The Bell Method

The Kern method is inaccurate for calculating the shell-side heat-transfer coefficient and shell-side pressure drop (Ref. E2, p. 545). Kern makes no account of the effect of bypss and leakage in the shell-fluid passage. For these reasons the Bell Method (Ref. E9) is employed to serve as a check on the preliminary design. 

The revised shell-side heat-transfer coefficient is given by the equation shown below. 

Each correction factor is determined using a series of correlations and figures in Ref. E2 (pp. 553-569). The overall heat-transfer coefficient is recalculated from Equation 10.4. 

The shell-side pressure drop is also recalculated by adjusting for the above factors. The new shell-side pressure drop is given by the equation below. 

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The design calculations highlighted the shortcomings of the Kern method of exchanger design. The Kern method fails to account for shell-side inefficiencies such as bypassing, leakage, crossflow losses, and window losses. This leads to a marked overestimate of the shell-side heat-transfer coefficient and shell-side pressure drop. The Bell method is recommended to correct these deficiencies. 

If this 33% reduction in the overall heat-transfer coefficient and the 90% reduction in pressure drop had not been discovered, this would have caused a significant underestimate in the design to occur. This example should therefore serve to highlight the need for a more rigorous design approach to shell-side evaluation than that proposed by Kern. The Bell method proved quite adequate in this regard. 

H.9 Shell-side Heat-transfer Coefficient (The Bell Method) 318 H.10 New Overall Heat-Transfer Coefficient (The Bell... 

H.11 New Shell-side Pressure Drop (The Bell Method) 321... 

The shell-side pressure drop must be recalculated using the Bell method, i.e. accounting for the various losses previously mentioned. 

Dyno has contributed to the development of a method, named the Bell method, for the quantitative determination of the formaldehyde emission from a panel surface ( 5). A glass flask or bell having a plane flange is placed on the surface to be measured. A tight sealing between the flange of the bell and the panel surface is very important. The air can be kept in circulation by means of a membrane pump, pumping about 2 liters per minute in a closed loop, which also contains a gas burette. After a predetermined time the formaldehyde concentration of the air in the gas burette is determined by a sensitive analytical method. 

The Bell method can be used to determine the equilibrium concentration of formaldehyde, C in the model above. When the formaldehyde concentration in the Bell system is plotted against time, the initial slope of the resulting curve can be used to determine the mass transfer coefficient, kg in the same model. 

Thus, although there is no air exchange between the glass bell and the surroundings, the Bell method can be used to provide data to calculate the steady state concentration in a ventilated system. 

The project plan involved the use of the Bell method to determine the equilibrium concentration and mass transfer coefficient for a number of particleboard samples with different surface finishes and overlays. 

The density of states increases rapidly with energy but the Boltzmann factor decrease exponentially, meaning that Pcanon(T, E) is bell-shaped, with values that can vary by mar orders of magnitude as the energy changes. In the multicanonical method the simulatic... 

The reader is referred the recent book by Bell and Pines [2] for a more complete overview of the various methods and objectives in NMR studies of solid acids and other heterogeneous catalysis. In the present contribution we illustrate the application of H, and MAS NMR to two archetypal solid acids, Brpnsted sites in zeolites and solid metal halides such as aluminum chloride and bromide powders which exhibit "Lewis superacidity". An important characteristic of the more recent work is the integration of quantum chemical calculations into the design and interpretation of the NMR experiments. 

Some of the first transient infrared data on heterogeneous catalysis were gathered by Heyne and Tomkins in 1966 (16). The method has been advocated and used by Tamaru, who has recently reviewed his work since 1967 in this field (17). Dent and Kokes used the transient method in IR studies in 1970 (18). Since then the method has been applied to kinetic studies in particular by Ueno et al. (19, 20) and most recently by Savatsky and Bell (21). 

It has been shown by H naff (1963) that the rate of reaction of several carbonyl reagents (bisulphite, hydrazine, phenylhydrazine, semi-carbazide and hydroxylamine) with aqueous formaldehyde solutions is independent of the nature and concentration of the reagent, and is therefore determined by the rate of dehydration of methylene glycol. He obtained catalytic constants for hydrogen and hydroxide ions, and a detailed study of acid-base catalysis has been made by the same method by Bell and Evans (1966). 

One of the early examples of the application of the SHG technique in electrochemistry, proving its high sensitivity, is the investigation of the sulfate monolayers adsorbed on pc-Ag electrodes [10]. Also, one should mention the paper by Gamp-bell and Gorn [11], who have evidenced that the SHG method is also applicable to studies in nonaqueous solutions, namely, to the investigations of hydrogen evolution in acetonitrile (AGN). 

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