OCR Text |
Show r o ind the stream function AFRC85-7 Y F = °: Y0 = Y0,e; YN " YN,e as y - -a(t) T = T s ,o 3T 3y = 0 (lib) (12a) (12b) •Initial Conditions at t < 0 : T = T : vF = o a* t > 0 and y = 0: T = T s w(t) dV P A -E„ /RT M ' ^ s s , p s,p s,w - • LE e <3t p.. (13a) (13b) (13c) 2.2. Transformation Define 2a PM 1/2.Y pdy 3 0 (14) P„M ax (15) where U = ax ( 16) • U.il) • <20 W 2 f <""> (17) where fill = 7J- (18) Dimensionless Activation Energy E • = -SI g RT RT 's,R 's,R RT (19) AFP.C85-8 Dimensionless Temperatures First and Second Damkdhler Numbers v„M„A p D = _F F gye (21) 1 2a Q _9_ (22) 2 c T P e where (h;v.MB + h«vM - h'vxi F F F 000 PPP (23) « vFMp Stoichiometric ratio 0 0 r = -rr- (24) Schmidt and Prandtl Numbers M MC g Also define <YF ' W ' (YF " We * = <YF " Ww" <YF " We (VF ; «/y - [Vp ; °/ye P " (YF + 0/D2)w- (Yp + e/D2)e It is clear from Eqs. (26) and (27) that •(O) = 8(0) = 0, and 4(.) = p(») = 0, then the solutions of • and B are identical. The governing equations are reduced to: |