Comparison With Exact and Linearized Solutions

The great advantage of the methods described in this section over those described earlier is, of course, rapidity in computation. This gain in computational simplicity is, however, at the expense of theoretical rigor. It is, therefore, important to establish the accuracy of the methods described above using the exact method of Section 8.3 as a basis for comparison. The extensive numerical computations made by Smith and Taylor (1983) showed that the explicit method of Taylor and Smith ranked second overall among seven approximate methods tested (the linearized method of Section 8.4 was best). For some determinacy 

The explicit method of Krishna (1979d, 1981b) is most successful if the are close together and, therefore (or for other reasons), the total flux is low. At high rates of mass transfer, the assumption of constant (or of [/3][B] ) is a poor one, particularly in 

It is the eigenvalues (literally characteristic values ) of [0] that characterize the correction factor matrix [S]. Thus, the scalar rate factor 0 and correction factor S when multiplied by identity matrices frequently are quite good models for the behavior of the complete matrices [0] (or [ ]) and [H] in the exact and linearized methods. 

One especially good use for the Taylor-Smith/Burghardt-Krupiczka method is to generate initial estimates of the fluxes for use with the Krishna-Standart or Toor-Stewart-Prober methods. It is a very rare problem that requires more than two or three iterations if Eq. 8.5.26 is used to generate initial estimates of the fluxes (Step 3 in Algorithm 8.2) (Krishnamurthy and Taylor, 1982). 

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