Overall coefficients

Overall Coefficients. Often overall coefficients of heat and mass transfer are available, rather than the film coefficients used eadier. In that case equation 35 can be rewritten as... 

U Overall coefficient of heat transfer for outside surface basis U for overall coefficient between liquid-vapor interface and coolant J/(s-m -K) Btu/(h-fF- F)... 

Overall Coefficient of Heat Transfer In testing commercial heat-transfer equipment, it is not convenient to measure tube temperatures (t,3 or t4 in Fig. 5-6), and hence the overall performance is expressed as an overall coefficient of heat transfer U based on a convenient area dA, which may be dAi, oi an average of dAi and dA whence, by definition,... 

U is called the overall coefficient of heat transfer, or merelv the overall coefficient. The rate of conduction through the tube wall and scale deposit is given by... 

T = absolute temperature. Subscript 1 (or G), radiating surface (or gas) temperature subscript E, exit-gas subscript o, base temperature subscript E, pseudoadiabatic flame temperature based on C averaged from to Te-U = overall coefficient of heat transfer, gas convec tion to refractory wall to ambient air. 

If it is desired to calculate the rate of transfer from the overall concentration difference based on bulk-hquid compositions (x° — x), the appropriate overall coefficient Kl is related to the individual coefficients by the equation... 

Experimental K g< and Ki a data are available for most absorption and stripping operations of commercial interest (see Sec. 15). The solute concentrations employed in these experiments normally are very low, so that Ki a — Ki/i and K g< Pt where pf is the total pressure employed in the actual experimental-test system. Unlike the individual gas-film coefficient /cg, the overall coefficient will... 

To integrate Eq. (11-3), and AT must be known as functions of Q. For some problems, varies strongly and nonlinearly throughout the exchanger. In these cases, it is necessary to evaluate and AT at several intermediate values and numerically or graphically integrate. For many practical cases, it is possible to calculate a constant mean overall coefficient from Eq. (11-2) and define a corresponding mean value of AT,n, such that... 

Work in connection with desahnation of seawater has shown that specially modified surfaces can have a profound effect on heat-transfer coefficients in evaporators. Figure 11-26 (Alexander and Hoffman, Oak Ridge National Laboratory TM-2203) compares overall coefficients for some of these surfaces when boiling fresh water in 0.051-m (2-in) tubes 2.44-m (8-ft) long at atmospheric pressure in both upflow and downflow. The area basis used was the nominal outside area. Tube 20 was a smooth 0.0016-m- (0.062-in-) wall aluminum brass tube that had accumulated about 6 years of fouhng in seawater service and exhibited a fouling resistance of about (2.6)(10 ) (m s K)/ J [0.00015 (fF -h-°F)/Btu]. Tube 23 was a clean aluminum tube with 20 spiral corrugations of 0.0032-m (lA-in) radius on a 0.254-m (10 -in)... 

U.S. customary). Fragen and Badger [Ind. Eng Chem., 28, 534 (1936)] correlated overall coefficients on sugar and sulfite hquor in the same evaporator for viscosities to 0.242 Pa-s (242 cP) and found a relationship that included the viscosity raised only to the 0.25 power. 

TABLE 11-5 Overall Coefficients for Air-Cooled Exchangers on Bare-Tube Basis... 

TABLE 11-8 External Coils Typical Overall Coefficients ... 

Typical overall coefficients to start a rough sizing are as below. Use these in conjunction with the NTU calculated for the process. The closer the NTU matches the plate (say between 2.0 and 3.0), the higher the range of listed coefficients can be used. The narrower (smaller) the depth of corrugation, the higher the coefficient (and pressure drop), but also the lower the abdity to carry through any particulate. 

Overall coefficients are determined hke shell and tube exchangers that is, sum all the resistances, then invert. The resistances include the hot-side coefficient, the cold-side coefficient, the fouhng factor (usually only a total value not individual values per fluid side) and the wall resistance. 

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. 

LMTD and overall coefficient are calculated like in PHE section above. 

Thermal conductivity of these materials is veiy low and affec ts the overall coefficient. When several materials are compatible, explore all of them, as final cost is not always the same as raw material costs. 

Only fair overall coefficient values may be expected, although heat-flux values are good. 

The overall heat-transfer rate is almost entirely dependent upon the film coefficient between the inner jacket wall and the solids, which depends to a large extent on the solids characteristics. Overall coefficients may range from 30 to 200 J/(m s K), based upon total area if the diyer walls are kept reasonably clean. Coefficients as low as 5 or 10 may be encountered if caking on the walls occurs. 

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... 

See also Treybal [Am. ln.st. Chem. Eng. J., 4, 202 (1958) 6, 5M (I960)] and Olander [Chem. Eng. Sci, 18, 47 (1963) 19, 275 (1964)]. The remaining discussion is confined to measured values of stage efficiency or volumetric overall coefficients. These are largely of value only for the particiilar systems studied. For this reason, one fairly complete study will be described, and the others will only be mentioned. 

Usually, however, it is not feasible to establi a stage or overall efficiency or a leaching rate index (e.g., overall coefficient) without testing small-scale models of likely apparatus. In fact, the results of such tests may have to be scaled up empirically, without explicit evaluation of rate or quasi-equilibrium indices. 

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