Parallel tube

For non-Newtonian fluids in slow flow, friclion loss across a square-woven or fuU-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to the average minimal opening between achacent wires, and length twice the diameter, without entrance effects (Carley and Smith, Polym. Eng. Set., 18, 408-415 [1978]). For screen stacks, the losses of individual screens should be summed. 

Although fluidized sand or alumina can also be used in the jacket of these somewhat larger reactors, the size makes the jacket design a problem in itself, hence these reactors are seldom used. An advantage of the jacketed reactor is that several—usually four—parallel tubes can be placed in the same jacket. These must be operated at the same temperature, but otherwise all four tubes can have different conditions if needed. This type of arrangement saves time and space in long-lasting catalyst life studies. Jacketed tubular reactors come close, but still cannot reproduce industrial conditions as needed for reliable scale-up. Thermosiphon reactors can be used on all but the most exothermic and fast reactions. 

The electronic properties of single-walled carbon nanotubes have been studied theoretically using different methods[4-12. It is found that if n — wr is a multiple of 3, the nanotube will be metallic otherwise, it wiU exhibit a semiconducting behavior. Calculations on a 2D array of identical armchair nanotubes with parallel tube axes within the local density approximation framework indicate that a crystal with a hexagonal packing of the tubes is most stable, and that intertubule interactions render the system semiconducting with a zero energy gap[35]. 

Diffraction patterns of well isolated SWCNT are difficult to obtain due to the small quantity of diffracting material present, and also due to the fact that such tubes almost exclusively occur as bundles (or ropes) of parallel tubes, kept together by van der Waals forces. 

Shell-and-tube exchangers contain several types of baffles to help direct the flow of both tube-side and shelbside fluids. Pass partition baffles force the fluid to flow through several groups of parallel tubes. Each of these groups of tubes is called a pass, . since it passes the fluid from one head to another. By adding pass partition baffles on each end. the tube-side fluid can be forced to take as many passe.s through the exchanger as desired. 

Plug flow A simple convective flow pattern in pipes and tubes that is characterized by a fluid velocity independent of radial position, complete mixing in the radial direction, and no mixing in the axial direction. Also called the parallel tube model or tubular flow. See Eqs. (7) and (8) and Figure 3. 

KS Pang, M Rowland. Hepatic clearance of drugs. I. Theoretical considerations of a well-stirred model and a parallel tube model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance. J Pharmacokin Biopharm 5/6 625-653, 1977. 

Parallel tube model (i.e. complete radial mixing model)]... 

Hydrodynamics Well-stirred model, i.e. uniform concentration inside intestine Parallel tube model, i.e. concentration decrease exponentially down the length of the intestine... 

The intestinal permeability may be determined from the rate of drug appearance in mesenteric blood (i.e. dM/dt) at steady state, using Eq. 2.12. Estimating the term C[ en will again depend on the flow dynamics of the model chosen. The most commonly used experimental procedure is the single-pass perfusion (i.e. parallel tube model) and the luminal concentration can be estimated using the logarithmic mean of inlet and outlet concentrations (i.e. ). 

The VNO of mammals consists of a pair of parallel tubes located above the palate on either side of the nasal septum (Fig. 5.9). The organ communicates with the outside by the nasopalatine duct, which, depending on the taxon, may open (a) to the mouth cavity via the incisive duct and incisive papilla (Fig. 5.10) (b) to the nasal cavity, as in alcelaphine antelopes, such as Topi, Damaliscus korrigum, and Coke s hartebeest, (Hart etal, 1988), and... 

So far, no reference has been made to the presence of more than one phase in the reactor. Many important chemicals are manufactured by processes in which gases react on the surface of solid catalysts. Examples include ammonia synthesis, the oxidation of sulphur dioxide to sulphur trioxide, the oxidation of naphthalene to phthalic anhydride and the manufacture of methanol from carbon monoxide and hydrogen. These reactions, and many others, are carried out in tubular reactors containing a fixed bed of catalyst which may be either a single deep bed or a number of parallel tubes packed with catalyst pellets. The latter arrangement is used, for exjimple, in the oxidation of ethene to oxiran (ethylene oxide)... 

If there were a first-order reaction taking place, M0 would decay exponentially, but so would Mi and M2, so that the mean and variance would be the same. If we had a number of parallel tubes communicating with each other, we would have to develop equations for the moments in each before averaging them to get the overall mean and variance. 

Numerous fin corrugations have been developed, each with its own special characteristics (Figure 15). Straight fins and straight perforated fins act like parallel tubes with a rectangular cross section. Convective heat exchange occurs due to the friction of the fluid in contact with the surface of the fin. The channels of serrated fins are discontinuous, and the walls of the fins are offset. For air flows,... 

The overall lattice structure contains slightly kinked, but unobstructed, parallel tubes, and so (15)2- (THF) is a compound of the tubulate type. The THF guest molecules can occupy two alternate disorder positions within a tube, one only of these being illustrated in Figure 24. 

For non-Newtonian fluids in slow flow, friction loss across a square-woven or full-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to... 

Finfan cooler tube-side pressure losses of 2 to 10 psi are common, and these losses seldom exceed 15 psi. Greater pressure losses indicate that more parallel tubes are needed and/or a parallel tube bundle is needed. 

However, a small-diameter tube gives more pressure drop for a given flowrate through each tube and a given tube length. Of course, a larger number of parallel tubes that are shorter can be used to keep pressure drop at a reasonable level, but this increases the shell diameter of the reactor, which increases the cost. Mechanical problems also limit the minimum tube diameter. Typical tube diameter in cooled tubular reactors is 0.03 m. Typical tube diameter in a furnace-fired heated tubular reactor is 0.15 m. 

The final tubular reactor system considered is one in which a single cooled reactor is used. Figure 5.19 shows the flowsheet. The cooled reactor, which is assumed to be simply a shell-and-tube heat exchanger, has catalyst packed inside the parallel tubes. Steam is generated on the shell side, serving as a coolant. The liquid level in the shell is controlled by bringing in BFW to keep the tubes covered. The steam-side temperature is constant at all axial locations in the reactor because the BFW is vaporized at a constant temperature. The temperature of the steam is assumed to be equal to the reactor inlet temperature, and the temperature of the BFW is assumed to be equal to the steam temperature. 

It might be wise to point out that there can be other problems with a cooled reactor that will influence the selection of reactor type. An adiabatic reactor with a bed of catalyst is certainly mechanically straightforward to construct and maintain. Catalyst is easily loaded or discharged. A cooled reactor with multiple parallel tubes is mechanically more complex. Loading and emptying the tubes of catalyst can be difficult. 

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