicaloiler calculations and surfaces are treated as !ray.

Ash depositsThe emittance and thermal properties of furnace ash deposits have a lar!e effecton oiler heat transfer. The emittance depends on the temperature, chemicalcomposition, structure and porosity ofthe particulate layer, and "hether deposits are partially fused or molten. Thesame ash at different locations "ithin the same oiler (or the same location indifferent oilers) may have si!nificantly different values of surface emittance.7eported values in the literature claim emittances et"een +. and +.0 for mostash and sla! deposits.

The effect of coal ash composition, structure, and temperature on depositemittance,# is sho"n in Fi!.. 1 friale particulate material has lo" emittance ecause radiation is scattered(and reflected) from individual particles and does not penetrate eyond a thinlayer (8* mm) near the surface. 4mittance of friale ash deposits decreases "ithincreasin! surface temperature, until sinterin! and fusion chan!es the structureof the deposit. 1 sharp increase in emittance is associated "ith ash fusion asparticles !ro" to!ether (pores close) and there are fe"er internal surfaces toscatter radiation. 'ompletely molten ash or sla! is partially transparent toradiation, and emittance may depend upon sustrate conditions. The emittanceof completely fused deposits (molten or fro9en sla!) on oxidi9ed caron steel isaout +.0. 4mittance increases "ith increasin! particle si9e of friale particulatedeposits(Fi!. a), ecause lar!er particles have less capacity to ack6scatter incidentradiation. 4mittanceincreases "ith increasin! iron oxide (Fe:) and unurned caron content of theash (Fi!. ) ecausethese components have a !reater capacity to asor radiation. ;o" emittance ofsome li!nitic ash deposits, kno"n as reflective ash, may e attriuted to lo"Fe: content, althou!h this alone is not a reliale indicator of a reflective ash.4mittance is also indirectly dependent upon oxidi9in! and reducin! environment


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of the flue !as, due to the effect on the meltin! characteristics and unurnedcaron content in the ash. The thermal and radiative effects of coal6ash depositsare further descried y Wall et al.

Combustion gases

1lthou!h many !ases, such as oxy!en and nitro!en, asor or emit onlyinsi!nificant amounts of radiation, others, such as "ater vapor, caron dioxide,sulfur dioxide and caron monoxide, sustantially asor and emit. Water vaporand caron dioxide are important in oiler calculations ecause of their presencein the comustion products of hydrocaron fuels. These !ases are selectiveradiators.

They emit and asor radiation only in certain ands ("avelen!ths) of thespectrum that lie outside of the visile ran!e and are conse$uently identified asnonluminous radiators. Whereas the radiation from a furnace "all is a surfacephenomenon, a !as radiates and asors ("ithin its asorption ands) at everypoint throu!hout the furnace. Furthermore, the emissivity of a !as chan!es "ithtemperature, and the presence of one radiatin! !as may have characteristicsthat overlap "ith the radiatin! characteristics of another !as "hen they are

mixed. The ener!y emitted y a radiatin! !aseous mixture depends on !astemperature, the partial pressures, p, of the constituents and a eam len!th, ;,that depends on the shape and dimensions of the !as volume. 1n estimate of themean eam len!th is ; < . =/1 for radiative transfer from the !as to thesurface of the enclosure, "here = is the enclosure volume and 1 is the enclosuresurface area. The factor . is approximate, and values et"een .- to . haveeen recommended dependin! on the actual !eometry.-

Fi!s. 0 and *+ sho" the emissivity for "ater vapor and caron dioxide.Theaccuracy of these charts has !ained !reater acceptance than the more "idelykno"n charts of 3ottel,- particularly at hi!h temperatures and short path len!ths.

The effective emissivity of a "ater vapor6caron dioxide mixture is calculated asfollo"s>

? ? ? ? = + 3 : ': (41)

"here is a correction factor that accounts for the effect of overlappin!spectral ands.

This e$uation ne!lects pressure corrections and considers oilers operatin! atapproximately * atm. The factors sho"n in Fi!. ** depend on temperature, thepartial pressures, p, of the constituents and the eam len!th, ;. The presence ofcaron monoxide and sulfur dioxide can typically e ne!lected in comustionproducts, ecause ': and &: are "eakly participatin! and overlap "ith theinfrared spectrum of 3: and ':.

When usin! Fi!s. 0 to ** to evaluate asorptivity, , of a !as, 3ottel- recommendsmodification of the p; product y a surface to !as temperature ratio. This isillustrated in 4xample at the end of this chapter.

7adiation properties of !ases can e calculated more accurately ased onfundamental models for spectral !as radiation. The exponential "ide andmodel0 predicts spectral asorption and emission properties of sin!le and multi6component !ases includin! 3:, ':, ':, '3-, @:, and &: as a function oftemperature and pressure. Aiatomic !ases @, : and 3 may contriute to the


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total !as volume and pressure of the mixture, ut are considered transparent toinfrared radiation. 7adiation properties are conveniently expressed as emissionand asorption coefficients that depend on local variations in !as composition,temperature, and pressure. This approach is suitale for numericalmodelin! of radiation "ith participatin! media, "hich re$uires fre$uentevaluation of !as properties

at a lar!e numer of control volumes.

Entrained particles

'omustion usually involves some form of particulate that is entrained incomustion !ases. articles are introduced as the fuel "hich under!otransformations of comustion and/or are formed y the processes ofcondensation and a!!lomeration of aerosol particles. 4ntrained particles havea si!nificant role in radiation heat transfer ecause they asor, emit, andscatter radiation. &catterin! effectively extends the eam len!th of radiation inan enclosure, ecause the eam chan!es direction many times efore it reachesa "all. 7adiation from entrained particles depends on the particle shape, si9edistriution, chemical composition, concentration, temperature, and the"avelen!th of incident radiation.

articulates in oilers are comprised of unreacted fuel (coal, oil, lack li$uor),char, ash, soot, and other aerosols. &oot is an example of an aerosol thatcontriutes to radiation from !as flames in oilers. @e!lectin! the effect of sooton radiation heat transfer in the flame could lead to si!nificant errors in thecalculated flame temperature, and radiation heat transfer to the furnace "alls inthe flame 9one. 1sh is an example of particulate that contriutes to radiation incoal6fired oilers. &catterin! y ash particles effectively redistriutes radiation inthe furnace, and smooths out variations in radiation heat flux, analo!ous to the"ay a cloud distriutes solar radiation on the earth. The asorption and emissioncharacteristics of flyash particles increase, and scatterin! decreases "ith therelative

amount of iron oxide or residual caron, "hich acts as a colorin! a!ent in theash.

1nalytical methods such as 4$uation 0 that depend upon emissivity andasorptivity of the participatin! media are inaccurate "hen particles other thansoot are involved, ecause the effects of scatterin! are ne!lected. @umericalmethods "hich solve the !eneral form of the radiative transport e$uation includethe effects of scatterin! (see Numerical methods).

2ie Theory*+ is a !eneral method for calculatin! the radiation properties ofspherical particles as a function of particle composition, concentration, diameterand "avelen!th. 7i!orous calculations y this method can only e performed"ith the aid of a computer and re$uire that optical properties (complex refractiveindex as a function of "avelen!th) of the particle materials are kno"n. Thecomplex refractive index of li!nite, ituminous, and anthracite coals, andcorrespondin! properties of char and ash have een measured, as "ell as othermaterials that are typically encountered in comustion systems. 7adiationproperties of particles are conveniently expressed as total emission,asorption, and scatterin! efficiencies that depend on particle composition,diameter and temperature.


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article properties must e comined "ith !as properties in an analysis ofradiation "ith participatin! media.

Working formulas for convection heat transfer

3eat transfer y convection et"een a fluid (!as or li$uid) and a solid is

expressed y 4$uation -. This e$uation is a definition of the heat transfercoefficient ut is inade$uate in descriin! the details of the convectivemechanisms. :nly a comprehensive study of the flo" and heat transfer "oulddefine the dependence of the heat transfer coefficient alon! the surface. %n theliterature, simple !eometries have een modeled and predictions a!ree "ell "ithexperimental data. 3o"ever, for the more complex !eometries encountered inoiler analysis, correlations are used that have een developed principally fromexperimental data.

'onvective heat transfer near a surface takes place y a comination ofconduction and mass transport. %n the case of heat flo"in! from a heated surfaceto a cooler fluid, heat flo"s from the solid first y conduction into a fluid element,

raisin! its internal ener!y. The heated element then moves to a cooler 9one"here heat flo"s from it y conduction to the cooler surroundin! fluid. Fluidmotion can occur in t"o "ays. %f the fluid is set in motion due to densitydifferences arisin! from temperature variations, free or natural convectionoccurs. %f the motion is externally induced y a pump or fan, the process isreferred to as forced convection. 'onvective heat transfer can occur in laminar orturulent flo"s. For laminar flo", the fluid moves in layers, or lamina, "ith eachelement follo"in! an orderlypath. %n turulent flo", prevalent in oiler passa!es, the local motion of the fluidis chaotic and statistical treatment is used to estalish avera!e velocity andheat transfer values.

4xperimental studies have confirmed that a flo" field can e divided into t"o9ones> a viscous 9oneadCacent to the surface and a nonviscous 9one removed from the heat transfersurface. The viscous, heated 9one is termed the oundary layer re!ion. Thehydrodynamic oundary layer is defined as the distance from the "all at "hichthe local velocity reaches 00D of the velocity far from the "all.1t the entrance of a pipe or duct, the oundary layer e!ins to !ro"E this flo"portion is called the developin! re!ion. Ao"nstream, "hen the viscous re!ion fillsthe pipe core or !ro"s to a maximum, the flo" is termed fully developed.Aevelopin! re!ion heat transfer coefficients are lar!er than the fully developedvalues. %n many applications it is sufficient to assume that the hydrodynamic andthermal oundary layers start to !ro" at the same location, althou!h this is notal"ays the case.

Flo" over a ody (around a circular cylinder) is termed external flo", "hile flo"inside a confined re!ion, like a pipe or duct, is termed internal flo".

Natural or free convection1 fluid at rest, exposed to a heated surface, "ill e at a hi!her temperature andlo"er density than thesurroundin! fluid. The differences in density, ecause of this difference intemperature, cause the li!hter, "armer fluid elements to circulate and carry theheat else"here. The complex relationships !overnin! this type of convective


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heat transfer are covered extensively in other texts.* 4xperimental studies haveconfirmed that the main dimensionless parameters !overnin! free convectionare the rashof and randtl numers>

r = ( ) g T T L s G H I (42)

r = c k p I (43)

The rashof numer is a ratio of the uoyant to viscous forces. The randtlnumer is the ratio of the diffusion of momentum and heat in the fluid. Theproduct, r r, is also called the 7aylei!h numer, 7a. %n oiler system desi!ns,air and flue !ases are the important free convection heat transfer media. Forthese desi!ns, the e$uation for the convective heat transfer coefficient h is>

h C T T s = ( ) * / (44)

This correlation is applicale "hen the 7aylei!h numer, 7a, is !reater than *+0,"hich is !enerally reco!ni9ed as the transition et"een laminar and turulent

flo". =alues of the constant C in the e$uation are listed elo">

The correlation !enerally produces convective heat transfer coefficients in theran!e of * to Btu/h ft

F (. to .0 W/m K).

Forced convectionDimensionless numbers Forced convection implies the use of a fan, pump ornatural draft stack to induce fluid motion. &tudies of many heat transfer systemsand numerical simulation of some simple !eometries confirm that fluid flo" andheat transfer data may e correlated y dimensionless numers.Jsin! these principles, scale models enale desi!ners to predict field

performance. For simple !eometries, a minimum of dimensionless numers isneeded for modelin!. 2ore complex scalin! re$uires more dimensionless !roupsto predict unit performance.

The 7eynolds numer is used to correlate flo" and heat transfer in closedconduits. %t is defined as>

7e= = H I I V L GL (45)

"here ; is a characteristic len!th of the conduit or an ostacle in the flo" field.This dimensionless !roup represents the ratio of inertial to viscous forces.

The 7eynolds numer is only valid for a continuous fluid fillin! the conduit. Theuse of this parameter!enerally assumes that !ravitational and intermolecular forces are ne!li!ilecompared to inertialand viscous forces. The characteristic len!th, termed e$uivalent hydraulicdiameter, is different for circular and noncircular conduits. For circular conduits,the inside diameter (%A) is used. For noncircular ducts, the e$uivalent diameterecomes>


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De = -

Flo" cross6sectional area Wetted perimeter (46)This approach, used to compare dynamically similar fluids in !eometricallysimilar conduits of different si9e, yields e$ual 7eynolds numers for the flo"sconsidered.

1t lo" velocities, the viscous forces are stron! and laminar flo" predominates,"hile at hi!her velocities, the inertial forces dominate and there is turulent flo".%n closed conduits, such as pipes and ducts, the transition to turulent flo"occurs near 7e < +++. The !enerally accepted ran!e for transition to turulentflo" under common tue flo" conditions is +++ 7e -+++.

For fluid flo" over a flat external surface, the characteristic len!th for the7eynolds numer is the surface len!th in the direction of the flo", x. Transition toturulence is !enerally considered for 7e *+. %n the case of flo" over a tue,the outside diameter (:A), D, is the characteristic len!th. %n tue undles "ithcrossflo", transition !enerally occurs at 7e L *++.

4xperimental studies have confirmed that the convective heat transfercoefficient can e functionallycharacteri9ed y the follo"in! dimensionless !roups>

@u = ( ) f 7e, r (47)

"here @u is the @usselt numer, 7e is the 7eynolds numer and r is the randtlnumer.

The @usselt numer, a ratio of the "all temperature !radient to reference!radients, is defined as follo"s>

@u = hL k (48)

The previously discussed randtl numer, representin! a ratio of the diffusion ofmomentum and heat in the fluid, is also the ratio of the relative thickness ofviscous and thermal oundary layers. For air and flue !ases, r *.+ and thethermal oundary layer is thicker than the viscous oundary layer.%n the literature, correlations are also presented usin! other dimensionless!roupsE the eclet and&tanton numers are the most common. The eclet numer is defined as follo"s>

e = 7e r (49)

The &tanton numer is defined in terms of the @usselt, 7eynolds and randtlnumers>

&t @u = 7e r (50)

Laminar flow inside tubes

For heatin! or coolin! of viscous fluids in hori9ontal or vertical tues "ithconstant surface temperature and laminar flo" conditions (7e ++), the heat


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transfer coefficient, or film conductance, can e determined y the follo"in!e$uation>**

@u = * * + *- . 7er / . D L b w I I (51)

:r

h k D GD c k D L b p b b w = * * + *- . / . I I I I (52)

"here the parameter G < V is defined as the mass flux or mass flo" rate perunit area and tue diameter, D, is the characteristic len!th used in the evaluationof the 7eynolds numer. The ratio of viscosities ( b / w) is a correction factorthat accounts for temperature dependent fluid properties.

roperties in 4$uations * and are evaluated at an avera!e ulk fluidtemperature, except w"hich is evaluated at the "all temperature. For lo"viscosity fluids, such as "ater and !ases, a more complex e$uation is re$uired toaccount for the effects of natural convection at the heat transfer surface. This

refinement is of little interest in industrial practice ecause "ater and !ases inlaminar flo" are rarely encountered.

Turbulent flow

&tudies of turulent flo" indicate several "ell defined re!ions as sho"n in Fi!.*. @ext to the heat transfer surface is a very thin laminar flo" re!ion, less than+.D of the characteristic len!th, "here the heat flo" to or from the surface is ymolecular conduction. The next 9one, kno"n as the ufferlayer, is less than *D of the characteristic len!th and is a mixture of laminar andturulent flo". 3ere the heat is transferred y a comination of convection andconduction. %n the turulent core, "hich comprises rou!hly 0D of the cross6section, heat is transferred mainly y convection.%n turulent flo", the local ut chaotic motion of the fluid causes axial and radial

motion of fluid elements.

This comination of motions sets up eddies, or local s"irlin! motions,au!mentin! the heat transfer from the core to the laminar sulayer. The laminarflo" in the sulayer and the laminar component in the uffer layer act as aarrier, or film, to the heat transfer process. %ncreasin! the fluid velocity haseen found to decrease this film thickness, reducin! the resistance to heattransfer.

Turbulent flow in tubes

The distance re$uired to otain hydrodynamically and thermally fully developedturulent flo" is shorter than that for laminar flo". The flo" len!th needed to

achieve hydrodynamically fully developed conditions is variale and dependsupon the specific 7eynolds numer (operatin! conditions) and surface !eometry.%t typically varies from to + diameters (x/D). Fully developed thermal flo" for!ases and air, important in oiler analysis, occurs at similarx/D ratios. 3o"ever,for li$uids, the ratio is some"hat hi!her and increases "ith the randtl numer.

4xtensive research data usin! lo" viscosity !ases and li$uids have eencorrelated. The follo"in! e$uation* is recommended for fully developed flo" "ithsmall to moderate temperature differences>


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@ufd

n = + + + . 7e r . (53)

"ith n < +.- for heatin! of the fluid and n < +. for coolin! of the fluid, andproperties evaluated at the ulk temperature. 4$uation applies to !ases and

li$uids in the ran!e +.# r *+, "hich covers all fluids in oiler analysis. %f theconditions are not fully developed, the correlation is corrected as sho"n elo">*

@u @u = +( ) fd D x * + # / . (54)

"ith the stipulation that x/D +. These correlations should only e used forsmall to moderate temperature differences.

1 correlation y &eider and Tate** is "idely used for heatin! or coolin! of a fluidand lar!er temperature differences. 1ll of the properties are evaluated at theulk temperature, except w "hich is evaluated at the "all temperature>

@ufd b w = + +# + * + *- . 7e r . / . I I (55)

The fore!oin! correlations may e applied for oth constant surface temperatureand heat flux conditions to a !ood approximation. For oiler applicationsinvolvin! turulent flo" in tues, 4$uation is re"ritten "ith the temperatureratio added to convert the properties from a ulk to film temperature asis>

@ufd f f b f T T = + + + + - + . 7e r . . . (56)

1ll properties are evaluated at the film temperature (T ), "hich is defined as thearithmetic mean temperature et"een the "all temperature (Tw) and the ulkfluid temperature (Tb)> T < (Tw M Tb)/ "ith all temperatures in asolute units (7or K). 4$uation is re"ritten usin! parametric !roupin!s>

h G D c k T T l e p f b f = + + + + + - + + - + . . . . . . I . (57)

"hich can e expressed in the form>

h h l l pp T = (58)

Fi!s. * to *# display the various factors that make up the ri!ht side of 4$uation. Jnlike non6dimensional parameters (@u, 7e, r), these terms do not have anyphysical si!nificance and are dependent upon the choice of en!ineerin! units.

The physical properties factor, pp, comines all of the properties of the fluid intoone term, and is evaluated at the !as film temperature for a particular fluid (!as,air or steam). @ote that if pp for steam can not e otained from Fi!. *, it cane calculated "ith values of cp, k and evaluated at the film temperature fromthe 1&24 &team Tales.

Turbulent cross flow around tubes

The most important oiler application of convection is heat transfer from thecomustion !ases to the tuular surfaces in the convection passes. erhaps themost complete and authoritative research on heat transfer of tues in crossflo"


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"as completed in an extensive pro!ram conducted y The Bacock N Wilcox'ompany (BNW).*-

The follo"in! correlation "as adapted from this study for different fluids> Fig. 12Structure of turbulent flow field near a solid boundary.

@u = + * + * + . 7e r . . f f a d (59)

The last terms are an arran!ement factor, a! and a depth factor d! that correctthe results from the ase confi!uration (OO /A+ < .+,O /A+ < *.#, numer ofro"s *+) "hich y definition a < d < *.

The e$uation applies to heatin! and coolin! of fluids for clean tues in crossflo".4$uation 0 is re"ritten usin! parametric !roupin!s sho"n elo">

h G D c k c p f a d =+ * + * + 0 + + # + . . . . .. I (60)

"hich can e expressed in the form>

h h c c pp a d = (61)

Fi!s. * to display the various factors that make up the ri!ht side of 4$uation*. Jnlike non6 dimensional parameters (@u, 7e, r), these terms do not

Fig. 1 Effect of film temperature, Tf, and moisture on the physicalproperties factor, Fpp, for gas; turbulent flow inside tubes orlongitudinal flow over tubes (English units only).Fig. 1! Effect of film temperature, Tf, and moisture on the physicalproperties factor, Fpp, for air; turbulent flow inside tubes or longitudinalflow over tubes (English units only).Fig. 1" Effect of film temperature, Tf, and pressure on the physicalproperties factor, Fpp, for steam; turbulent flow inside tubes or

longitudinal flow over tubes (English units only).Fig. 1# Basic convection velocity and geometry factor, hl , for air,gas or steam; turbulent flow inside tubes or longitudinal flow overtubes (English units only).

have any physical si!nificance and are dependent upon the choice of en!ineerin!units. The physicalproperties factor, pp, similar to the one previously defined, is evaluated at the!as film temperature fora particular fluid (!as or air). The mass flux or mass flo" per unit area, G, and the7eynolds numers used in 4$uations 0 and + and Fi!s. *, * and arecalculated ased on flo" conditions at the minimum free area (maximumvelocity) et"een tues.

The arran!ement factor, a! depends on the !eometric confi!uration of tues, theratio of tue spacin! to diameter, 7eynolds numer, and the presence of ash inthe flue !as. =alues of a for clean tue conditions "ith air or flue !as "ithout ashare !iven in Fi!. *.

=alues of a for commercially clean tue conditions "ith ash6laden flue !as are!iven in Fi!. .

The depth factor, d! accounts for entrance effects for anks of tues "hich areless than ten ro"s deep


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in the direction of !as flo". For undistured flo" Pflo" that is strai!ht anduninterrupted for at least - ft (*. m) efore enterin! a tue ankQ approachin! aank of less than ten ro"s, the film conductance must include the correctionfactor, d! sho"n in Fi!. . d is unity "hen the tue ank is preceded y a end,screen, damper or another tue ank in close proximity.

Turbulent longitudinal flow around tubes'orrelations that "ere developed ased on turulent flo" in tues (4$uations and #, and Fi!s. * to *#) can also e applied for external flo" parallel to tues.%n this case, the e$uivalent diameter De (defined y 4$uation -) is used in theevaluation of 7eynolds numer. For flo" parallel to a ank of circular tuesarran!ed on rectan!ular spacin!, the e$uivalent diameter ecomes>D D D e o o = - * O O R (62)

"here Do is the tue outside diameter and O* and O are the centerline spacin!et"een tues. The mass flux or mass flo" per unit area, G, in 4$uations and#, and Fi!. * is calculated ased on the free area et"een tues.

Fig. 1$ Effect of film temperature, Tf, and moisture on the physical

properties factor, Fpp, for gas in turbulent crossflow over tubes(English units only).Fig. 2% Effect of film temperature, Tf, and moisture on the physicalproperties factor, Fpp, for air in crossflow over tubes (English units only).Fig. 1& Temperature factor, FT, for converting mass velocity frombul to film basis for air, gas or steam; turbulent flow inside tubes orlongitudinal flow over tubes.

'hapter !Boiling Heat Transfer! T"o#$hase Flo" an% &irc'lation1 case of heat transfer and flo" of particular interestin steam !eneration is the process of oilin! andsteam6"ater flo". The oilin! or evaporation of "ateris a familiar phenomenon. %n !eneral terms, oilin!is the heat transfer process "here heat additionto a li$uid no lon!er raises its temperature under constantpressure conditionsE the heat is asored as theli$uid ecomes a !as. The heat transfer rates are hi!h,makin! this an ideal coolin! method for surfaces exposedto the hi!h heat input rates found in fossil fuel

oilers, concentrated solar ener!y collectors and thenuclear reactor fuel undles. 3o"ever, the oilin!phenomenon poses special challen!es such as> *) thesudden reakdo"n of the oilin! ehavior at very hi!hheat input rates, ) the potential flo" rate fluctuations"hich may occur in steam6"ater flo"s, and ) the efficientseparation of steam from "ater. 1n additionalfeature of oilin! and t"o6phase flo" is the creationof si!nificant density differences et"een heated and


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unheated tues. These density differences result in"ater flo"in! to the heated tues in a "ell desi!nedoiler natural circulation loop.2ost fossil fuel steam !enerators and all commercialnuclear steam supply systems operate in the pressureran!e "here oilin! is a key element of the heat

transfer process. Therefore, a comprehensive understandin!of oilin! and its various related phenomenais essential in the desi!n of these units. 4ven atoperatin! conditions aove the critical pressure, "here"ater no lon!er oils ut experiences a continuoustransition from a li$uid6like to a !as6like fluid, oilin!type ehavior and special heat transfer characteristicsoccur.

(oiling process and fundamentals

(oiling point and thermophysical properties

The oilin! point, or saturation temperature, of ali$uid can e defined as the temperature at "hich itsvapor pressure is e$ual to the total local pressure. Thesaturation temperature for "ater at atmospheric pressureis *F (*++'). This is the point at "hich netvapor !eneration occurs and free steam ules areformed from a li$uid under!oin! continuous heatin!.1s discussed in 'hapter , this saturation temperature(Tsat) is a uni$ue function of pressure. The 1merican&ociety of 2echanical 4n!ineers (1&24) and the%nternational 1ssociation for the roperties of &team(%1&) have compiled extensive correlations of thermophysicalcharacteristics of "ater. These characteristicsinclude the enthalpy (or heat content) of "ater, theenthalpy of evaporation (also referred to as the latentheat of vapori9ation), and the enthalpy of steam. 1sthe pressure is increased to the critical pressure P++psi (.* 2a)Q, the latent heat of vapori9ation declinesto 9ero and the ule formation associated "ith oilin!no lon!er occurs. %nstead, a smooth transition fromli$uid to !aseous ehavior occurs "ith a continuous increasein temperature as ener!y is applied.

T"o other definitions are also helpful in discussin!oilin! heat transfer>*. "ubcooling For "ater elo" the local saturation

temperature, this is the difference et"een thesaturation temperature and the local "ater temperature(Tsat S T ).. #ualityThis is the flo"in! mass fraction of steam(fre$uently stated as percent steam y "ei!ht orD&BW after multiplyin! y *++D)>

xmm m


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=+

OO Osteam"ater steam

(1)

"hereO msteam = steam flo" rate, l/h (k!/s)O m"ater = "ater flo" rate, l/h (k!/s)Thermodynamically, this can also e defined as>x$ $$or$ $$ $ffgfg f

= (2)"here$ = local avera!e fluid enthalpy, Btu/l (/k!)$f = enthalpy of "ater at saturation, Btu/l (/k!)$g = enthalpy of steam at saturation, Btu/l (/k!)$fg = latent heat of vapori9ation, Btu/l (/k!)When oilin! is occurrin! at saturated, thermale$uilirium conditions, 4$uation provides the fractionalsteam flo" rate y mass. For sucooled condi


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ater#t'e oiler sectionsThe energy from the heat source may be e/tracted as either radiant or convection and

conduction.

The f'rnace or ra%iant sectionThis is an open area accommodating the flame's( from the burner's(. f the flames were

allowed to come into contact with the boiler tubes, serious erosion and finally tube failure

would occur. The walls of the furnace section are lined with finned tubes called

membrane panels, which are designed to absorb the radiant heat from the flame.

"ig. 0.0.0 Neat transfer in the furnace or radiant section

&on*ection sectionThis part is designed to absorb the heat from the hot gases by conduction and convection.


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arge boilers may have several tube banks 'also called pendants( in series, in order to

gain ma/imum energy from the hot gases.

Fig. 3.3.4 Heat transfer in the con*ection section

hand out kuliah boiler heat transfer

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