Table Of Contenthf. J. Heat Mass Transfer. Vol. 5, pp. 109-112. Pergamon Press 1962. Printed in Great Britain.
PIONEER PAPERS IN CONVECTIVE MASS TRANSFER
.K :SIWEL ehT noitaropave fo a diuqil otni a gas, .)2291(
3. W. Mechanical Engineering, 44, 445
detnirpeR yb noissimrep fo ehT naciremA yteicoS fo lacinahceM .sreenignE
EZtor’s Foreword
syadawoN eht mret siweL“ ”rebmuN si deilppa ot eht oitar fo eht noisuffid tneiciffeoc fo a tnenopmoc ot eht lamreht
ytiviktid fo eht .erutxim nI na reilrae egasu revewoh eht mret deifingis eht oitar fo a ssam refsnart tneiciffeoc semit
a cificeps taeh ot a taeh refsnart .tneiciffeoc nI rehtie ,esac eht sselnoisnemid ytitnauq ni noitseuq serusaem eht evitaler
esae fo ssam dna fo taeh refsnart ni eht emas ;noitautis sti eman si a etubirt ot eht rohtua fo eht repap detnirper .woleb
nI siht ,repap .W .K siweL ”sevorp“ eht evoba noitaler neewteb eht stneiciffeoc .e.i( h/k = 1) dna secudda -irepxe
latnem data ni .troppus eW won wonk taht eht foorp sniatnoc a ycallaf dna taht eht noitaler neewteb eht stneiciffeoc
sdloh ylno nehw eht siweL rebmuN ni( eht nredom )esnes si lauqe ot .ytinu ,yletanutroF siht noitidnoc si ylesolc
dellifluf ni tsom refsnart-ssam sessecorp gnivlovni ;sesag s’siweL tluser si erofereht ylediw dna ylbaifitsuj desu ni eht
ngised fo gnilooc ,srewot ni eht sisylana fo leuf noitsubmoc dna ni ynam rehto .smelborp
.S.B.D
THE EVAPORATION OF A LIQUID INTO A GAS
W. K. LEWIS*
,ecnereffid tub dedda a small noitcerroc mret
The author investigates the mechanism of the
lanoitroporp ot eht erauqs fo eht .ecnereffid
evaporation of a liquid into a gas as applied to
sworraB and 3bbaB edam a egral rebmun fo
such processes as are found in gas scrubbers,
snoitanimreted fo noitaropave morf eht ecafrus
humidifiers, dehumidifiers, water coolers, air
fo eniaM ,sekal and elihw rieht latnemirepxe
driers, etc. He establishes a formula for calculating
snoitanimreted erew tcejbus ot a egral egatnecrep
the humidity of air from wet- and dry-bulb
,noitairav enon eht less rieht stluser substantiate
thermometer readings, and shows that the co-
this .ytilanoitroporp eroM yltnecer Willis .H
eficient of heat transfer divided by the coeficient
+eirraC has nwohs that eht etar fo retaw
of diflusion equals the humid heat of the gas.
noitaropave is, nihtiw latnemirepxe ,rorre -orp
A tnuoma fo krow has neeb enod no eht lanoitrop ot erusserp-laitrap .ecnereffid ehT
LARGE
noitaropave fo retaw otni ria at serutarepmet gniwollof is an sisylana fo eht msinahcem fo hcus
woleb eht gniliob .tniop ehT cimanyd muirbiliuqe .noitaropave
gnidnopserroc ot eht noitaropave fo retaw otni
ria decnalabretnuoc yb eht wolf fo taeh morf eht eilseL s’noslohciN ,lanruoJ .lov 3, .p 401. ,tsuguA
ria otni eht retaw is eht basis fo blub-tew .ggoP ,.nnA .lov 5, .p 69, 1825; ,nbojpA .snarT layoR
hsirI ,.dacA .lov 17, .p 275, 1834; ,nnamrelieW
,yrtemomreht eht tsom lufesu dohtem fo -reted
.loroeteM ,.tieZ .lov 12, .pp 268 dna 368, 1877;
gninim eht ytidimuh fo l.ria nI 1886 dnomseD
.llewxaM .tieZ .f ..loroeteM .lov 16, u. 177, 1881.
2dlaregztiF detniop tuo that eht etar fo -aropave .D ,noslowohC Trait6 ed ,euqisyhP .lov 3, trap 3,
noit fo retaw otni ria is a noitcnuf fo eht -fid .p 807, 1911.
ecneref ni laitrap erusserp neewteb eht erutsiom lanruoJ ,.E.C.coS.mA 1886.
.S.U .tpeD fo ,roiretnI ,notgnihsaW ,.C.D retaW
ni muirbiliuqe htiw eht gnitaropave retaw and eht
,.lppuS nitelluB .oN 279.
lautca erutsiom tnetnoc fo eht ria ni tcatnoc htiw
.coS.mA gnitaregirfeR ’sreenignE ,lanruoJ 1916, .lov
.ti tI is eurt that dlaregztiF did ton assume eht 2, .on 6, .p 25.
etar fo noitaropave ylraenil lanoitroporp ot this
repaP detneserp at eht gnirpS ,gniteeM ,atnaltA Ga.,
yaM 8 ot 11, 1922, fo
THE AMERICAN SOCIETY OF
* daeH fo tnemtrapeD fo lacimehC ,gnireenignE LACINAHCEM .SREENIGNE ylthgilS .degdirba llA srepap
sttesuhcassaM etutitsnI fo .ygolonhceT era tcejbus ot .noisiver
109
110 REENOIP SREPAP NI EVITCEVNOC SSAM REFSNART
PR~LII~~ARY ASSUMPTIOBS s :z: dimuH heat, or rebmun of heat stinu
roF sesoprup of alumrof noitavired emussa a yrassecen ot egnahc the erutarepmet
gnol lennut hguorht hcihw detarutasnu ria si of tinu thgiew of eerf-ropav gas, v.ul)/
gniwolf at tnatsnoc ssam .yticolev ehT sllaw the rapou it contains, eno :eerged
of siht lennut are srotcudnoc-non of heat. gnolA W== thgieW of diuqil .detaropave
the mottob of the lennut si decalp a tam or kciw
yltnenamrep wet htiw water deilppus morf woleb INTERACTION OF WATER WITH AIR
as noitaropave takes ecalp .evoba ehT water si Now redisnoc for the tnemom the snoitidnoc
dehsinruf ot siht kciw at yreve tniop at a -met at yna nevig tniop gnola the htgnel of siht .lennut
erutarep yltcaxe lauqe ot that of the water no tA siht tniop the ,erutarepmet etulosba ,ytidimuh
the reppu ecafrus of the kciw at that .tniop dna erusserp of water ropav ni the ria lliw eb
erehT si on noitom of the diuqil water lellarap ot detneserper yb ,t H dna 11. ecniS the sutarappa
the sixa of the .lennut ehT ssam yticolev of the si suounitnoc ni sti noitarepo these snoitidnoc
ria revo the water si tnatsnoc dna yitneicil’tus wol lliw niamer degnahcnu at siht ralucitrap .tniop
so that heat detareneg yb noitcirf yam eb tub lliw yrav morf tniop ot tniop gnola the
.detcelgen .lennut ehT gnidnopserroc seititnauq -tneserper
ehT detarutasnl~ ria gniretne siht lennut lliw gni the noitidnoc of the diuqil water ni tcatnoc
emoceb deifidimuh ni gnissap hguorht ti gniwo htiw the ria at siht ralucitrap tniop are f,,., H,,, dna
ot the noitaropave of water. nI .ecneuqesnoc .KP
the erutarepmet of the ria lliw ,llaf dna fi the ehT msinahcem of noitcaretni of the water
lennut eb yltneiciffus ,gnol the water dna ria lliw htiw the ria si as :swollof erehT stsixe revo the
yletamitlu emoc ot .muirbiliuqe water what si tnelaviuqe ot a yranoitats mlif of
,ria hcihw setalusni the water morf the niam
ydob of the .ria hguorhT siht ria mlif heat si
gnisuffid morf the ria otni the water dna hguorht
NOTATION
the emas mlif there si ,gnisuffid ni the etisoppo
nI the alumrof ot eb ,devired the gniwollof
,noitcerid the water ropav demrof yb -aropave
noitaton si :desu
noit no the ecafrus of the .diuqil sihT noitaropave
A= aerA of diuqil ni tcatnoc htiw ;sag slooc the ecafrus of water, ,dna ecnis ti si -liava
H= etulosbA ytidimuh of gas, or parts yb elba morf on other ,ecruos heat tsum eb -pus
thgiew of ropav per part yb thgiew of deilp ylelos yb noisuffid morf the .ria ehT heat
ropav free ;sag of noitaziropav tsum therefore eb ylevitatitnauq
h = ecafruS tneiciffeoc of ytivitcudnoc of detasnepmoc yb the heat woA hguorht the -rus
heat neewteb gas dna diuqil or .u.t.B face ,mlif dna the rate of noitaropave si detimil
per tinu emit per tinu ecafrus area per yb the rate of noisuffid of ropav hguorht the
tinu erutarepmet ;ecnereffid emas .mlif
k’ =T tneiciffeoC of ,noisuffid or parts yb morF the gniogerof eno nac yletaidemmi
thgiew of ropav desuffid per tinu emit etirw the gniwollof snoitauqe :
per tinu area per tinu etulosba ytidimuh
dW
;ecnereffid _ 8dA._. =I k’(pM - P)
k = tneiciffeoC of ,noisuffid or parts yb
thgiew of ropav desuffid per tinu emit
per tinu area per tinu ropav erusserp AddQB = k(t - tw) (21
ecnereffid ;
laitraP erusserp of ;ropav dQ := .--.-r&W (3)
“,s latoT erusserp of ropav dna eerf-ropav ecnehW
gas ,.e.i( ;)retemorab
lg ==; ; emiT :uP - P = ;ttt, (t - &“I (4)
t ZZZ ;erutarepmeT sihT tsal noitauqe si the eno yllamron desu for
r = tnetaL heat of ;noit~iropav gnitaluclac the ytidimuh of ria morf -tew dna
PIONEER SREPAP IN EVITCEVNOC MASS REFSNART 111
blub-yrd* retemomreht .sgnidaer‘ nI ,ti noitairav tnuoma dH. ehT taeh nevig up yb gnilooc must
ni ,r is detcelgen and eht mret ,r’kjh is assumed dnopserroc ot eht taeh fo noitaziropav fo eht
.tnatsnoc roF p ni sretemillim fo yrucrem and 2 retaw dekcip up, ,.e.i
ni .ged ,.tnec ti slauqe 0.5. ehT noitauqe -mi
-sdt = r,dH (8)
ylticilp assumes that eht gnilooc fo eht ria is
,laitnereffid ,.e.i os small ni eht doohrobhgien ,ecnehw assuming ycnatsnoc fo s and r,,,,
fo eht tniop ni noitseuq that eht lautca segnahc
ni erutarepmet and ytidimuh fo eht ,ria t and y H = - ;:. t + .tsnoc )9(
ro( ,)H era .elbigilgen
Assuming eht lennut yletinifedni ,gnol eht ria
ecniS lliw yletamitlu emoceb detarutas at emos
H
erutarepmet ,,t and ytidimuh H,. ecniS eseht
18
p-__p (5) snoitidnoc tneserper muirbiliuqe neewteb eht
H 1 ria and eht ,retaw noitaropave lliw ,esaec and ,t
1s ! 29 and N, era erofereht eht ,tnatsnoc dexif -dne
stniop fo eht .ssecorp gnitresnf eseht ,stimil
,H H = ;” (t - tJ.
eW evah won devired owt salumrof gnitcennoc
H and ,t htob gniylppa ot this emas ssecorp
erehW H is small, as is yllausu eht esac woleb fo ,noitaropave ,.e.i
,H
150 .ged ,.rhaf Cg and i era elbigilgen -moc
,H H = r‘, (t - t,)
1
derap htiw 3, and eno yam ,etirw as a esolc
and
H, - H = E; (t - >wt
,noitamixorppa
!U
esehT owt snoisserpxe must erofereht eb
(7)
.lacitnedi yB eht dohtem fo denimretednu
erehw- P stneicifeoc this nac eb eurt ylno dedivorp eht
k = &k92
gnidnopserroc stneiciffeoc era ,lauqe ,.e.i
tI is suoivbo that h and k dneped no eht -kciht s h h
ness fo eht ria mlif and era erofereht snoitcnuf - ,vcx-= ro s = k
wr
fo eht yticolev fo eht .ria tI is, ,revewoh yllauqe
suoivbo that fi ria yticolev eb desaercni -iffus and ,,t = ,,t a :tnatsnoc and H, = H,, osla
yltneic ot elbuod eht ,eno eht rehto lliw elbuod .tnatsnoc
.osla ehT oitar fo h/k erofereht sniamer ,tnatsnoc oS raf eht noissucsid has neeb detimil ot retaw
tnednepedni fo .yticolev sihT snialpxe yhw eht and .ria ,ylsuoivbO ,revewoh eht emas -noitaler
gnidaer fo a blub-tew retemomreht is -ulfninu ships must ylppa ot yna diuqil and yna gas htiw
decne yb eht yticolev fo ria passing ,ti dedivorp hcihw its ropav is .dexim
eht yticolev is tneiciffus os that yna taeh tsol yb ehT tsrif fo eseht ,snoitauqe h/k = s, states
noitaidar is elbigilgen ni nosirapmoc htiw that that eht tneiciffeoc fo taeh refsnart dedivid yb eht
dekcip up yb .noitcudnoc tneiciffeoc fo ropav noisuffid hguorht eht gas
mlif is ,tnatsnoc and lauqe ot eht dimuh taeh fo
THE RELATION h[k = s eht gas. yB snaem fo alumrof }4( eht oitar h/k
woN redisnoc eht egnahc ni ytidimuh and nac eb detaluclac morf eht devresbo -tew and
erutarepmet fo eht ria as ti sevom gnola eht blub-yrd serutarepmet rof yna sag-ropav -xim
.lennut gnitratS at eht emas tniop ylsuoiverp erut fo a nwonk gas .ytidimuh ehT latnemirepxe
,deredisnoc eht ria lliw pord ni erutarepmet yb snoitanimreted fo blub-tew serutarepmet rof
na tnuoma dt and esaercni ni ytidimuh yb an ,ria-retaw nobrac-retaw ,edixoid ria-loulot and
112 PIONEER SREPAP IN EVITCEVNOC SSAM REFSNART
,ria-loznebrolbc and snoitaluclac rof k/h nevig ylidaer detaluclac rof yna esac sseldrager fo
ni elbaT 1 wohs that this oitar is ni all sesac rehtehw eht melborp is yliramirp eno fo taeh
yllaitnatsbus lauqe ot eht dimuh taeh fo eht refsnart ro fo .noisuffid ecneH fi eht -taeh
gniretne gas, hcihw ni this esac was lacitnedi htiw refsnart tneiciffeoc h has neeb yllatnemirepxe
eht cificeps taeh esuaceb eht gas hcihw was desu den~reted rof a niatrec epyt fo apparatus
was ropav .eerf gnitarepo rednu etinifed ,snoitidnoc eht -iFfeoc
tneic fo noisuffid slauqe ,sJzI and eht yticapac fo
-- Table_ _ 1. seulaV ~~~ B-..__ of .- k/h for various vapor-gas - _.-_____ mixtures m this emas apparatus yam eb detciderp nehw
k/h detaluclac cificepS gninoitcnuf ni noisuffid ,sessecorp .g.e as a gas
morf latnemirepxe taeh .rebburcs ,ylesrevnoC fi k and s era nwonk rof
stluser fo sag etinifed ,snoitidnoc h slauqe ks; ni rehto ,sdrow
. - .-__-.
eno nac tciderp eht ecnamrofrep fo a nevig
ria-retaW 0.236 0.238
nobrac-retaW edixoid 0.217 0.220 apparatus rof taeh refsnart morf data nopu eht
ria-louloT 0,238 0.238 emas tnempiuqe gninoitcnuf as a .rebburcs
ria-loznebrolhC 0.248 0.238 esehT sessecorp fo noisuffid fo taeh and fo
__-__._..~~~: z :-Yr?.. -. -r --- z :7
ropav era at eht basis fo eht ecnamrofrep fo all
eW evah erofereht detartsnomed that, gnitnarg
hcus tnempiuqe as ,sreifidimuh ,sreifidimuhed
substantial ycnatsnoc fo s and Y,, and assuming
retaw ,srelooc gas ,srebburcs ria ,sreird thgil lio
II ot eb small, eht oitar fo eht tneiciffeoc fo gnippirts ,snmuloc and eht .ekil ehT evoba
noisuffid fo taeh ot that fo yna ropav hguorht eht spihsnoitaler ekam ti elbissop ot yduts eht
gas mlif no eht ecafrus fo eht diuqil is lauqe ot ecnamrofrep fo hcus tnempiuqe no a erom
eht “humid” taeh fo eht gas. ,eromrehtruF lanoitar basis than otrehtih and ot erapmoc eht
gnirud lyycitabaida“ noitaropave fo a diuqil ssenevitceffe fo tnereffid sepyt fo tnempiuqe neve
otni a gas, eht diuqil gnieb ni cimanyd -iliuqe nehw eht data no eht laudividni sepyt era
muirb htiw eht gas eht erutarepmet fo eht diuqil deniatbo rednu ylediw gniyrav .snoitidnoc ehT
sniamer degnahcnu tuohguorht eht ssecorp and tnemtrapeD fo lacimehC ,gnireenignE Massa-
eht tniop-dne fo eht ssecorp is dehcaer nehw eht sttesuhc etutitsnI fo ,ygolonhceT stcepxe ot
gas has delooc flesti ot noitarutas at a -arepmet publish ni eht raen erutuf a seires fo selcitra
erut lacitnedi htiw that fo an yranidro blub-tew gniwohs suoirav snoitacilppa fo eseht
2.retemomreht
*.snoitaler
-_____-_ ---
ECNATROPM FO THE PIHSNOITALER h/k = s * Edifur’s footnote: tI saw ni eno ,eseht yleman Mech.
ehT ecnatropmi fo eht pihsnoitaler k/h = s. is Engng vol. 55 (1933), .p 567, taht siweL flesmih detniop
yrev .taerg ehT mret s, eht dimuh ,taeh yam eb tuo eht ycallaf ni eht tnemugra fo sih 1922 .repap erofeB
____- -_____ gninrut ot eht retal repap rof ,noitamrifnoc sredaer thgim
1. .W I-I. ,reirraC lanruoJ ,.E.M.coS.mA 1912, .p 1321. ekil ot ekam up rieht nwo sdnim tuoba erehw eht ycallaf
2. Ibid. .seil
_-- ---_- ~__.____ _. ~~_ __._~.
ATARRE
.H .L EVANS: Mass refsnart hguorht ranimal yradnuob 6-sreyal sdohteM fo gnitaulave eht wall
tneidarg )B/Q( rof ralimis ;snoitulos emos wen seulav rof orez maerts-niam erusserp ,tneidarg
ht.
.J. Heat Moss Tram$?r, 3, No. 4, 321-339 (1961).
ehT gniwollof snoitcerroc dluohs eb edam ot -ealumrof
)a( noitauqE )52( dluohs :daer P
-e ,- )52(
./,”
)b( ehT etamitlunep mret fo noitauqe )33( dluohs :daer
3e577S-
)c( noitauqE )45( dluohs :daer
)45(
