The rate of mass transfer in a solar regenerator

IN H E ~ T A N D M ~ S S ~ R A N S F ~ Vol. 4, pp. 185 - 192, 1977

Perga~onPress Printed in Great Britain

THE RATE OF mASS TRANSFER IN A SOLAR REGENERATOR

V. Sriramulu and R.C. Gupta Dopsrtsant of Mechanical Engineoring Indian Institute of Technology

P. Gandhldasan,

Phldras,

India

(Ctzm~nicatsd by J.H. Nhitelaw) ABSTRACT A study o f the e f f e c t o f s moving l i q u i d f i l m and an a i r stream on gas-phase c o n t r o l l e d c o n v e c t i v e heat and mass t r a n s f e r has been aads,whl©h would f i n d widespread a P p l i c a t i o n I n devices which u t i l i z e s o l a r energy. The governing equations f o r a i r phase have been solved f o r v a r i o u s v a l u e s of' the r a t i o o f l i q u i d t o a i r v e l o c i t y . Profiles o f v e l o c i t y , toapsrature~and c o n c e n t r a t i o n as w e l l ae t h e i r g r a d i e n t s are p:esanted. The r e s u l t s , c o m p a r e d w i t h experimental f i n d i n g s obtained v i t h mass t r a n s f o r beln 9 extended to the l i q u i d phaee as w e l l , s h ~ an encouraging trend.

Introduction

W i t h l n c r e a e l n g importance b s l n 9 given to the u t i l i z a t i o n o n o r o y , s i a p l e and r e l i a b l e

of solar

methods o f o p e r a t i o n o f devices t h a t convert

s o l a r energy t o u s e f u l fotnm are ve~f much at a the main o b j e c t i v e s o f the u t i l i z a t i o n

of solar

premium.

For, one o f

energy, I s to

the dwelopmont o f 8uch devices and t h i s i e l i n k e d w i t h f i n d i n g but e f f e c t i v e and economical processes.

185

hasten siaplop

The present work considers the

186

P. Gandhidasan, V. Sriram/lu and M.C. Gupta

Vol. 4, No. 3

processes that govern the per?crashes or • solar ccll ootor-Qun-raganerator , an i m p o r t a n t component o f a s o l a r a i r o o n d i t i o n s r c a l vlew point.

~ 1,2

~ from a t h e o r e t i -

In such a u n i t , the absorbent solution flows down the

c o l l e c t o r and an a i r stream that f l o r a

past i t ,

removes moleturs from the

solution thereby ooncontrotlng i t . Statement or Problem In t h e p r o b l e m d i s c u s s e d above, am i n t i m a t e the solution

end t h e a i r

tion

flov

as a t h i n

unit

s i m p l e [ 3,4 ] .

film

has been found t h a t

ever the collector

film,

making t h e s o l u -

renders the operation of the

with the letter

energy.

flowing over n flat

Since t h e thtckMOee Of t h e l i q u i d

r e g a r d e d ee n e g l i § i b I y s m a l l , solely

It

between

The p r o b l e m c o n s i d e r e d I s one o f • s o - c u r r e n t

s t r e a m and • s o l u t i o n which a b s o r b s s o l a r

stream.

contact exists

from t h e gem phase.

the r e s i s t a n c e

Tks i n s o l a t i o n

t o ames t r a n s f e r

foiling

air

plato, film

la

atoms

on t h e a b s o r b e r i s

assumed c o n s t a n t s The e f f e c t for

tirol

o f a mevimg I R t o r f e o o on c o n v e c t i v e h e a t and osss t r i n e -

betmamn l i q u i d

investigated

to • limited

o f h e a t and mass t r a n s f e r Intezeetingl~t be s u c c e s s f u l l y

and 9 e l has boon t h e o r e t i c a l l y extent [ S,4,7]

Is a related

s t u d y an analysis

h a s boon made s s i o g an a p p r o x i m a t e method [ 8 ].

rot s problem of this employed.

•

and e x p e r i m e n t a l l y

nature the Slaoiue tronefoz~atien

The g o v e r n i n g d i f f e r e n t i a l av

-

- y

san

equations a:a

C1)

O

02. 2

(2)

oy aT

aT

(3) ~T 2

- B

02q aT =

(4)

Vol. 4, NO. 3

M~SS~]NAS(XARRBG~2~%~TC~

These equations with the following boundary conditions are to be y

~

O.

U t Ue~

T n Te~

q t

qe

u =uod

T . Too, Cl =

qm

187

aolvedl

(s) y-..~.ao,

The above set of pertLel d l f r e r e n t L a l equatLons are reduced t o o r d i nsry dLfferentLal equstLons by def/nLng a dLmmeLonlees vezLeble

and a

stzsam runctLon as I'ollows! J' ual

It

oan

be shown that these functLone s a t S s f y thm ¢ontLnu£ty equations.

Rolmrltum, anez~jy~and dSffueLon equations ere reduced to the follouLng dLmonslonlsss forms I rr t + 2r'*

e" + ~

"v" + ~ r

.

o

(?)

r e, . 0

(8)

"v'" o

(9)

The boundary c~ndLtLons ere reduoed to the roZlo~Lng dLaeneLonlese foz~s8 u

r(o)

-

o,

r,(o)

.

_s~,

e(o)

.

o,

e(m)

.

1

%(o)

.

o,

"vCa=)

.

1

r,(m).l (lo)

Rweulto and OlmouamJont The above dLfl'erer~LI1 squat/one v£th theL: ~©omanying boundary randLtLone wez~ solved on an ZBR 370/155 Compute: by Con~Lnuous System IqodellLng P : o g : l l (c.qflP).

Figure 1 Ihaue typ£cel valrJ.atJ.ons Ln velocLty~

188

Vol. 4, No. 3

P. Gandhidasan, V. Sriramulu and M.C. Gupta

08

/.0

:.

010.2

-"

0

2

0

4

6

8

FIG.1 P r o f i l e s o f V e l o c i t y , Temperature, C o n c e n t r a t i o n ,

and thelr gtadlents for

o.t5

1

i

I

u/uao= 0.2

I

1

F

I

~1

Air- Woter 5yMern Plote Temperoture : 50"C

0.4

Us~Urn

=0.2

~ o.3 E

0.2

2

0.;

o 0

I

I 0.2

I

l

1

0.4

1 G6

I

I OJI

Gr FIG.2 V a r i a t i o n o f k w i t h Gwaetz number

Vol. 4, NO. 3

~%SSTRANSFI~ IN A S C E A R ~ T Q R

189 u

tmparature

and c o n c e n t r a t i o n

as wall ae thoir

gradianto

for

a

u

= 0.2.

~D

The average mass t r a n s f e r : o a f J ' i o l o n t given b e l ~

k

Am e v aluat ed from t he equatian

far 5c = 0 . 6 . So

oq

[ r"(o)]

(--)

0y

.

.

(q~-ql)

y.o

f

m

[r']

x = _ y

sc

(.)

o

Figure 2 ohowo the v a r i a t i o n o? putad f o r • t e s t p l a t e

1 •

k

2ono and

ated mbovI t h e absorber aur~aoI. two e u r f a o I I and t h i absorber.

wll;h G~iotz number, which h a l been oom0.3 m wade, w i t h 8 0 1 a u p l a t o s i t u -

The o£r s t r u m 18 o o n f l n o d between

thrum

o b N r b o n t s o l u t i o n (CaloJ~Jm C h l o r i d e ) ?2owI over

Figure 3 d e p l o r e the v a r i a t i o n o f

I t h a n o l - ~ a r b o n d l o x £ d e :yotom.

k

t he

w i t h Craotz number f o r an

This I I p a z ~ l o u i l r i y ohoaen i n view o f the

f a c t t h a t both e x p e r i m e n t a l and ~hoorotlc81 : o e u l t o have boon zl)ozt;ed [ 8 , 7 ] f o r t h e case o f t h e ZLquid stream o f f e r i n g r e s i s t a n c e owing t o Ate f i n i t e t h i c k n e e l | hence, i t

a f f o r d s a roman: o f oomparlann w i t h t h e pr as o n t

obtained for a thin film.

I t i s d i s c e r n i b l e t h a t w i t h t he l i q u i d flmd£no

as a t h i n ? f i n , t h e M a l l t r a n l f o r expoot I n t u i t i v e l y .

da~,s

c ~ a f f l o L e n t 11 hLOhor, as one

~ouid

The l n © : e a N i s me muoh e l 200 per l e n t , • oon~lLuelon

which would a i d th e development o f a #molar 14~enerarl~or.

I r l g u r l 4 ottawa

u

k

ploL~md a o a i n e t

water,

I uGo bflth l r m r o o e i n 0

f o r the expected r a t e o f o p e r a t i o n el* a rogenou

~

,

k

ol

t o d e t e z u l n e the optimum v a /u o o f inmalotlon.

lnoroalml.

F u r t h e r wed( 18 i n pro|Items

u u

#m f o r given oondlt£ona of' am

190

P. ~ s a n , 0.4

V. Sriranlllu ard M.C. Gupta

l

i

l

I

I

I

C02-Ethano/ 5ystem Plate Temperature = 25°C - 0.3

EcJ "- 0.2

0.1

o

1 0

l

I

0.2

I

I

0.4

I 0.6

Gr

FI~.3 Va~latlon of k v l t h G~aotz number

o.5

i

I

I

Re = 1.645 x I0 5

t ~¢ 0.4

o.~

o.

I i o.%/:~

I o.,

FIG.4

Va=i=tl=. =f k vith v / v

Vol. 4, No. 3

Vol. 4, NO. 3

K%SS~I~ANmrER IN A S C ~ A R ~ T O R

191

N~men:l~u~

0

dlrrusLon o o e f r t e i e n t

r(~ )

d£eensLonle88 v a r i a b l e

(;it

Graetz nuabo~

k

ma88 t~ert8~er o o e r r i c i o n t

Pit

P : a n d t l ntmber

qoo~qs the concentratLon or the s o l u t e outoide the boundary l a y e r , and at the l i q u i d 8urfa©e r e s p e c t i v e l y Re

Reynolds ntmber

Sc

Schmldt number

Too ,T O temperature o f f r e e o t r stream end l i q u i d 8urfaoo ]respectively uW , u a v e l o c i t y or al~ or:earn outside the boundary l a y e r and at 1LquLd eurPaoe : e e p e o t i v e l y u, v

gas phase v e l o c i t y ~mponento i n the

x

and

y

dLrectLon

~oopootLvoly x

the dLotanco pare t l e l

to the 11quLd outface

y

the dLotance noz~al to the 11qutd surface

G

d£monoLonleoo tampor~u~op

T-T T-T 8 10

ii ¥

dimme/onleoo ooncentrskLon, qo-q qm'q~

"(

klnemetlo v l o o o e l t y

"1;

thel~al dLPfuolvlty

?

eklmam funot :Lon

Superscript prime ( e ) denotee d i f f e r e n t i a t i o n

e i t h :aspect to l~

192

P. GaIKihidasan, V. Sriramllu and M.C. Gupta

Vol. 4, No. 3

Refezences 1. G.O.G. Lof, "House heating and cooling with solar energy", Solar Energy Research, Univezsity of Wisconsin Press, Madison, Wisconsin, 1955, pp. 33-46. 2. S.C. Mullick, "Solar airconditioning: Regeneration of absorbent s o l u t i o n " , Ph.O. Thesis, I I T , Madras, 1976. 3. S.C. Mullick and M.C. Gupta, "Solar desorption of absorbent solutions", Solar Energy, Vol. 16, 1974, pp. 19-24. 4. P. Gandhidasan and M.C. Gupta, "A new method of sun powered airconditioning", Paper presented at International Institute of R e f r i g e r a t i o n , Melbourne, Sept. 6-10, 1976.

5. C. Prasad, C.S. Chert and 3.T. Beard, "Forced convection heat and mass tcansfer From a moving gas-liquid intecfacs", Presented at the Winter ~nnual meeting of the Pmerican Society of Mechanical Engineers, Washington, O.C., Nov. 30, 1971. 6. C.H. myers and C.3. King, "Gas-liquid mass transfer with a tangentially moving interface: Pazt I - Theory", A.I.Ch.E. 3ournal, 3uly 1967, pp.628-636. 7. C.H. Bye=s and C.3. King, "Gas-liquid mass transfer with a tangentially moving interfaoss Part II - Experimental studies", A.I.Ch.E. 3ournal, 3uly 1967, pP.637-644.

B. A. Activos, "On the r a t s of mass tzansfor from a gas to a moving l i q u i d f i l m " , Chemical Engineering Science, Vol.9, 1958,pp.242-249.