Lecture 3 Convective Mass Transfer

7/29/2019 Lecture 3 Convective Mass Transfer

1/33

Lecture

3

Convec

tive

Mass

Trans

fer

[Geankoplis:7

.2;Treybal:

3]


2/33

Introduc

tion

InLect

ure

2,

we

hav

eemp

has

ise

dmo

lecu

lard

iffus

ion

ins

tagnan

tflu

idsor

flu

ids

inlam

in

ar

flow

(fluids

flow

in

stream

lines

).

Inman

ycases

ther

ateo

fdiffusio

niss

low

,an

dmore

rap

idt

rans

fer

is

de

sire

d.

Thus

the

flu

id

velo

city

is

increas

ed

un

tilturbu

len

t/conve

ctive

mass

t

rans

fer

occurs

.


3/33

ConvectiveMassTransfer

Mass

tra

ns

feroccurrin

gun

der

thein

fluenceo

fmo

tion

in

aflu

idm

edium

isca

lle

dconvec

tive

mass

trans

fer

.

Thereare

two

types:

Forced

convectionmas

stransfer

Freeco

nvectionmasstransfer


4/33


Figureshow

sthe

visualisation

ofthe

dissolutionp

rocessofa

solid

.


5/33


(a)

Natura

l

convec

tion

dueto

advers

e

density

gradient.

(b)

Higher

density

at

thebottom

,

nonatural

convec

tion

.


6/33

MassTransferCoefficients

Sinceou

run

ders

tand

ingo

fturbu

len

tflow

isincom

plete

,

wea

ttem

pttowri

tetheequa

tionssim

ilar

totha

tfo

r

mo

lecular

diffus

ion

.

Thus

,fo

rcons

tan

ttota

lconcen

tra

tio

n,

(

)

dz

dc

D

J

A

M

AB

A

+

=

*

(1)

Molecular

diffusivity

(m2/s)

Masseddy

diffusivity

(m2/s)


7/33


Integrat

ing

&rearrang

ing

,

where

isused

since

isavaria

ble

Distance

ofthepa

th,

(z2

z1)iso

ften

no

tknow

,thus

(

)

2

1

1

2

1

*

A

A

M

AB

A

c

cz

zD

J

+

=

(2)

M

M

(

)

2

1

1

*

'

A

A

c

A

c

c

k

J

=

(3)

Con

vectivemass

trans

fercoefficient


8/33


For

thecaseo

fequ

im

olarcoun

terdi

ffus

ion

,

where

NA

=-NB,

inte

gra

tinga

ts

tea

dys

tate

,

where

(

)

(

)

B

A

A

A

M

AB

A

N

N

x

dz

dx

Dc

N

+

+

+

=

(4)

(

)2

1

'

A

A

c

A

c

c

k

N

=

(5)

1

2

'

z

zD

k

M

AB

c

+

=


9/33



10/33

(with=z2

z1;

)

(

)

1

2

1

2

/

ln

B

B

B

B

BM

p

p

p

p

p

=


11/33

Typeso

fMassTra

nsferCoe

fficients


12/33

TypicalMagnitude

sofMass

Transfer

CoefficientandFilm

Thickne

ss


13/33

MassTransferCoefficientsforVarious

Geometries

Theexp

erimen

taldata

formass

tran

sfercoe

fficien

ts

obtained

us

ingvarious

kindso

ffluid

s,

differen

t

ve

loc

itie

s,

an

ddifferen

tgeome

tries

arecorre

lated

us

ing

dimension

lessnum

be

rs.

Dynamica

llys

imilarsy

stemsw

illhaveequa

l

dimension

lessnum

be

rs.

Thisdynam

ics

imilari

tyis

an

importan

trequ

iremen

tinthesca

leupo

fc

hem

ical

process

equ

ipmen

tan

dinthe

desig

no

fs

hipsand

airp

lane

s.


14/33

ImportantDimensionlessGroupsInMa

ss

Transfer

Reynoldsnum

ber

(Re)

Mostim

portant,indicatesdegreeofturbu

lence

Sc

hm

idt

num

ber

(Sc

)

Sherwoo

dnum

ber

(Sh)

Stan

ton

num

ber

(StM)

Pec

letnum

ber,

Pe

M

Co

lburn

fac

tor,

jD

Gras

hof

num

ber,

Gr

Lew

isnu

mber,

Le


15/33


16/33

Typeso

fFluidFlow

indicatedbyRe

(a)LaminarFlow

insidePipes(Re2,1

00)

This

isthebesttype

offluid

flow

obtainableinpractice.


17/33

TheoriesofMassTransfer

Forman

yyearsmass

trans

fercoeff

icien

tsw

hichwere

base

dp

rimari

lyonem

pirica

lcorrela

tions

,have

be

en

use

dinthe

des

ignofprocessequipmen

t.

Some

th

eorieso

fconvec

tivemasst

rans

ferw

illbe

presente

dnex

ttosee

how

theycan

beuse

dtoex

ten

d

emp

irica

lcorre

lations

.


18/33

TheoriesofMassTransfer

Film

The

ory

Pene

tration

Theory

Boun

dary-l

ayer

Theor

y

Surface-r

enewa

lTheo

ries

Com

bina

tion

Film

Surface-r

enewal

Theory


19/33

1.

FilmTheory(or

Film

Mode

l)


20/33


21/33

TheFilm

Theory


22/33

TheFilm

Theory


23/33

2.

PenetrationThe

ory(Higpie

,1935)

Bas

icas

sump

tions:


24/33

Timeofexp

osureistooshortandconstant

forall

theeddies

;

Nopossibilityofformationof

concentrationgra

dient;

Liquidpartic

leissubjectedto

unsteadystated

iffusion;hence

,

2

2ZC

D

C

A

AB

A

=

Forsolutepointofview

,the

depthZ

bisconsid

eredasinfinite

.

2.

PenetrationThe

ory(Higpie

,1935)


25/33

Thecon

dit

ionsare

CA

=

CA0

at

t=

0

fora

llZ;

CA

=

CAi

at

Z=

0

t

>

0;

CA

=

CA0

at

Z=

fora

llt

So

lving

the

equa

tion

Averagem

ass

trans

ferc

oe

fficien

ttD

C

C

N

AB

A

Ai

ave

A

)

(2

0

,

=

kL,a

vispropor

tionalto(D

AB

)0.5

fo

rdifferentsolutesunderthesame

circumstance

s.

TherangeofexponentsonDvariesfrom

0to0

.8

or0

.9

2.

PenetrationThe

ory(Higpie

,1935)

t

D

k

AB

av

L

,

=


26/33

SurfaceRenew

alTheory(Danckwerts

,1951)

Inreality

,alleddiesareexposedforvaryingle

ngthsoftime

.

IfSisthef

ractionalrateofreplacementofthe

elements

,then

S

D

C

C

N

AB

A

Ai

ave

A

)

(

0

,

=

kl

ispropo

rtionalto(D

AB

)0.5

CombinationofFilm

Surface

renewalTheory

(Dobbins

,1956,

1964)

IfZ

bisoffin

itelength

,thenthe

B.C

becomes

CA

=

CA0

at

Z=

Zb

forall

ABb

AB

ave

l

DSZ

S

D

k

2

,

coth

=

Casei)

Forrapidpenetration&rateofsurfacerenewalissmall

,kfollows

Film

Theory

Caseii)For

slow

penetration

&rapidsurfacer

enewal,kfollowssurface

renewalTheory


27/33


28/33

Momentum

,HeatandMass

Transfer

Analogies


29/33

Momentum

,HeatandMass

Transfer

Analogies

Inturbu

len

tflow


30/33

Momentum

,HeatandMass

Transfer

Analogies

Three

transport

lawst

ore

lateheatt

rans

fercoe

ffic

ien

t

an

dthe

mass

trans

fer

coe

fficien

tto

the

friction

fac

tor:


31/33

Momentum

,HeatandMass

Transfer

Analogies

The

Pra

ndtlAna

logy:


32/33

Momentum

,HeatandMass

Transfer

Analogies

The

Col

burn

Ana

logy:


33/33

EndofL

ecture3

Nex

tLectu

re:

nterp

hase

Mass

Trans

fer

Lecture 3 Convective Mass Transfer

Documents

Transcript of Lecture 3 Convective Mass Transfer