Boundary Lyer Theory

308 X11. 'I'hrr~nnl hotrnclnry I:ryrrs in lnn~iunr flow g. Tl~cr~nal boundary layers in forcrtl flow 30!)
w11rrrn.s t,l~c c\xa.rt sol~~l,io~~, cqn. (12.79a), showed the numerical coefficient to b~
eq11:1l lo 0.:1:12.
Alt.rrn:~l ivc :~pproxirnat,c proccdores for the calculation of-the tjhcrmalq!o~ndary
1j1,ycr on 1)otlit:s of n.rl)itmry sl~apcs have baeq intlicnlc;i_Ly...E ..lj;ckert [l-)j and Gy
JC. I~~C:I.~ worlc, b111 thir ancur:~ey is improved. 111 this connexion the
p a l ~ I)y ~ s \V. I)ic~nrniann 11 I], 11. J. Merlc 1851, M.B. Skopek [I181 and A. G. Smit,ll
n.1~1 1). 1%. Spnltlit~g 1.1 In] rnny I)? usrful t,o t h rcadcr. In ronf,ra.st. with 11. 13. Squit.~'s,
t.l~c: I:~t.Ivr prorwl~~rrs rn:~.lco us(: of t.lw rcsulI,s of t,hc t,hcory of similar lhcrn~:il Iwur~tl:rry
I:~.yrrs 011 l.liwt l in t.11~ prrnctling scc:tion. 'I'l~is improvcs the accuracy of the calculation.
r
I . hn v:irio~~s :~l)lrroxirnat,c nlct.l~otls have Imw examined crit.ically and comparctl with
rxch ol hor in n pnprr hy 1). 13. Spnlding and W. M. Pun [I221 : their accumcy has been
jutlgrtl I)y pc:rlimning c:ornpn.risons with the exact solut,ion for the circular cylintlcr
proritlvtl Ily N. 1~rorssling. According t.o ~JICSI: studies, the methods due t,o IT. J. Mcrlc
/85] nntl A.G. Sn1it.h and D. R. Spnlding [lln] t,ulm onl, to I)c rcht~ivcly t,hc most,
~~cIII.:~I(: in spiIlc of l.l~rir simpli(:ily. 'I~IC Iattcr relerencc shows that at a PrantU1
nurnl)cr of P :-= 0.7, t.hc similar wcdgc profiles satisfy with good accuracy thc relation
'I'his c.ql~at.io~~ is rx:ic% for /3 - 0 (plnlr) :~ntl /3 -- 1 (stfaanat,ion point). If it is supposctl
(I~nl rqn (12 100) vnjoys ~~r~ivrrs:d vnlitlily, it, is possil)lc immetlintcly to writ.? down
I lrrc IT,, and I tlonok c.onsl,:~nt, rcfcrcltcc values. This equation corresponds to eqn.
(10.37) which W:IS tl(vived I)y A. Wnlz for t,hc momcnt~nm thiclrncss. The local NussclL
~~u~nl)cr is n.gait~ tlcl,cmni~~otl I)y cqn. (12.98). At, the st.ngnalion point we ol)t.:~it~
,. ,
-.
i . ~,~~i~~j~l:,ij