高等傳熱學(xué)

Advanced

Heat

TransferChap.

1

Fundamental

concepts

of

convectionand erning

equationsConvection:Refresh

the

knowledge

offluid

mechanics

and

heat

transferAim

to

improve

the

capability

of

dealing

with

complicatedengineering

problems

byusingpropermethods.Fromcomplexity

to

simplicity,

then

modifythesolutions

toapply

to

the

complexity.工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer§1-1

Introduction1.

DefinitionConvection:

Heat

transfer

process

caused

by

mixing

of

coldand

hot

fluids

when

relative

displacement

occurs

betweendifferent

parts

of

the

fluid.工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferConvection

heat

transfer:

Heat

transfer

process

takingplace

when

fluid

flows

through

solid

wall.Onlyoccurring

in

the

fluid;

macroscopic

displacement;

coupledwith

heat

conduction;

related

to

the

heat

conduction

across

athin

layer

adjacent

the

wall工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferEffective

factorsThe

cause

ofmotion

ForcedconvectionNatural

convectionRe2Mixed

convect0i.o1n

Gr

10NaturalconvectionmixedForcedconvection

Nun

Nun

Nunforcednatural= -4. same

direction,

+; reverse

direction,

-工程熱物理高等傳熱學(xué)Advanced

Heat

Transfer2.2

Flow

regimesLaminar

flowFluid

mechanics

experiment:a

drop

of

red

ink

into

thefluidTurbulent

flowRe

ud1883,

Reynolds工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferReynolds

Tube

Experiment

(1883)工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer工程熱物理高等傳熱學(xué)Advanced

Heat

TransferGeometric

factorsinternal

flowshexternal

flowscalesurface

roughnessPhase

changeBoiling,

Condensation工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer2.5

Thermophysical

properties

,

,

c

p

,

t

f

cplh

f

(u,

twThe four

factors

constitute

the

basis

for

classification

ofconvection

heat

transfer.Physical

properties

of

the

fluid

could

be

reflected

through

thenondimensional

parameters.工程熱物理高等傳熱學(xué)3.

ClassificationAdvanced

Heat

TransferForced

convectionInternal

flowExternal

flowFlow

in

circular

tubesFlow

in

noncircular

tubesFlow

over

a

plateHeat

transfer

withoutphase

changeInfinite

spaceConvectionheat

transferNatural

convectionFlow

along

atubeFlow

across

tube

bundlesVertical

pipeHorizontal

pipeHorizontal

wallCondensationPhase

changeheat

transferFinite

spaceMixed

convectionCondensation

o tical

plateCondensation

along

horizontal

tubesand

across

tube

bundlesCondensation

in

tubesBoilingPool

boilingIn-tube

boiling工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer4.

Fundamental

equationsq

tyt∞u∞Fourier’s

law

ofheat

conductionwyw,xyqc

h

tw,

x

ttwwxxyw,xtw,x

t

y

qh

＝－

tNewton’s

law

ofcoolingqw

qct∞

for

external

flow:

the

fluid

temperature

away

from

the

wall,

t∞t∞

for

internal

flow:

the

average

fluid

temperature

of

the

pipe,

tbAcmu

udAcpAbc

tudAt

cApAcc

udA工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferAttention

points:In

heat

conduction,

h

is

known;

here,

h

is

unknown.In

heat

conduction,

λ

is

thermal

conductivity

of

solid;

here,λ

is

thermal

conductivity

of

fluid.In

heat

conduction,

t

is

the

solid

temperature;

here,

t

is

thefluid

temperature.4.

In

the

above

equation,

h

is

local

convective

heat

transfercoefficient,

however,

Newton’s

law

of

cooling

is

applied

to

thewhole

surface

to

obtain

the

convective

heat

transfer

coefficientof

the

whole

surface.Question:

to

obtain

the

average

h,

integration

of

qx

through

the

heat

transfer

surface

or

integration

of

hx

directly

？

Whatconditions

can

we

integrate

hx

directly?工程熱物理高等傳熱學(xué)

Advanced

Heat

TransfermxAh

dAAh

＝

1h

AtdA

t

h

t

t

dA

tmw,mf

,mx

w,xf

,xAAyw,xyTwo

common

boundary

conditions

in

convection

heat

transfer:Uniform

wall

temperatureUniform

heat

flux工程熱物理高等傳熱學(xué)Advanced

Heat

TransferConvective

heatttransfer

coefficientqw,x

yyw,xFluid

temperature

fieldespecially

thetemperature

distributionnear

thewallKey

to

obtain

hxt

x,

y,

z,

TemperaturefieldAffected

byflow

fieldsolve

the

mathematicalequationsFlowfieldEnergy

conservation

lawContinuity

Eq. Mass

conservation

lawMomentum

Eq. Momentum

conservation

law

field

Temperature

Energy

Eq.工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer5.

Researethod

of

convection

heat

transferyticalsolutionSolved

by

mathematical

methods

and

this

methodprovides

theoretical

guidanceObtain

correlations

of

convective

heat

transferExperimentalmethodcoefficient

through

lots

of

experiments,

and

this

is

themain

method

to

get

the

convection

heat

transfercoefficient.ogytheoryNumericalmethodEstablish

the

relationship

between

convective

heattransfer

coefficient

and

drag

coefficient

by

examining

thesimilarity

between

heat

transfer

and

momentum

transfer:Only

valid

for

certain

conditions.Through

numerical

calculations

to

obtain

theconvection

heat

transfe

coefficient

:

develop

fast工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer6.

Similarity

principle

and

dimensional

ysisExperiment

method

is

still

the

main

method

to

solve

thecomplex

convection

heat

transfer,

and

similarity

principle

canprovide

a

theoretical

guidance

for

experiment

study.h

f

(u,

,

cp

,

,

,

l)Similarity

principle

can

answer

the

following

questions:How

to

arrange

experiment

and

what ties

should

bemeasured?How

to

process

data

after

experiment?What

is

the

condition

that

the

results

obtained

can

be

applied?工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferPhysical

meaning

of

the

similarity

parameters

t

t

/

t

tww

fNu-

dimensionless

excess

temperature

gradient

of

fluid

at

wall1.

Nusselt

number

Nu

hl

y

/

ly

02.

Reynolds

numberRe

ulPr-the

ratio

of

momentum

diffusivity

to

thermal

diffusivityaRe-

the

ratio

of

inertial

forces

to

viscous

forces3.

Prandtl

number

Pr

4.

Grashof

number

2Gr

gtL3Gr-the

ratio

of

the

buoyancy

to

viscous

force

acting

on

a

fluid工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferRelationship

between

thesimilarity

parametersThe

solution

oftransfer

can

bedifferential

equations

describing

the

heatexpressed

by

correlations

of

similarityparameters

in

principle.□Forced

convection

heat

transfer

without

phase

change:Nu

f

(Re,Pr

)□Natural

convection

heat

transfer:Nu

f

(Gr,

Pr)□Mixed

heat

transfer:Nu

f

(Re,

Gr,

Pr)Process

experimental

data

according

to

above

rules

to

obtainthe

practical

correlations

that

can

reflect

the

heat

transfer.This

is

the

basic

rule

on

how

to

process

the

experiment

data.工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferSimilarity

principle

gives

answers

to

the

following

questions:①

Similarityparameters

should

be

the

basis

for

arrangingties

included

in

similarityexperiment,

and

the

physicalparameter

shouldbemeasured.②

Experimental

results

should

be

processed

to

the

correlations

ofsimilarity

parameters.③

Experimental

results

can

be

applied

to

the

practical

conditionssimilar

to

the

experiment.工程熱物理高等傳熱學(xué)

Advanced

Heat

Transferf

f

f1.

Experimental

correlations

of

turbulence

flowin

pipe

(D-B),

heating

fluidNu

0.023

Re0.8

Prn,

cooling

fluid7.2

Experimental

correlations

of

laminar

forcedflow

in

pipe(Sieder-Tate)7.

Experimental

correlations

of

forced

convectionheat

transfer

in

internal

flow

Re

Pr1

3.

f

f

f

l

dNuf

1.86

w

工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer8.

Experimental

correlations

of

forced

convectionheat

transfer

in

external

flow1.

Laminar

flow

over

an

isothermal

pla

aminarflow,

Re<5×105)1/

2

1/

3Nux

0.332

Re

x

PrNum

0.664

Rel

1/

2

Pr1/

3Flow

across

single

cylinderFlow

across

tube

banks工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer9.

Experimental

correlations

of

naturalconvection

heat

transferExperimental

correlations

of

natural

convectionheat

transfer

in

infinite

spaceNu

C

Gr

Prn

C

RanExperimental

correlations

of

natural

convectionheat

transfer

in

enclosuresqHTw1Tw2工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer10.

Comprehensive

correlation:Nu

0.023Ref.fPrn

C

C

Cf

l

r

t

0.8p,

d0.8

0.40.4

0.60.2n

0.4,

h

f

u,

,

,

c

,

①

ρ,

power

is

0.8,

is

the

most

influencing

factor,

next

isλ②

u,power

is0.8:

1m/s→

1.5m/s,

h↑40%③

d↓,

h↑工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferDevelopment

ofthe

cooling

technology

for

power

plants100MW

H2

cooled

generator

set300MW

H2-H2O

cooled

generator

setmaxpower<100MW<500MW<600MW>1000MWcooling

mediumAircoolingH2coolingH2O-H2coolingH2Ocooling工程熱物理Advanced

Heat

Transfer高等傳熱學(xué)medium

ρλ

ηcp1.090.0769881005143044174airH2H2O0.0239

2x10-60.167

0.96x10-6.

56.6x10-6Large

Thermal

power

air

cooling

units(direct

cooling

or

indirectcooling)200MW，300MW，600MWAreas

with

abundant

coal

and

deficient

water:Compared

with

water

cooling,

air

cooling

can

saveup

to

75%

water.Outline

of

the

National

Program

for

Long

and

Medium

Term

Scientificand

Technological

Development(2006-2020):

One

of

the

16

majornational

science

and

technology

ro

ects:

Large-scale

advanced

PWR

andhigh

temperature

gas

cooled

reactor

nuclear

power

plants工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer§1-2

erning

equations1.

Continuit

E

.Law

of

massconservationMethod:

control

volume

methodMass

into

control

volume

per

unit

time-

Mass

out

of

control

volume

per

unit

time+

Net

value

of

internal

mass

source

and

sink=

Mass

changing

rate

in

control

volume工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer1.3

Derivationx,intovolume:

udydzx+dx,

outofvolume:Net

value

intovolume:

u

u

xdx

dydz

u

dxdydz

x

u

v

w

dxdydz

x

y

zNet

value

of

allthe

directions:

dxdydzRate

of

mass

change

withtime:工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferAssume

mass

source

and

sink

equal

zero

u

v

w

0

y

z

div

u

0

x

?

u

0

u

j

0j

x

u

u

v

w

0

x

v

w

y

z

x

y

z

工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferD

d

i

v

u

0

?

u

0D

D

D1.4

Special

casessteady?

u

0pressible?

u

01.5

Other

coordinate

systems工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer2.

Momentum

Eqs.2.1

Law

of

momentum

conservation

(vector)Momentum

into

control

volume

along①i

direction

per

unit

time-

Momentum

out

of

control

volumealong

i

direction

per

unittime+

Momentum

changing

rate

along

i

direction

②=

Sum

of

forces

acting

on

the

fluid

ofcontrol

volume

along

idirection

③工程熱物理高等傳熱學(xué)Advanced

Heat

Transfer2.2

Derivationu

udydz

u

2

dydzx,

into

volume:x+dx,

out

ofvolume:

u2

u

d

x

d

y

d

z2

xdxdydz2Net

value

on

the

leftand

right

interfaces:

u

xNet

value

along

xdirection:

u

2

w

u

d

x

d

y

d

z

x

vu

y

z①:工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferRate

of

momentum

changewith

time

along

x

direction:

u

dxdydz②

+

①:Acting

force:

u

u

u

v

u

w

u

dxdydz

Du

dxdydz

D

x

y

z

body

force

(gravity,

centrifugal

force,

electromagnetic

force)surface

force

(static

pressure,

viscous

stress)Assumption:body

force

at

x

direction

is

Fx.surface

stress

τ

is posed

intothree

components.static

pressure

p

is

perpendicular

toacting

surface.工程熱物理高等傳熱學(xué)Advanced

Heat

TransferFx

dxdydz

p

pdxdydz

xx

p

dydzxx

xxyxyx

xdy

dxdz

dxdz

zxzx

yx

ydz

dxdy

zx

z

dxdy

x

F

yx

p

xx

x

x

zx

z

d

x

d

y

d

z

y③:

工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferxD

Du

F

yx

p

xx

zx

x

x

y

zFor

Newtonian

fluid

(there

is

a

simple

linear

relationship

betweenstress

and

strain)xyy

x

u

v

ujijj

i

u

i

x

x

x

u

u

D

Du

F

p

u

x

x

x

y

y

z

z

1

u

v

w

3

x

x

y

z

i

Dui

F

p

ui

1

u

j

jjijDix

x

x

3

x

x

工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer2.3

Special

casepressi f

uid,

constant

viscosityjiDuD

2

u

p i

Fi

i

x

x

21823,

Navier1845,

Stokes2.4

Other

coordinate

systems工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer3.

Energy

Eq.law

ofthermodynamicsAssumption:Nointernal

heat

source;Neglect

the

change

ofkinetic

energy

andpotential

energy;

neglectradiation

heattransfer3.3

Derivationd-Q?conv

d-Qc.,-ond

d?-W

d?-E2①

②

④

③Total

energy

of

fluid

per

unit

mass:e

U

1

u

2

v

2

w

2

electromagnetic工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer①

u

e

dydzx,

into

control

volume:

uedydz

ue

dxdydz

xx+dx,

outofcontrol

volume:Net

value:

ue

dxdydz

xNet

value

of

all

directions:

ue

ve

we

dxdydzconvdQ

x

y

z

dxdydz

u

j

e

j

x工程熱物理高等傳熱學(xué)

Advanced

Heat

Transfer②q

x

dydz

q

qx

xdx

dydz

x

qx,

into

control

volume:x+dx,

out

ofcontrolvolume:Net

value:dxdydzx

xFourier’s

law

of

heat

conduction:Net

value

of

all

directions:

t

dxdydz

x

x

conddQ

t

t

t

dxdydz

x

x

y

y

z

z

t

dxdydzjj

x

x工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferdE

e

dxdydz③

Rate

of

total

energychange

with

time:

u

j

ejjj

dxdydz

x

x

x

t

dxdydz

dW

e

dxdydz

dxdydzDe

D

dxdydz

e

u

j

x

jAjj

t

dxdydz

dW

x

x工程熱物理④高等傳熱學(xué)

Advanced

Heat

Transferysis

of

dWNet

workbetween

fluid

in

control

volume

andsurroundings

includes

the

work

done

by

bodyforce

and

surface

stress.dW

dW

S

＋

dW

VdW

V

Fx

u

F v

Fz

w

dxdydz工程熱物理高等傳熱學(xué)

Advanced

Heat

Transferysis

of

dWSLeft

wall: Right

wall:xx

p

udydz

p

xx

p

dx u

dx

dydz

u

xx

x

x

v

x

xy

vdydzdx

v

x

dx

d

ydz

xy

x

xz

wdzdyxzdx

w

w

dx

dydz

xz

x

x

The

stress

and

velocityThe

stress

and

velocityare

in

the

oppositedirection,

negative

workare

in

the

same

direction,positive

work工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferTaylor

expansion

he ight

wa

:xx

p

u

p

u

xx

xdx

dydz

xy

v

x

xy

v

dx

dydz

xz

w

xz

w

dx

dydz

x

Net

value

of

leftand

rightwall:

w

xxp

u

xy

vxz

x

x

x

dxdydz工程熱物理高等傳熱學(xué)Advanced

Heat

TransferNet

value

of

all

walls:

p

u

xy

v

w

xz

dxdydz

x

x

xx

xyxyz

u

w

yy

p

vdxdydz

y

y

y

p

w

u

zz

zyv

zx

z

z

zdxdydz工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferdW：

u

u

yx

u

xx

x

yzx

zdW

dxdydz

yydxdydz

v

v

vxy

xzy

z

y

yzw

xz

w

zzw

x

z

dxdydzB

pu

pv

pw

dxdydz

x

y

z

Fx

u

F

y

v

Fz

w

dxdydz工程熱物理高等傳熱學(xué)Momentum

Eq.Advanced

Heat

Transfer

yx

p

xx

zxxD

Du

Fudxdydzudxdydz

?

x

x

y

z

p

xy

yy

zy

y

zyD

Dv

Fvdxdydzvdxdydz

?

y

x

p

xz

z

x

yz

y

zz

zzwdxdydz

?

Dw

FDAdding

to

get:wdxdydz2u

D

1

u2

v

2

wdxdydz

dxdydz

xzv

x

zx

y

zD

2

xy

yy

zydxdydz

w

yz

zz

dxdydz

x

y

z

x

y

z

x

y

z

u

p

v

p

w

p

dxdydz

F

u

F v

F

w

dxdydzC

x

y

z

工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferB

CdW

D

1

u

2

v

2

w

2

dxdydz

yxzxyy

u

x

D

2

u

u

v

v

x

y

xx

xy

y

z

v

z

zy

dxdydz

xz

w

w

w

yz

x

yzz

z

p

u

v

w

dxdydz

x

y

z

dW

D

1

u

2

v

2

w

2

dxddz

d

x

d

dz

D

2

u

v

w

p

x

y

z

dxdydzD

D

De

dxdydz

t

dxdydz

dW

x

xAjj工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferPutDequation

into

A

equation:

DU

t

p

u

v

w

internal

energy

expression

ofenergy

equationD

yz

Φ:

u

2

v

2

w

2

2

x

2

y

2

z

Put

the

expression

of

Newtonian

fluid

viscous

stress

into

u

v

2

w

2

u

w

2

v

y

x

z

x

z

y

22

u

0

v

w

3

x

y

z

Physicalinterpretationviscous

dissipation

function,

the

work

done

tothe

fluid

in

control

volume

by

viscous

stress

perunit

time

which

is

converted

into

thermal

energyof

Φ:

irreversibly.

工程熱物理高等傳熱學(xué)

Advanced

Heat

TransferEnerg equation

inenthalpy:h

U

p

2DD

DDh

DU

1

Dp

p

DpD

0p

D

0D

D

u

j

x

jD

p

u

j

x

jj

p

u

jD

x

2

DU

p

D

DUp

D

D

D

DD

jj

x

x

t

DUD

D

D

D

Dh

1

Dp

Dh

Dp

Energy

equation

expressed

by

enthalpyjj

Dh