Enhancement factor, heat transfer

Longitudinal fins can also be used, but their application is restricted to small heat exchangers in the form of a concentric pipe heat exchanger, similar to the schematic in Figure 15.5a. In this arrangement, the inner tube would be the extended surface tube with the fins in the annular space to enhance the heat transfer. Longitudinal fins can increase the surface area by a factor of 14 to 20 relative to plain tubes. 

A, cross-sectional area, [m ] F, enhancement boiling heat transfer factor. 

Koch [4] employed suspended rings and disks as inserts, as well as tubes packed with Raschig rings and round balls. The disks give maximum enhancement with moderate increases in friction factors, as indicated in Figs. 11.26 and 11.28 (curve d). Enhancement of heat transfer with rings and round balls is quite comparable to that with disks, but rings and balls increase the friction factor by more than 1600 percent (curves c and d). For further comments on packed tubes, see the chapter on heat transfer in fluidized and packed beds. 

Fluidized beds represent the other end of the spectrum in terms of solids loading (this subject is covered in the chapter on heat transfer in fluidized and packed beds). The very considerable enhancement of heat transfer coefficients, up to a factor of 20 compared to pure gas flow at the same flow rate, has led to applications in such areas as flue gas heat recovery. 

Fog formation is favored by conditions which slow the mass transfer rates and enhance the heat transfer rate. Factors which favor fog formation by slowing the mass transfer rates are a high ratio of noncondensables to condensable vapor, and a high molecular weight (low diffusivity). Factors which favor fog formation by speeding the heat transfer are a high temperature difference between the vapor and interface and low initial superheat. 

The linkage between the enhancement of heat transfer at boiling of dilute polymer solutions and the elastic properties of the system is confirmed by the existence of the optimal concentration corresponding to (Figure 7.2.14). Similar optimal concentration was established in addition of polymers to water to suppress turbulence - the phenomenon that also owes its origin to elasticity of macromolecules. Therefore, it is possible to expect that the factors favoring the chain flexibility and increase in the molecular mass, should lead to strengthening of the effect. 

Values for the various parameters in these equations can be estimated from published correlations. See Suggestions for Further Reading. It turns out, however, that bubbling fluidized beds do not perform particularly well as chemical reactors. At or near incipient fluidization, the reactor approximates piston flow. The small catalyst particles give effectiveness factors near 1, and the pressure drop—equal to the weight of the catalyst—is moderate. However, the catalyst particles are essentially quiescent so that heat transfer to the vessel walls is poor. At higher flow rates, the bubbles promote mixing in the emulsion phase and enhance heat transfer, but at the cost of increased axial dispersion. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

Thus, all of the tube inserts will potentially provide the required enhancement without the need for extra heat transfer area. However, it would be preferred to have the enhancement with minimum increase in pressure drop. Table 15.9 shows the increase in friction factor for the various inserts. 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

For G/S particle systems, enhancement in convective heat transfer is achieved at the expense of increased pressure drop in moving the gas at higher velocities. A measure of the relative benefit of enhanced heat transfer to added expenditure for fluid movement can be approximated by an effectiveness factor, E, defined as the ratio of the heat transfer coefficient to some kind of a pressure drop factor. For G/S systems in which particles are buoyed by the flowing gas stream, this pressure drop factor is expressed by the Archimedes number Ar, and E can be written... 

It is obvious that re-atomization yields decrease the mean diameter of the liquid droplets and thus an increased interface area at the same time, it results in reduced average transfer coefficients, because heat and mass transfer coefficients between gas flow and particle or droplet are in positive correlation with the diameter of the particle or droplet, while coalescence of droplets yields influences opposite to those described above. In their investigation on the absorption of C02 into NaOH solution, Herskowits et al. [59, 60] determined theoretically the total interface areas and the mass transfer coefficients by comparing the absorption rates with and without reaction in liquid, employing the expression for the enhancement factor due to chemical reaction of second-order kinetics presented by Danckwerts [70],... 

To explain the imbalance, O Nions and Oxburgh (1983) and Oxburgh and O Nions (1987) proposed that a barrier, which is suggested to exist between the upper and the lower mantle from seismic observation, has trapped helium in the lower mantle and retarded the heat transport from the lower mantle to the upper mantle. O Nions et al. (1983) suggested, from a semiquantitative discussion, that delayed heat transfer from the lower mantle to the upper mantle with a time constant of about 2Ga would enhance the present heat flow by a factor of two. McKenzie and Richter (1981) made numerical calculation on a two-layered mantle convection and showed that heat transfer from the lower mantle to the upper mantle is considerably retarded to give rise to an enhancement of the present surface heat flow up to a factor of two. If the thermal barrier not only retards the heat transfer and hence enhances the present surface heat flow but also essentially prevents the 4He flux from the lower to the upper mantle, this would qualitatively explain the imbalance. If this indeed were the case, we would expect a large amount of 4He accumulation in the lower mantle. However, it is difficult to conclude such a large accumulation of 4He in the lower mantle from the currently available scarce noble gas data derived from mantle-derived materials. 

Experiments have shown that Eq. (11.63) tends to underestimate the heat transfer rate from a column of tubes, and is thus conservative for design purposes. The actual heat transfer rates are enhanced by several factors not accounted for in the theoretical model discussed above. These factors include such effects as splashing of the film when it impinges on a lower tube, additional condensation on the subcooled film as it falls between tubes, and uneven run-off because of bowed or slightly inclined tubes. 

E(, enhancement factor for heat transfer coefficient due to the presence of radial component of the liquid velocity helical coil... 

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