Effects of tube walls

As experiments on detonation waves in tubes were refined, it soon became apparent that these waves do not propagate precisely at the 

Chapman-Jouguet speed. For example, detonation velocities decrease approximately linearly with the reciprocal of the tube diameter at fixed initial conditions standard experimental practice is to plot the detonation velocity as a function of the reciprocal of the tube diameter and to extrapolate to zero to obtain the true experimental wave speed (for example, [57]). Also, detonation velocities have been observed to decrease approximately linearly with the reciprocal of the initial pressure in a tube of fixed diameter. The first satisfactory explanation of these effects was presented by Fay [58], who accounted for the influence of the boundary layer behind the shock front in a Chapman-Jouguet wave with the ZND structure. 

The calculation of detonation velocities from the quasi-one-dimen-sional flow equations is considerably more difficult than the calculations discussed in Chapter 2. For example, the wave speed now depends on the 

FIGURE 6.7. Schematic diagram of a detonation near a tube wall [58]. 

---

The values of CJs are experimentally determined for all uncertain parameters. The larger the value of O, the larger the data spread, and the greater the level of uncertainty. This effect of data spread must be incorporated into the design of a heat exchanger. For example, consider the convective heat-transfer coefficient, where the probabiUty of the tme value of h falling below the mean value h is of concern. Or consider the effect of tube wall thickness, /, where a value of /greater than the mean value /is of concern. 

Tables 10-16, 10-17, 10-18, and 10-18A give general estimating overall coefficients, and Table 10-19 gives the range of a few common film coefficients. Table 10-20 illustrates the effect of tube-wall resistance for some special construction materials. Table 10-20A lists estimating coefficients for glass-lined vessels. Also see Reference 215. See Table 10-24 for suggested water rates inside tubes.

Effect of Tube Wall Material and Film Conditions on Overall Coefficient... 

Fig. 16. Effect of tube-wall thickness on the film flow rate [from Hewitt el al. (H6)]. Based on tests with water in uniformly heated stainless steel tubes, d — 0.366 in., P = 55 psia, G = 0.219 x 106 lb/hr-ft2.

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

U = temperature of vapor, °F = temperature of tube wall, °F X,. = distance from top (effective) of tube, ft... 

Tube wall temperature is an important parameter in the design and operation of steam reformers. The tubes are exposed to an extreme thermal environment. Creep of the tube material is inevitable, leading to failure of the tubes, which is exacerbated if the tube temperature is not adequately controlled. The effects of tube temperature on the strength of a tube are considered by use of the Larson-Miller parameter, P (Ridler and Twigg, 1996) ... 

The overall effect of catalyst pellet geometry on heat transfer and reformer performance is shown in the simulation results presented in Table 1. The performance of the traditional Raschig ring (now infrequently used) and a modern 4-hole geometry is compared. The benefits of improved catalyst design in terms of tube wall temperature, methane conversion and pressure drop are self-evident. 

Here Kjj is obtained from Fig. 9.5. Equation (9-27) and the equations of Chapter 5 can be used to determine the decrease in Sh for a rigid sphere with fixed settling on the axis of a cylindrical tube. For example, for a settling sphere with 2 = 0.4 and = 200, Uj/Uj = 0.76 and UJUj = 0.85. Since the Sherwood number is roughly proportional to the square root of Re, the Sherwood number for the settling particle is reduced only 8%, while its terminal velocity is reduced 24%. As in creeping flow, the effect of container walls on mass and heat transfer is much smaller than on terminal velocity. 

A. Kaczmarek et al., Effect of tube length on the chemisorptions of one and two hydrogen atoms on the sidewalls of (3,3) and (4,4) single-walled carbon nanotubes A theoretical study. Int. J. Quantum Chem. 107, 2211 (2007)... 

As is evident from the results shown graphically in figs. 20 and 21, the size of the tube exerts an important influence upon the flame speed. In tubes of small diameter, say less than about 5 cm., the cooling effect of the walls results in appreciable retardation of the flame speed. It will be observed that there is not much difference in speed in tubes from 5 to 10 cm. in diameter, whereas -when the diameter of the tube is only 2-5 cm., the speed is reduced by about 30 per cent. Cooling by the walls thus interferes with the measurement of the true speed of the uniform movement of flame in mixtures of methane and air unless the diameter of the tube exceeds about 5 cm. 

Effect of Tube Diameter. For 1" tubes,the radial profiles of activity are parabola -like functions with minimum value at the center of the tube. For tubes with higher values of the diameter, e.g., 2" tubes, the picture can be rather different. High radial temperature gradients result also in large gradients of benzene and poison. For a deactivation process with high E, a minimum on the activity profile can occur between the reactor axis and wall, see Figure 8. Blaum ( 3) observed radial hot spots of temperature between the reactor axis and wall for a very rapid deactivation. For slow deactivation,these hot spots are not likely. 

Solve for the drag on a sphere in a flowing stream with a uniform velocity profile upstream. Solve for Reynolds number from 1 to 100. Put the sphere in a cylindrical tube with a diameter of 5. For this problem, use zero velocity on the cylindrical tube, which mimics the effect of the wall. 

Eventually, sufficiently far downstream from z = 0, the heating effect of the walls will propagate entirely across the tube, and only then should we expect the length scale characteristic of radial gradients of the temperature to be the tube radius. How far downstream do we need to go before this is true The characteristic time required for the radial conduction process to transport heat a distance equal to the tube radius a is a2 Ik. This requires a distance down the tube of order U(a2/k). In other words, we must be at a dimensionless distance downstream ... 

In heat transfer at the wall of the tube to or from the fluid stream, the same hydrodynamic distributions of velocity and of momentum fluxes still persist, and in addition, a temperature gradient is superimposed on the turbulent-laminar velocity field. In the following treatment both gradients are assumed to be completely developed and the effect of tube length negligible. 

It should be noted again that the effect of the wall thermal boundary condition on the Nus-selt number for coils is not significant for the fluids with Pr > 0.7. Equation 5.286 can also be used for the , , and thermal boundary conditions. Furthermore, the appropriate correlation for circular cross section coiled tubes can be adopted with the substitution of the appropriate hydraulic diameter for 2a to calculate the Nusselt number when the parameters are out of the application range as is the case in Eq. 5.286. 

Note that the column dimensions, the gas properties, and the bubble size do not appear in the correlation. However, some effect of tube diameter is expected for tubes or cooling coils placed in the bubble column, since coefficients for coils in stirred tanks are larger for small-diameter tubes. Also, Eq. (7.71) could be modified by adding the term (/i//i ) if there is a large difference between the bulk and wall viscosities. 

When do we cross over from the weak penetration regime of eq. (III.57) to the strong penetration regime for concentrated systems A detailed answer to this question could be obtained from a study of the chain chemical potential, but the essential features may be reached more simply. Let us start from a tube with a diameter D somewhat larger than the correlation length in the bulk. Then we expect to have a depletion layer of thickness near the tube walls, as described in Section ni.3.1. The perturbing effects of the wall do not extend further than... 

Fig. 26.1 Diameter (wall thickness) dependence of the elastic modulus of MWCNT. Data in solid circles are sourced from [46] diamonds from [47] and open circles from [12, 17]. The drop at 8 nm in bending modulus corresponds to the wrinkling effect of the wall of the nanotube during bending [46]. Inset shows no remarkable change in the Lorentzian line shape of the resonance for tubes in measurement...

---