Laminar flow-through design

Here AH ° = -155 kJ mol". By suitable combination of (2.41) and (2.43) the overall enthalpy difference may become approximately zero. There are still problems in controlling the temperature across the reactor, because the oxidation reaction (2.43) is considerably faster than the steam reforming (2.41). Proposed solutions include the use of a catalyst filament wire design leading to near-laminar flow through the reactor (Horny et ah, 2004). 

Several designs have evolved, many with horizontal axes (i.e. both ends closed) with the outer cylinder rotating and the inner cylinder fixed, which provides best hydrodynamic stability. Some horizontal-axis Couette flocculators are flow-through designs, even with a tapered gap to provide taper flocculation However, horizontal-axis apparatuses suffer from end effects which cause secondary circulation, so only a limited central zone (about one quarter of the length) is in defined laminar flow. 

The basic equations for filmwise condensation were derived by Nusselt (1916), and his equations form the basis for practical condenser design. The basic Nusselt equations are derived in Volume 1, Chapter 9. In the Nusselt model of condensation laminar flow is assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film. In practical condensers the Nusselt model will strictly only apply at low liquid and vapour rates, and where the flowing condensate film is undisturbed. Turbulence can be induced in the liquid film at high liquid rates, and by shear at high vapour rates. This will generally increase the rate of heat transfer over that predicted using the Nusselt model. The effect of vapour shear and film turbulence are discussed in Volume 1, Chapter 9, see also Butterworth (1978) and Taborek (1974). 

Another variety of the continuous-coupling technique operates by transporting the coupling component suspension as a laminar flow upwards inside a vertical reaction tube. Portions of the diazonium compound, dissolved in an acidic aqueous medium, are added through appropriately located inlets in the walls of the reaction tube. The concentration of the added solution decreases as the reaction mixture flows upward and is designed to synchronize the uppermost inlet for the diazonium salt solution with the stoichiometric end point of the coupling reaction. 

If only rotational viscometric data are available, the design of pipe lines is somewhat more complex. Such data are usually expressed in the form of a relationship between shear stress and shear rate. The shear stress on a cylindrical element of fluid of radius r flowing through a pipe in laminar motion is equal to rAP/2L. If the corresponding shear rate — du/dr) can be expressed analytically, i.e., if the functional relationship... 

Internal flows of the type here being considered occur in heat exchangers, for example, where the fluid may flow through pipes or between closely spaced plates that effectively form a duct Although laminar duct flows do not occur as extensively as turbulent duct flows, they do occur in a number of important situations in which the size of the duct involved is small or in which the fluid involved has a relatively high viscosity. For example, in an oil cooler the flow is usually laminar. Conventionally, it is usual to assume that a higher heat transfer rate is achieved with turbulent flow than with laminar flow. However, when the restraints on possible solutions to a particular problem are carefully considered, it often turns out that a design that involves laminar flow is the most efficient from a heat transfer viewpoint. 

Factors Influencing Apparatus Design. Practical application of the theory presented above depends on the validity of a number of assumptions. One, which has already been mentioned, is the assumption that the flow is laminar. It has been shown by dimensional analysis that, for any given type of hydrodynamic experiment, the conditions for onset of turbulent flow depend on the magnitude of a certain combination of pertinent experimental variables that is a pure number, called the Reynolds number Re. For flow through a long, round, straight tube. 

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