Chen approximation

The Chen approximation has the advantage that when either ATj or AT2 equals zero, then the LMTD is approximated to be zero, while the Paterson (1984) approximation yields a nonzero value. The Paterson (1984) approximation tends to slightly underestimate the area, while the Chen (1987) slightly overestimates the actual area. 

See the CD-ROM that accompanies this book for the GAMS input file, COST.l, which obtains a solution using the Chen approximation to the log-mean temperature difference. ... 

Figure 5. Input file for NLP in Example 10.16 using Chen approximation.

This algorithm was improved by Chen et al. [78] to take into account the surface anhannonicity. After taking a step from Rq to R[ using the harmonic approximation, the true surface information at R) is then used to fit a (fifth-order) polynomial to fomi a better model of the surface. This polynomial model is then used in a coirector step to give the new R,. 

Annuli Approximate heat-transfer coefficients for laminar flow in annuh may be predicted by the equation of Chen, Hawkins, and Sol-berg [Tron.s. Am. Soc. Mech. Eng., 68, 99 (1946)] ... 

There are 17 human type I IFN genes, all clustering on chromosome 9. They are intronless and encode secretory signal peptide sequences that are proteolytically cleaved prior to secretion from the cell. Type I IFNs are genetically and structurally closely related. They range in length from 161 to 208 amino acids and have apparent molecular weights of 15-24 kDa (Table 1) (Chen et al. 2004). The different subtypes of human IFN-a have approximately 50% amino acid sequence identity, whereas IFN-a shares approximately 22% amino acid identity with human IFN-p and 37% with human IFN-m (Chen et al. 2004). 

Despite the availability of an effective HBV vaccine, the virus is still a major health problem with approximately 350 million persons infected worldwide. Hepatitis an infection of the liver that is caused by a variety of RNA viruses (hepatitis A virus, hepatitis B virus, hepatitis C virus). RNAi has been used to inhibit HBV replication both in vitro and in vivo (Carmona et al. 2006 Ely et al. 2008 Hamasaki et al. 2003 Klein et al. 2003 Konishi et al. 2003 Weinberg et al. 2007 Ying et al. 2003). HBV is a member of the Hepadnaviridae and its genome is a 3.2-kb double-stranded circular DNA. Synthetic siRNAs and shRNA expression constructs showed potent inhibition of HBV replication in mice (Chen et al. 2005, 2007 GUadi et al. 2003 McCaffrey et al. 2003 Morrissey et al. 2005b Shin et al. 2006 Wu et al. 2005b ... 

High levels of isoflavone consumption are reached only in typical Asian diets (Chen et al., 1999 Nagata et al., 1997 Adlercreutz et al., 1991), with a peak at approximatively 100 mg/day in the Hong Kong Chinese population (Ho et al., 2000). In Western countries, isoflavone intake is much lower. The most recent evaluations in the USA (de Kleijn et al., 2001), as well as in different European countries, indicate a mean intake of isoflavones of less of 1 mg/day. Even amongst EU consumers eating mainly soy foods it does not exceed 6-10 mg/day (van Erp-Baart et al., 2003). 

Figure 4. Time series profiles of and temperature, potential density, Chi a, and nitrate (Slagle and Heimerdinger 1991) at 47°N, 20°W (Atlantic Ocean) in April-May 1989. Dashed vertical line represents estimated activity (Chen et al. 1986). The evolution of " Th/ U disequilibrium with time follows that of Chi a and nitrate, confirming the observations illustrated in Figure 3. The series of profiles taken approximately one week apart permits application of a nonsteady state model to the data. [Reprinted from Buesseler et al., Deep-Sea Research /, Vol. 39, pp. 1115-1137, 1992, with permission from Elsevier Science.]...

Chen et al. [70] suggested that temperature gradients may have been responsible for the more than 90 % selectivity of the formation of acetylene from methane in a microwave heated activated carbon bed. The authors believed that the highly nonisothermal nature of the packed bed might allow reaction intermediates formed on the surface to desorb into a relatively cool gas stream where they are transformed via a different reaction pathway than in a conventional isothermal reactor. The results indicated that temperature gradients were approximately 20 K. The nonisothermal nature of this packed bed resulted in an apparent rate enhancement and altered the activation energy and pre-exponential factor [94]. Formation of hot spots was modeled by calculation and, in the case of solid materials, studied by several authors [105-108],... 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

As a conclusive comment to the Miedema model, especially with reference to the enthalpy evaluation, we have to underline that while it may be useful in order to define a reference behaviour, however, its approximate (in a way qualitative) character cannot be forgotten. A critical discussion on the application and limits of this model has been published for instance by Chen et al. (2004) see the comments on the thermochemistry of the Laves phases in 3.9.3, see also a few more remarks on this subject in 4.4.7.1. 

The fourth is a cube synthesized by Chen and Seeman, the components of which are based upon DNA (Fig. 9.12c). [35] The directionality and ability of the double helix to form branched junctions are exploited for the edges and vertices, respectively. Interestingly, each face of this molecule forms a cyclic strand which is catenated with strands of adjacent faces. Molecular modeling experiments indicate the length of each edge to be approximately 6.8 nm. 

Chen [8] studied mixtures of the pure surfactants Ci2(EO)4 and sodium dodecyl sulfate (SDS) at 30 °C. At this temperature the former is a liquid which does not dissolve in water (see Fig. 3), and the latter is a solid. The SDS was doubly recrystallized from ethanol to remove n-dodecanol and other impurities. The solubility of SDS in pure Ci2(EO)4 at 30 °C was found to be approximately 9 wt. %. When small drops of an 8 wt. % mixture were injected into water at 30 °C, complete dissolution was observed, the time required being a linear function of the square root of initial drop radius. For instance, a drop having an initial radius of 70 (xm required approximately 100 s to dissolve, significantly more than the 16 s cited above for a slightly larger drop of pure Ci2(EO)6. Behavior was similar to that of nonionic mixtures below their cloud points discussed previously in that most of the drop dissolved rapidly, but the final small volume dissolved rather slowly with some observable emulsification. 

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