Hungarian journal of industrial chemistry, 1990
1. szám - Boyadjiev, Chr.: Asymptotic Theory of Non-Linear Transport Phenomena, II.: Heat Transfer
2 Chr. Boyadjiev Vol. 18 Introducing the similarity variables [1] in Equation (1) leads to the following boundary value problem : Т” + ё,ФГ = 0(2) Г(0)=1, Г(оо) = 0, where : D et= as, a = — = Le , a T = Т-Пч), In Equation (2) Ф(г]) is determined from a <9 series expansion [3] and the solution of Equation (2) can be found from : т= то + вт1 + 02т2 +.... (4) Introducing Equation (4) in Equation (2) leads to equations for the separate approximations, where Ф0, Фх and Ф2 are determined in [1]. In the zeroth - order approximation is directly obtained: /'o ^ ё,Ф0 T) — 0 ro(0)=l, ro(oo) = 0 The solution of (5) can be obtained analogous to the one in [I]: where : <Po, = Í E(e„ p) dp « 3.0Ц °-7 P h = (e«,)°5 The first-order approximation for the small parameter 0 is: T1 + e,(0oTi + Ф lT0) — 0 r,(0) = 0, Tj(oo)= 0 т0(ч) = 1 - —<Pot J E(e„ p) dp, z = - 4, e (6) (7) (3) (5) (8) dt dt Ô2t — +v —— о —г 5x dy ду2 x = 0, У-0, t=t* у-»00, t=t 0 E(e„ p) = exp -ÍÍ T I f(s) ds