Wall, cylindrical

Axial-tlow impellers rnav also be mounted near the bottom of the cylindrical wall of a cssel as shown in Fig, 18-10, Such side-entering agitators are used to blend low- iscositv fluids [<(), Pa-s (100 cP)] or to keep slowly settling sediment suspended in tanks as large as some 4000 rn (1(P gal). Mixing of paper pulp i.s often carried out by sideentering propellers. 

An open cylindrical tank 500 mm diameter and I m deep is three quarters filled with a liquid ol density 980 kg/mJ and of specific heat capacity 3 kj/kg K. If the heat transfer coefficient from the cylindrical walls and the base of the tank is 10 W/m2 K and front the surface is 20 W/m3 K, what area of heating coil, fed with steam at 383 K. is required to heat the contents from 288 K to 368 K in a half hour The overall heat transfer coefficient for the coil may be taken as 100 W/m2 K, the surroundings we at 288 K and the heal capacity of the tank itself may be neglected. 

Determine the required thickness of a reactor with cylindrical walls that must be designed to safely contain a deflagration (hydrocarbon plus air). The vessel has a diameter of 4 ft and is constructed with stainless steel 304. The normal operating pressure is 2 atm. 

Using the data and results of Example 12-6, determine the wall thickness required to eliminate future failures. Assume that the vessel s cylindrical wall height is equal to the vessel s diameter. 

A particle of mass M in contact with the cylindrical wall is subject to the following two centrifugal forces acting simultaneously ... 

Reproducible correlations for the heat transfer coefficient between a fluid flowing through a packed bed and the cylindrical wall of the container are very difficult to obtain. The main difficulty is that a wide range of packing conditions can occur in the vicinity of the walls. However, the results quoted by Zenz and Othmer(44) suggest that ... 

Solution The limit f -> 1 corresponds to a small gap between the two cylindrical walls. We are therefore justified in saying that the area of contact between the liquid and wall is 2ttRcF, if we divide both sides of Equation (8) by this area A, we obtain... 

Fig. 6.24 Air flows radially outward from a relatively cool porous tube toward an outer relatively hot cylindrical wall. Exhuast flows axially outward.

The end pieces are normally forged hemisperical or flat plates, either welded on or joint to the cylindrical vessel by means of threaded bolts for all dimensions required. The hemisperical end pieces require less wall thickness (around 60 %) of the cylindrical wall and offer a good distribution of the stresses from the hemispherical to the cylindrical shape [14]. 

Flat end pieces (plates) are frequently chosen for production reasons. For monobloc forgings of high pressure vessels or welded on end pieces it is important to avoid stress risers at the transition locations. For conical transition the stresses yield only slightly larger than those in the cylindrical wall (Fig. 4.3-8). 

The term solid-wall or monobloc vessel is applied to all components where the cylindrical wall consists of a single layer. Solid-wall vessels are suitable for all types of pressure vessels, in particular for those operated under high temperatures. Thermal stresses arising during heating or cooling are smaller than in multilayer vessels because of the good thermal conduction across the wall. Therefore solid-wall vessels are especially suitable for batchwise operation. 

MODAR Inc. (Massachusetts. USA) developed the first reactor vessel [13]. It comprised an elongated, hollow cylindrical pressure-vessel, capped at both ends so as to define an interior reaction chamber. Defined within the reaction chamber are a supercritical temperature zone, in the upper region of the reactor vessel, and a subcritical temperature zone in the lower region of the reactor vessel. Oxidation of organics and oxidizable inorganics takes place in the supercritical temperature zone. Dense matter, such as inorganic material initially present and formed by reactions, if insoluble in the supercritical-temperature fluid, falls into the liquid phase provided in the lower-temperature, subcritical zone of the vessel. A perimeter curtain of downward-flowing subcritical-temperature fluid is established about a portion of the interior of the cylindrical wall of the vessel to avoid salt-deposits on the walls of the reactor vessel. 

Figure 8.1. Temperature profiles in one-dimensional conduction of heat, (a) Constant cross section, (b) Hollow cylinder, (c) Composite flat wall, (d) Composite hollow cylindrical wall, (e) From fluid A to fluid F through a wall and fouling resistance in the presence of eddies, (f) Through equivalent fluid films, fouling resistances, and metal wall.

The results of the typical case of Example 8.2, however, indicate that the correction may be significant. A case with two films and two solid cylindrical walls is examined in Example 8.3. 

Contactors with flat-sheet and cylindrical walls are used but only hollow fiber (HF) contactors in cylindrical modules in several sizes are available commercially [31]. Flat-sheet contactors are widely used in analytical chemistry [32-34]. There are two main types of H F contactors, those with parallel flow of phases in fiber lumen and in shell or crossflow of phases. A FIF contactor with crossflow of phases is shown in Figure 23.2. More details on their construction and sizes available are presented in the producer s web site [31]. 

Parallel elongate cavities 13 and a layer of optical isolating material 18, surrounding each of the cavities, are formed within a substrate 10 of CdTe. The cavities each have a vertical wall 15 and a pyramidal floor 16. The wall and floor of each cavity has a body of detector material, HgCdTe, formed as a layer thereon. The body of detector material is comprised of a layer of a first type 22 and a layer of a second type 24. Individual electrical contacts 28 and a common electrical contact 29 are provided. An insulating layer 32 insulates the common contact from the substrate. A diffusion layer 34 of semiconductor material of the second type provides electrical communication between the common contact and the material of the second type formed in the cavity. The cavities may have cylindrical walls and a round floor. 

Here we will consider the problem of heat transfer through a cylindrical wall, for example, the wall of a pipe or tube in a shell-and-tube heat exchanger (Figure 6). 

The thermal-resistance concept may be used for multiple-layer cylindrical walls just at it was used for plane walls. For the three-layer system shown in Fig. 2-4 the solution is... 

A membrane-puncturing theory has been proposed by Davis (Dravnieks 1967). According to this theory, the odorous substance molecules are adsorbed across the interface of the thin lipid membrane, which forms part of the cylindrical wall of the neuron in the chemoreceptor and the aqueous phase that surrounds the neuron. Adsorbed molecules orient themselves with the hydrophilic end toward the aqueous phase. When the adsorbed molecules are desorbed, they move into the aqueous phase, leaving a defect. Ions... 

Boundary conditions are also applied for the variable r, at the two cylindrical walls, from which explicit expressions are obtained for the constants in the solution. Figure 20 presents an example of a distribution of local incident radiation inside the reactor, as a function of the longitudinal and radial coordinates... 

Figure 6.7-3 Sealing of high-pressure optical windows according to Poulter (1932) 1 cylindrical wall of the autoclave, 2 cap, 3 window, 4 sealing ring, positioned on the polished surface of a steel plug, 5 stainless steel plug.

In this section we consider a tubular reactor in which heat is added or removed through the cylindrical walls of the reactor (Figure 8-5), In modeling the reactor we shall assume that there is no radial gradient in the reactor and that the heat flux through the wall per unit volume of reactor is as shown in Figure 8-5,... 

---