Boundary Lyer Theory

286 X11. 'IY~rrrr~al bo~~ndnry layers in laminar flow
11ni1.y. Tn ot,her words, t .1~ \vorIz due to frict.ion and compression must he taken into
accol~nt, when the t,crnpcrnf.ure increase drlc to friction nnd cornprcssion is comparable
with f h tmnpcr:~t.urc tlilTcrcncc prcscri0ccl as a bourdary condition (tnmpcrature
tliffrrenco I)ct,\r;rc:~~ I)otly and fluid). If t h prescribed tenlperatlire difference is of
t.ho ortlcr of t.hc mmn at)solrrt2c t.rmpcral,nrc, t h work duo to frict,ion and cornprcssion
1)rcorncs ilnlwrtallt, only if t,hc vrloc.il.y of llow is compnr:ll)lc wit,ll t.hat, of sol~ntl.
2. Atlinlmtic wall. I~in:~lI,y it, is IICC~-SSRI.~ to mrnti~n t.l~i~t. the vi~rict~y of possiI)Ic
sds of 1)ounclary contlitions is much grontcr for the ttcrnpcrat~~re field t,Ilan for
t,hc: vrlocit,y fieltl. Tllc tcmpcmtnre on the surface of the body may bc constant
or w~riable but., moreover, it is also possil)lo to encountm pro1)lcrns for wl~ich tho
hrat flux is prescribetl. In view of eqn. (12.30), this means that t,lle t,crnperaturc
gmtlirnt at the wall may appear as a boundary condit,ion. The so-callctl rtrlinbalic
wr/l constiLutos a pnrticulnr rxn.nlplo of the Iatt.er class of cases, since it rnnst be
post,ulat,cd thn.t there is no heat flux from the wall to the fluid, i. e., the borlr~clary
t:ontlit.ion at, t,he wall is
r 1
1 his case c:Ln 1)c visrrnlizotl Ily imagini~lg 1,hat the wall of the body is perfectly
it~sul.ztctl against I~cst, Row. 'I'lic heat generated l)y the fluid through friction serves
1.0 l1cn.t 1,ho wall 11nt.il tho contlit,iorl (a7'/an),,. , = 0 is reachctl. Thus the t.crnperat~rrc
of t.llt, wnll wl~ic:li we may :~lso call the rdirtbcclic unll tempernlure Imxmes higher
t,l~:~.tl thaL of the lluitl at, some clist,nnco from it. Srtcll conditions are satisfied in
pr:~ct,ic*c \vhrn a so-called plate t.hcrmornct,c:r is usctl, i. (:. when t.llc ternperabnre of
:I, fll~itl st.rrnm is rnc~as~~rctl with t.hc aid of a flat plat,c which is placed parallel to
t,lit. sl.rc~nm 1. 'l'hc PXC~SS l.wq)crats~~rc 011 1.110 plnt,r const~it,ut,c*s t.hc rrror of t.hc pink
t.lwrmon~ct.c~r. 'I'llc error mns0 I)c tlrtl~~c:t.t-tl ill ortlrr t.o obtain t.hc 1,rnc t,empcrat.urc
of t.Iit: tnovirl~ Il~~id. 'l'llis tlifkrcnc:c is somctimrs cnllctl the kinetic. lemperntwe.
It, hns i)c~n showt~ ill Stw. VI 11 :I t.llnt nlk solni.ions of t.llcr two-tlirncnsional
I)ol~ntlnry-l:tycr cq~~;l.t.iorts for an inron~prc~ssil)lc flnitl I~xvc the form
If t.1~ work of compression as well :IS t,hc cvolut.ion of Ilo:~t. tltro~~gll tlissipat,ion
c : be ~ neglect,etl, tile same reasoning shows that, rtll solut,ions of oqr~:~t.ions (12.51 P)
wl~id~ tlcsrril~t: th: i,l~rrm;tl 1m1ntIa.r~~ l;~,yt:r, nii~st, I)(: of the form:
Iloncc, the heat flux from rqn. (12.30) can I)(; writ,t.cn
1