(11-101) 



(11-102) 



(11-103) 



(11-104) 



and in order to determine o, it is necessary to solve equations II-85 through II-88 for (B w /A). 



Boundary Conditions 



Equations II-85 through II-88 contain five unknown coefficients. Thus, five boundary conditions are 

 required for the solution of this set of equations. These conditions are the continuity of normal velocity, u r , and 

 normal stress, T rr , at both interfaces and continuity of temperature at the inner interface. The first step in 

 solving for B w /A, therefore, is to obtain u r , T rr and T in terms of P w , P,, ifj, and i|j 2 . 



Equation II-50 gives T a in terms of P a . Substitution of equations II-58 and II-60 through II-63 into equation 

 II-50 leads to 



j [Ya- lp0a to Y a Cpa ]^i + (Ya-1)^} • (H-105) 



Po a Ca 2 P 



u rw is given in terms of P w by equation II-96. Following the same procedure to obtain u rf , equation 11-31 may 

 be written as 



P, + VPQ, - p 0f 3 -A = . ( IM 06) 



Then substitution of equation II-26 into 11-106 yields, with introduction of the harmonic time dependence: 



Qf = ^[ 1 -p^] P « • (H-107) 



Similarly, from equation II-46 and 11-61: 



Q * = m5"(*i + V*) ■ C 1 ' 108 ) 



Thus, 



and 



U ra 



[. ico^ i 3P, 

 1 "P^J aT ( |M09 > 



^P 0a La7 + arJ- ("-no) 



16 



