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An Introduct ion to Fluid Mechanics and Heat Transfer

3rd Edit ion . By J . M. Kay and R. M. Ned derm an. Ca m-

br idge Univ ers i ty Pre ss , New York (1975) . $18.95 .

This tex t , in the opin ion of th is r ev iew er , wil l be a very

u s e f u l p o ck e t h an d b oo k f o r th e p r a c t i c in g o r r e s e a r c h e n g i -

neer who has to dea l with a var ie ty of fundamenta l ideas in

f lu id me c h a n ic s a n d t r a n s p o r t p h e n o me n a . I t s p r in c ip a l

v ir tue , as the au th ors s ta ted in the i r Pre fac e , l ies in i ts

h ighly condensed account of the bas ic phys ic a l and ma the-

ma t ic a l p r in c ip le s r e l a t in g to ma n y e n g in e e r in g p r o c e s s e s .

Th i s r e v ie w e r f in d s n o c o mp a r a b le b o ok b y a n y A me r ic a n

p u b l i s h e r .

Although the a u tho rs d id not expl ic i t ly s ta t e the ir in-

tended readers , the book mus t be v iewed pr imar i ly as a

tex tbook becau se i t is based on the i r le c tu res g iven a t

Cam br idge Univ ers i ty ov er a per io d of many ye ars . When

viewed as a c la ss ro om textbook, the pr inc ipa l pa r t of the

book is wr i t ten extre me ly well in te rm s of i ts l i te ra l s ty le

and mater ia l content .

Admit ted ly , in t ry ing to in troduce any sc ient i f ic subjec t ,

a f ew fundame nta l concep ts m us t be accepted as ba s is for

subsequent deve lopment . The essent ia l contr ibut ion of an

autho r is the se lec t i on of those bas ic con cepts tha t wil l be

the eas ies t to com prehend . But in many p l aces where a

phy s ica l not ion is f i r s t in troduced, the au thors tend to u se

an approa ch tha t is c omp lica ted for the unin i t ia ted and

u n n e c e s s a r y f o r th e ma tu r e r e a d e r s .

For examp le , in Chap. 1 the concept of hy dros ta t ic

p r e s s u r e i s in t r o d u c e d wi th Th i s f o l lo ws d i r e c t ly f r o m

th e a b s e n c e of s h e a r s t r e s s . S in c e i t i s a s s u m e d th a t th e

r e a d e r i s f a mi l i a r w i th th e p r in c ip le s in h y d r o s ta t i c s a n d

tha t i t has a lrea dy been s ta ted tha t the f lu id is a t r e s t , the

concept of pr es su re ca n be in troduced without m entioning

th e mo r e d i f f i c u l t n o t io n of s h e a r s t r e s s . M o r e o v e r , l a t e r

in the same chapter , when the v iscos i ty is in troduced, i t is

s t a t e d th a t a f u l l d i s c u s s io n of th e s e s h e a r s t r e s s e s wi ll

b e g iv e n in a l a t e r Ch a p t e r .

S im ila r ly , the concept of tem per a tu re is in troduced by

f i r s t r e q u i r in g th e r e a d e r to a c c e p t th e id e a of th e r m a l

equi l ibr ium and by then def in ing the te m pe ra t ure of the

equi l ibr ium s ta te of two bodies in contac t . S ince the

auth ors a lread y mentione d ea r l i e r the d if f icu l ty of def in ing

tem pe ra t ure without the not ion of hea t , i t is ha rd fo r th is

reviewer to see why the idea of thermal equi l ibr ium should

be an eas ie r not ion for the reader to accept than tha t of

hea t .

Th e g e n e r a l th r e e - d ime n s io n a l p a r t i a l d i f f e r e n t i a l e q u a -

t ion of cont inui ty is in troduced by mean s of co ntour

in t egr a ls in Chap. 2 . The par t ia l d if fe ren t ia l equa t ion

governin g hea t conduct ion is der ived in Chap. 8 by a

s im ila r app roach . Although the au thor s c la im tha t to save

space , vec to r nota t ion (hence the contour in te gra l s ign) is

used occas iona l ly , th is r e v ie we r ques t i ons the need to

deve lop the equa t ions of cont inui ty and energy in th is

fashio n . F i r s t , none of these d if fe re nt ia l fo rm s of equa-

t ions a re needed in subsequen t dev e lopm ent . Second, in an

in trodu c tory tex t i t would be be t te r to concen tra te on the

phy s ica l concept without the advanced math em atica l juxta -

pos i t ion to d if fuse the presen ta t io n (u nless th e in tended

r e a d e r i s v e r y p r o f i c i e n t in ma th e ma t ic s b u t s h o r t in

phy s ica l concept) . Thi rd , to keep on the sa m e leve l of

ma th e ma t ic a l s o p h i s t i c a t io n a s th e p r e s e n ta t io n s in th e

o th e r c h a p te r s , s imp le o n e - d ime n s io n a l e q u a t io n s o f c o n t i -

nuity in Chap. 2 and of energy in Chap. 8 would be suff icient.

The g ene ra l equa t ion of cont inui ty should be in trod uced in

Chap. 12 , s ince Chaps . 12 through 18 g ive the genera l

ma them atica l th eor ies of f lu id f low and convec t ive h ea t

t ra nsf e r , which inc lude the genera l hea t conduct ion equa t ion

as a spec i a l case . The m ate r ia ls conta ined in Chaps . 12

through 18 mu s t be v iewed sep ara t e ly f ro m the re s t of the

book (see below).

The book is d iv ided in to 3 main sec t ions and 23 chapter s .

Ch a p te r s 1 th r o u g h 1 1 c o n s t i tu te a n e le m e n ta r y in t r o d u c t io n

to f lu id me c h a n ic s a n d h e a t t r a n s f e r . Ch a p te r s 1 2 th r o u g h

18 g ive the bas i c m athem atica l the or i es in flu id flow and

hea t t r ansfe r , inc luding the der iva t ions of the Navier -Stokes

equa t ion and Prandt l ' s boundary layer and mixing length

th e o r ie s . Ch a p te r s 19 th r o u g h 2 3 a r e c o n c e r n e d wi th

appl ica t ions of f lu id mechanics and t ranspor t phenomena in

pro ces s in g en ginee r ing . S ince Chaps . 19 through 23 a r e on

the sam e leve l as , and indeed can be c ons i dered as a con-

t inua t ion of , the f i r s t e leven chap ter s , Chaps . 12 through 18 ,

wh e r e mo r e a d v a n c e d ma th e ma t ic s a r e u s e d , mu s t b e

viewed as a sep ara te en t i ty . As bef i t t in g an in trod uc tory

text, the conten t in Cha ps. 12 throu gh 18 is co nci se and can

be taken as a convenient advan ced r e fe ren ce fo r the o ther

pa r t of the book or a poss ib le sou rce of se lec t ion for

prese nta t ion if used a s a tex tbook. The th rus t of the book

mu st re ly h eavi ly on the content of Chaps . 1 through 11 and

19 through 23.

Af te r an in troduc t ion in Chap. 1, whe re som e of the

p h y s ic a l t e r min o lo g y s u c h a s p r e s s u r e a n d t e m p e r a tu r e

ar e def ined , the funda men ta l pr in c ip l es in f lu id m echa nics

a n d h e a t t r a n s f e r a r e p r e s e n te d in th e n e x t t e n c h a p te r s :

f lu id mec hani cs in Chaps . 2 through 7 and hea t t r a ns fe r in

Chaps . 8 through 11. F lu id s in motion a r e d isc usse d in

Chap. 2 by us ing the vor tex motion as an i l lus tra t ion and by

a p p ly in g Be r n o u l l i ' s e q u a t io n to v a r io u s f low me a s u r in g

d e v ic e s . Th e mo m e n tu m a n d e n e r g y r e la t io n s f o r f lo ws

ar e descr i bed in te rm s of a cont ro l volum e in Chap. 3 , and

the ir appl ica t ions to p ipe f lows , je t pum ps , and reac t ion

turb ines a r e g iven in Chap. 4 . The fu ndam enta l conce pt of

d imens iona l ana lys is for f lu id f low is in troduced in Chap. 5 .

This is fo l lowed by the p rese nta t ion in Chap. 6 of both the

lam ina r and turbulent f r i c t i on coef f ic ien t s in te rm s of the

Reynolds number and the roughness fac tor for open-channel

f lows . The f lu id me chan ics aspec t is conc luded with the

p r e s e n ta t io n of c e n t r i f u g a l p u mp s a n d c o m p r e s s o r s in

Chap. 7 . The phenom enon of hea t conduct ion is in trodu ced

in Chap. 8 , fo l lowed by the ana lys is of both para l le l- f low

and counter - f l ow hea t exch ang ers in Chap. 9 . T he d im en-

s iona l ana lys i s is aga in d iscus sed in Chap. 10 to in trod uce

th e n e e d e d d ime n s io n le s s n u mb e r s in h e a t t r a n s f e r . Th e

Re y n o ld s a n a log y a n d th e Ta y lo r - P r a n d t l a n a lo g y a r e me n -

t ioned in Chap. 11 to show cor re la t io ns in te rm s of d im en-

s io n le s s n u mb e r s f o r th e tu r b u le n t h e a t - t r a n s f e r c o e f f i c i e n t .

Fr om a pedagogica l v iewpoint , th is r ev iew er would l ike to

see the phenomenon of convec t ive hea t t r a ns fe r d isc usse d

in Chaps . 10 and 11 preced e d isc uss i on of the he a t ex-

changers g iven in Chap. 9 .

As mentioned ear l ie r , the mater ia l in Chaps . 19 through

23 is , essent ia l ly , a cont inua t ion of tha t g iven in C haps . 1

through 11 . If there is any d if fe renc e , i t mus t be tha t in

e a c h c h a p te r th e s u b je c t m a t t e r t r e a te d i s t r a d i t io n a l ly

cons idered to be long to a spec if ic branch of engineer ing .

Fro m the v iewpoint of pro ce sse s , i t is d if f icu l t to see tha t

th e f lo w th r o u g h a c o n v e r g e n t - d iv e r g e n t n o z z le d i s c u s s e d

in Chap. 19 is p ar t i cu l a r ly d if fe ren t f rom the f low be tween

com pre sso r va nes g iven in Chap. 7 . In addi t ion to nozz le

f low, f lu id f lows through p ipes with f r ic t ion and hea t t r ans-

fe r a r e a lso d iscus sed in Chap. 19. In Chap. 20 , open-

channel f lows and the concept of c r i t ica l depths a r e

i l lu s tra t ed by f lows over we ir s and hydrau l ic jum ps . The

subje c t of so l id p ar t ic l es in f lu id f lows is in trod uced in

Chap. 21 and i l lu s tra t ed with the an a lys es of a cyc lone

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co l l ec to r and a ven tu r i s c r ub be r . F low s th rough packed

beds a r e d i scu ssed i n C hap . 22 and i l l u s t r a t ed w i th t he

phenom enon of f i l t r a t i on . In t he sam e c hap t e r , t he c r i t i ca l

f l ow ne ces sa r y t o f l u id i ze a packed bed i s a l so d i scu ssed .

In C hap . 23 , f i lm condensa t i ons a r e ana lyzed by a s sum ing a

l i ne a r t em per a tu re p ro f i l e , and t he hea t t r a ns fe r t o bo i l i ng

l i qu id i s d i sc usse d w i th a f ew em pi r i ca l co r r e l a t i on s .

T he m a te r i a l s i n C haps . 12 t h rough 18 , t he m a them at i ca l

t heo r i e s of f l u id m echan ic s and hea t t r a ns fe r , con s i s t

e s sen t i a l l y o f t he de r iva t i ons o f t he va r iou s gove rn ing

equa t ions . T hes e w e l l -know n equ a t ions can be eas i l y s een

f ro m the r e sp ec t i v e t i t l e s used fo r each c hap t e r . T hes e

t i t l e s a r e E qu a t ions o f M ot ions fo r a V i scous F lo w ,

B o u n d a r y L a y e r , T u r b u l e n t F l o w , P o t e n t i a l F l o w ,

D i f f u s i o n a n d M a s s T r a n s f e r , T h e E n e r g y E q u a ti o n a n d

H e a t T r a n s f e r , a n d F o r c e d C o n v e c t i o n . T h e s e d e r i v a -

t i ons a r e fu r the r supp lem en ted by s ix append ices .

Throughout the book, the metr ic (S i ) system is used, and

a conve r s ion t ab l e t o t he B r i t i sh sys t em i s g iven i n A ppen-

d ix 7 . T he re a r e 40 sam p le p rob l em s w i th a co r r e spon d ing

number of solut ion out l ines given a t the end of the book.

In conclusion, the book contains a weal th of fundamental

i n fo rm a t ion fo r ea sy r e f e r e nc e and w i l l be an exce l l en t

col lege textbookif the lecturer modif ies some of the

i n t r o d u c t o r y a p p r o a c h e s d i s c u s s e d e a r l i e r .

Chen Ya Liu

Ba t te l l e Co lum bus L a bora to r ie s

505 King Avenue

Colum bu s , Oh io 43201

March 13, 1975

About the Reviewer: C. Y. Liu has been engaged for 20

years in research and development in the areas of fluid

mechanics and heat transfer, first at B. F. Goodrich Com-

pany and, since 196 5, at Battelle Mem orial Institute. He is

currently a Fellow at Battelle. He taught courses on fluids

and heat transfer at New York U niversity 1955-1959) an d

at Carnegie Institute of Technology 1959-1961). Dr. Liu

was also a visiting lecturer at the University of Michiga n

1960). H e received his BS degree in mechanical engineer-

ing from Central University, China, in 1948 and MME and

DSc degrees in engineering and applied mathematics from.

New York University in 1955 and 1959, respectively.