METZNER

Metzner and Friend [Ind. Fng. Chem., 51, 879 (1959)] present relationships for turbulent heat transfer with nonnewtouiau fluids. Relationships for heat transfer by natural convection and through laminar boundaiy layers are available in Skelland s book (op. cit.). 

The generahzed approach of Metzner and Reed (AIChF J., 1, 434 [1955]) for time-independent non-Newtouiau fluids defines a modified Reynolds number as... 

Tinkler and Metzner (1961) executed a large number of computations for simultaneous equations by approximate and exact methods and presented their results on numerous graphs. One of those is shown in Figure 1.6.1. Please note that on this figure the parameter is e=y P De/at in the notation of this book, and the abscissa = is the Thiele modulus. 

Reprinted with permission from Tinkler and Metzner in Ind. Eng. Chem., Vol. 53, No. 8, J96J American Chemical Society. 

Consider the mixing in both small and large-seale systems to oeeur in the turbulent region, designated as S and L respeetively. Using the Norwood and Metzner s eorrelation [26], the mixing time for both systems is... 

CB213 W. Weinmann, F. Metzner, H. Pritzkow, W. Siebert, and L. Sneddon,... 

Metzner et al. also prepared the selenium analogue 17 of their C2 symmetric chiral sulfide and tested it in epoxidation reactions (Scheme 1.6) [8]. Although good enantioselectivities were observed, and a catalytic reaction was possible without the use of iodide salts, the low diastereoselectivities obtained prevent it from being synthetically useful. 

The C2 symmetry of sulfide 13 means that a single diastereomer is formed upon alkylation (Scheme 1.10). Attack from the Si face of the ylide is preferred as the Re face is shielded by the methyl group cis to the benzylidene group (28). Metzner postulates that this methyl group also controls the conformation of the ylide, as a steric clash in 27b renders 27a more favorable [16]. However, computational studies by Goodman revealed that 27a was not particularly favored over 27b, but it was substantially more reactive, thus providing the high enantioselectivity observed... 

Metzner and co-workers reported a one-pot epoxidation reaction in which a chiral sulfide, an allyl halide, and an aromatic aldehyde were allowed to react to give a trons-vinylepoxide (Scheme 9.16c) [77]. This is an efficient approach, as the sulfonium salt is formed in situ and deprotonated to afford the corresponding ylide, and then reacts with the aldehyde. The sulfide was still required in stoichiometric amounts, however, as the catalytic process was too slow for synthetic purposes. The yields were good and the transxis ratios were high when Ri H, but the enantioselectivities were lower than with the sulfur ylides discussed above. 

In special literature many other theoretical or empirical equations were suggested for describing t sp vs cp dependence. Thus Thomas suggested [20] and Metzner cited [21] [21] the following empirical equation as successful ... 

Though experimental data on suspensions of fibers in Newtonian dispersion media give more or less regular picture, a transition to non-Newtonian viscoelastic liquids, as Metzner noted [21], makes the whole picture far or less clear. Probably, the possibility to make somewhat general conclusions on a longitudinal flow of suspensions in polymer melts requires first of all establishing clear rules of behavior of pure melts at uniaxial extension this problem by itself has no solution as yet. 

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