Carnahan

Carnahan N F and Starling K E 1969 Equation of state for nonattracting rigid spheres J. Chem. Phys. 51 635... 

Carnahan, B., Luther, H. A. and Wilkes, J. O., 1969. Applied Numerical Methods. Wiley, New York. 

J. Carnahan and co-workers, "Investigations into the Mechanism for Phosphoms Elame Retardancy in Engineering Plastics," Proc. 4th Inti Conf. Fire Safety, Product Safety Corp., San Erancisco, Calif., 1979. 

Carnahan, B., and J. O. Wilkes. Numerical Solution of Differential Equations—An Overview in Foundations of Computei-Aided Chemical Fi ocess Design, AIChE, New York (1981). 

Multiple-Effect Evaporators A number of approximate methods have been published for estimating performance and heating-surface requirements of a multiple-effect evaporator [Coates and Pressburg, Chem. Eng., 67(6), 157 (1960) Coates, Chem. Eng. Prog., 45, 25 (1949) and Ray and Carnahan, Trans. Am. Inst. Chem. Eng., 41, 253 (1945)]. However, because of the wide variety of methods of feeding and the added complication of feed heaters and condensate flash systems, the only certain way of determining performance is by detailed heat and material balances. Algebraic soluflons may be used, but if more than a few effects are involved, trial-and-error methods are usually quicker. These frequently involve trial-and-error within trial-and-error solutions. Usually, if condensate flash systems or feed heaters are involved, it is best to start at the first effect. The basic steps in the calculation are then as follows ... 

The implicit Crank-Nicholson integration method was used to solve the equation. Radial temperature and concentrations were calculated using the Thomas algorithm (Lapidus 1962, Carnahan et al,1969). This program allowed the use of either ideal or non-ideal gas laws. For cases using real gas assumptions, heat capacity and heat of reactions were made temperature dependent. 

Another family of techniques is chromatography (Carnahan 1993), which can be applied to gases, liquids or gels this postwar technique depends typically upon the separation of components, most commonly volatile ones, in a moving gas stream. 

Carnahan, Jr., C. (1993) Gas and liquid chromatography, in Concise Encyclopedia of Materials Characterisation, eds. Cahn, R.W. and Lifshin, E. (Pergamon Press, Oxford) p. 169. 

As is seen in Fig. 2(b), the results of Eqs. (33) and (34) are in fair agreement with computer simulation results. Carnahan and Starling (CS) [18] have made the observation that the result... 

Now, let us consider a model in which the association site is located at a distance slightly larger than the hard-core diameter a. The excess free energy for a hard sphere fluid is given by the Carnahan-Starling equation [113]... 

Fig. 10(b)). One of the reasons for the differences between both theories is a different form of a hard sphere part of the free energy functional. Segura et al. have used the expression resulting from the Carnahan-Starhng equation of state, whereas the Meister-Kroll-Groot approach requires the application of the PY compressibility equation of state, which produces higher oscillations. 

The results for the chemical potential determination are collected in Table 1 [172]. The nonreactive parts of the system contain a single-component hard-sphere fluid and the excess chemical potential is evaluated by using the test particle method. Evidently, the quantity should agree well with the value from the Carnahan-Starling equation of state [113]... 

J. Carnahan, W. Haaf, G. Nelson, G. Lee, V. Abolins, P. Shank, Fourth Int. Conf. of Flamability and Safety, San Francisco, January 1979. 

Solutions of aiyl-substituted vinyl cations have been reported to be stable for at least a short time at low temperatures. The NMR spectra have been obtained Abram, T.S. Watts, W.E. J. Chem. Soc., Chem. Commun., 1974, 857 Siehl, H. Carnahan Jr., J.C. Eckes, L. Hdnack, M. Angew. Chem. Int. Ed. Engl., 1974, 13, 675. The 1-cyclobutenyl cation has been reported to be stable in the gas phase Franke, W. Schwarz, H. Stahl, D. J. Org. Chem., 1980, 45, 3493. See also Siehl, H. Koch, E. J. Org. Chem., 1984, 49, 575. 

To Anally complete the model a formula for the contact value of the pair correlation function g must be given. We choose the Carnahan formula... 

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