Boundary Lyer Theory

XI 11. I,nrninnr bo~~ntl:~ry Inycrs in rornprrsnil~lc flow
and wrik tlo\vn (IIP t.ransformcrl l)o~~ntlnry-layer rquations (13.50) and (13.51) in
tlrr form of tl~r following two ordinary tliiTercntial eqr~at~ions:
in wl~ich primrs tlrrrot,c tliKcrcnliat,ion with respect to 11. 'rhc pnratnetcr 8, in the samr
way r7.s oarlicr in cqn. (9.7), is tlcfinctl by
it, rlr:lr:~vIrrixt.s tl~r prrssltrc gmtlicnt of t,lrc cxtcrnal stream.
we corrclr~clo wit,h tJrc aitl ofeqn. (13.60) tl~:~t J' constitntcs a tlimcrisionloss form of tlrr
1ongit.11tlinal vrlorit,y component in t . 1 ~ bo~~ntl:~ry layer, because
Sinrr ?/ -- 0, or ?/ --r oo implirs 71 = 0 arid 71 = ro, rrspect,ivcly, the boundary contlitions
for t11t- systrm (13.til) rnr~st he wril,t,rn
In the case of an crditrhrrtic loall, the srcond equation (10.01) is sn.t,isfictl itlcnticnll~~,
:r~itl it. is ncrcssnry t,o solve t,he singlc c.qn;~t,ion
/"' -1- //" = P(/'" 1) ,
\\~11rn IIIC \vnll pcrrnits thr /rrrirn/pr o/ hccrl, it brcomcs necessary to solvr thr
system of rquntions (13 01). Sincr thr wnll tcmperatnre, T,, can he prescribed in an
arbitrary manner, it will be fol~ntl that thc solutions depcntl on the paratnrter
in addition to their dcpcndcncc on P. Solutions for a largr nrmbcr of valws of thsc
two par;~mrt,rrs have brcn workcd out by 'l'. Y. Ii tintl 11. '1'. Naf;nmatsrl [(ill ris well
as by C. J3. C!ohen and E. Reslrotko [16n].
Pig. 13.13. Vrlocity arid rntl~nlpy dislril~~~lions in
ro~nprrssiblr, 1:trninar honntlnry lngrrn with prwsuro
grndirnt, and hrnt tr:lnsl'rr, nftcr C. 13. Colrrrr and
E. hshotko [lGn]. and in conforrr~ity with cqtls. (13.62)
and (13.35)
I'rn~~(l tl N111n1)cr: P -- 1 ; OI - 1 . rJ(x) = (z) tlcnolm
t.111, vdor.il.,y of I.lm t:sl.cr~tr~l flow. n), I,), c) vc:locily
distsil)ut,ions; tl), e) cnthlpy dint,rihrttions; n) IS,,, = 0;
T,,, = 7'0; ntlinlmtic wnll; h), d) 8, = -0.8; T,, - 0.2
7'" cooled wll; c), e) S,, 1.0; T,, = 2 TO; hcnt.ctl \vall