Film coefficients

Providing film coefficients vary by less than one order of magnitude, then Eq. (7.6) has been found to predict network area to within 10 percent of the actual minimum. ... 

The relationship of the overall gas-phase mass transfer coefficient to the individual film coefficients maybe found from equations 4 and 5, assuming a straight equiHbrium line ... 

Log arithmic-Mean Driving Force. As noted eadier, linear operating lines occur if all concentrations involved stay low. Where it is possible to assume that the equiUbrium line is linear, it can be shown that use of the logarithmic mean of the terminal driving forces is theoretically correct. When the overall gas-film coefficient is used to express the rate of absorption, the calculation reduces to solution of the equation... 

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... 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

Representation of Heat-Transfer Film Coefficients There are two general methods of expressing film coefficients (1) dimensionless relations and (2) dimensional equations. 

Simultaneous Loss by Radiation The heat transferred by radiation is often of significant magnitude in the loss of heat from surfaces to the surroundings because of the diathermanous nature of atmospheric gases (air). It is convenient to represent radiant-heat transfer, for this case, as a radiation film coefficient which is added to the film coefficient for convection, giving the combined coefficient for convection and radiation (h + hf In Fig. 5-7 values of the film coefficient for radiation are plotted against the two surface temperatures for emissivity = 1.0. 

Coils For flow inside helical coils, Reynolds number above 10,000, multiply the value of the film coefficient obtained from the apphcable equation for straight tubes by the term (1 + 3..5 D /DJ. 

In atmospheric air-cooled finned tube exchangers, the air-film coefficient from Eq. (5-64) is sometimes converted to a value based on outside bare surface as follows ... 

For the general case, the treatment suggested by Kern (Pmcc.s.s Heat Transfer, McGraw-Hill, New York, 1950, p. 512) is recommended. Because of the wide variations in fin-tube construction, it is convenient to convert all film coefficients to values based on the inside bare surface of the tube. Thus to convert the film coefficient based on outside area (finned side) to a value based on inside area Kern gives the following relationship ... 

The physical properties of the liquid, rather than those of the vapor, are used For determining the film coefficient for condensation. Nus-selt [2. Ver. Dt.sch. Ing., 60, 541, 569 (1916)] derived theoretical relationships for predicting the film coefficient of heat transfer for condensation of a pure saturated vapor. A number of simplifying assumptions were used in the derivation. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

FIG. 5-9 Chart for determining film coefficient for film-type condensation of pure vapor, based on Eqs. 5-88 and 5-93. For vertical tubes multiply by 1.2. If 4F/ J exceeds 2100, use Fig. 5-10. is in U.S. customary units to convert feet to... 

Heat transfer by nucleate boiling is an important mechanism in the vaporization of liqmds. It occurs in the vaporization of liquids in kettle-type and natural-circulation reboilers commonly usea in the process industries. High rates of heat transfer per unit of area (heat flux) are obtained as a result of bubble formation at the liquid-solid interface rather than from mechanical devices external to the heat exchanger. There are available several expressions from which reasonable values of the film coefficients may be obtained. 

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... 

Film coefficients for the boiling of liquids other than water have been investigated. Coulson and McNelly [Trans. In.st. Chem. Eng., 34, 247 (1956)] derived the following relation, which also correlated the data of Badger and coworkers [Chem. Metall. Eng., 46, 640 (1939) Chem. Eng., 61(2), 183 (1954) and Trans. Am. Jnst. Chem. Eng., 33, 392 (1937) 35, 17 (1939) 36, 759 (1940)] on water ... 

Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side the flutes tend to collect the condensate and leave the lauds bare [Caruavos, Proc. First Int. Symp. Water Desalination, 2, 205 (1965)]. The coudeusiug-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation... 

The boiling-film coefficient is about 30 percent lower for pure water than it is for salt water or seawater. There is as yet no accepted explanation for the superior performance in salt water. This phenomenon is also seen in evaporation from smooth tubes. 

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