Chemical Engineering Hand Written_Notes_Part_55

Chemical Engineering Hand Written_Notes_Part_55 - 112 3....

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112 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES which can to be solved simultaneously for unknown vector y using Newton- Raphson method . In particular, if we choose (7.32) p 0 ( z )=1 , p 1 ( z )= z, . ..... p n +1 ( z z n +1 then, matrices S and T can be computed using M = 1 0 .... 0 1 z 1 .... ( z 1 ) n +1 .... .... .... .... 11 .... 1 (7.33) N = 0 1 .... 0 0 1 .... ( n +1)( z 1 ) n .... .... .... .... 01 .... ( n +1) (7.34) Q = 0 0 .... 0 0 0 .... 0 2 6 z 0 .... 0 2 6 z 1 .... n ( n z 1 ) n 1 .... .... .... .... 26 z n .... n ( n (7.35) where z i are collocation points. Example 48 . [ 6 ] Consider the ODE-BVP describing steady state conditions in a tubular reactor with axial mixing (TRAM) in which an irreversible 2nd order reaction is carried out (7.36) 1 Pe d 2 C dz 2 dC dz DaC 2 =0 (0 z 1) dC dz = ( C 1) at z =0; (7.37) dC dz at z =1 ; (7.38) Using method of orthogonal collocation with n =3 and de f ning (7.39) C = h C 0 C 1 ... C 4 i T we get following set of f ve nonlinear algebraic equations (7.40) 1 h £ t ( i ) ¤ T C i h ¡ s ( i ) ¢ T C i DaC 2 i i , 2 , 3
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7. SOLUTIONS OF ODE-BVP AND PDES BY ORTHOGONAL COLLOCATION
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_55 - 112 3....

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