Estimation of Overall Coefficients

Ihe values of the film coefficients of heat transfer h, and accordingly those of the overall coefficient U, vary by orders of magnitudes, depending on the fluid properties and on whether they undergo phase change, that is, condensation or boiling. Thus, the correct estimation of U is very important in the design of heat transfer equipment. 

The first consideration when designing or evaluating heat transfer equipment is as to which side of the heat transfer wall the controlling heat transfer resistance will exist on. for example, when air is heated by condensing saturated steam, the air-side film coefficient may be 30 kcal h m -°(E, while the steam-side film coefficient might be on the order of 10 000 kcalh m °C . In such a case, we need not consider the steam-side resistance. The overall coefficient would be almost equal to the air-side film coefficient, which can be predicted by 

Condensing steam Clean water Dirty water 

The values of the film coefficient for liquids without phase change are usually larger than those for gases, by one or two orders of magnitude. Nonetheless, the liquid-side heat transfer resistance may be the major resistance in an equipment heated by saturated steam. Film coefficient for liquids without phase change can be predicted by correlations such as those in Equations 5.8a, 5.12a, or 5.13. 

In the case of gas-gas or liquid-liquid heat exchangers, the film coefficients for the fluids on both sides of the metal wall are of the same order of magnitude, and can be predicted by correlations, for example, with Equation 5.8a or 5.12a. Neither of the fluid film resistances can be neglected. In a gas-liquid heat exchanger, the controlling resistance is on the gas side, as mentioned before. 

In the case of gas-gas or liquid-liquid heat exchangers, the film coefficients for the fluids on both sides of the metal wall are of the same order of magnitude, and 

In practice, we must consider the heat transfer resistance of the dirt or scale which has been deposited on the metal surface, except when the values of U are small, as in the case of a gas heater or cooler. Usually, we use the so-called fouling factor hf, which is the reciprocal of the dirt resistance and hence has the same dimension as the film coefficient h. The dirt resistance sometimes becomes controlling, when U without dirt is very large - as in the case of a liquid boiler heated by saturated steam. Thus, in case the dirt resistance is not negligible, the overall resistance for heat transfer 1/ U is given by the following equation  

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D-optimal criterion being the most usual, based on optimization of the overall precision of estimation of the coefficients of the modelJ This method and type of design is extremely flexible because ... 

Estimation of Overall Mass Transfer Coefficients A Simplified Result... 

The two estimates of the flux agree within the round-off error. Notice that in this example it was not necessary to calculate the interfacial concentrations to estimate the ammonia flux since the use of overall coefficients was appropriate. They were calcu-... 

These methods find the best estimate of the coefficients of an equation by minimizing the sum of the squares of the deviations (errors) between the observed and the fitted log (1/C), or log of relative biological potency in the case of QSAR. They generally assume that the errors are normally distributed. The validity of a statistical fit is usually evaluated by calculating the probability that the overall fit is significantly better than simply using the mean value and, if more than one descriptor is used, each descriptor contributes significantly to the quality of the fit. 

The characterisation of mass transfer is essential for the design of the micro-reactor. In liquid-liquid flows most studies have focused on the estimation of overall mass transfer coeflicients, while no model based on theory has been developed so far. The overall volumetric mass transfer coeflicient (kua) is a characteristic parameter of a system used to evaluate the performance of the contactors, and is a combination of the mass transfer coefficient (kp), which depends mainly on the difiusivity of solute, characteristic diffusion length and interfacial hydrodynamics, and of the specific interfacial area (a), which depends on the flow pattern. The prediction of the overall volumetric mass transfer coeflicient remains difficult due to secondary phenomena, tike interfacial instabilities. 

It also became necessary to consider interactions between the nuclear and the thermal-hydraulic performance. Iterative calculations, notably between the AIMAZ (nuclear) and CUSH (core and primary circuit hydraulic models) were needed to reach final estimates of overall reactor power distributions and void coefficients. 

The overall inaccuracy for the four properties is 1.7 kJ mol with respect to the chemical potentials, corresponding to a factor of 2 for the nonlogarithmic equilibrium constants. This is comparable with the results of incremental methods for the estimation of partition coefficients. Considering the relatively small number of parameters, the short history, and the broad applicability of the COSMO-RS approach, this accuracy is very satisfactory. Although there are several possibilities for further improvements of the approach, a substantial decrease of the inaccuracy below this factor of 2 will be hard to achieve. 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

The performances and estimating methods of welded PHEs match those of gasketed PHEs in most cases, but normally the Compabloc, with larger depth of corrugations, can be lower in overall coefficient. Some extensions of the design operating conditions are possible with welded PHEs, most notably is that ciyogenic applications are possible. Pressure vessel code acceptance is available on most units. 

Overall Coefficients and Stage Efficiency If it is assumed that values of a, ., kc, ko (and therefore Kd) can somehow be estimated, the stage efficiency can be calculated through... 

Mass Transfer As mentioned earlier, spray columns rarely develop more than 1 theoretical stage due to the axial mixing in the column. Nevertheless, it is necesary to determine what column height will give this theoretical stage. It is recommended by Cavers in Lo et al. Handbook of Solvent Extraction p. 323 and p. 327, John Wiley Sons, New York, 1983 that the following equation be used to estimate the overall efficiency coefficient ... 

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.

Estimate the heat transfer area required for the system considered in Examples 9.1 and 9.36. assuming that no data on the overall coefficient of heat transfer are available. 

From Table 9.17, an estimated value of the overall coefficient is U = 500 W/m2K and hence, the provisional area, from equation 9.212, is ... 

A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kg K and the overall coefficient of heat transfer is 1.5 kW/m2 K. 

Integration of Eq. (6) for S02 in Table V estimates the conversion achieved. Simulation of periodic symmetrical switching between a reactant mixture and air gave an estimate of 99.4% at 12 min after the switch to the S03/S02 reactant mixture in reasonable agreement with the overall conversion of 98.8% measured by Briggs et al. (1977). With respect to model sensitivity, it was found that bed midpoint temperature was sensitive to the wall and gas to particle heat transfer coefficients. An extensive study of sensitivity, however, was not undertaken. 

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