Transfer coefficient Subject

The small-spiral-large-sbaft type (Fig. ll-60b) is inserted in a solids-product line as pipe banks are in a fluid line, solely as a heat-transfer device. It features a thin burden ring carried at a high rotative speed and subjected to two-sided conductance to yield an estimated heat-transfer coefficient of 285 W/(m °C) [50 Btu/(h fU °F)], thereby ranking thermally next to the sheU-fluidizer type. This device for powdered solids is comparable with the Votator ol the fluid field. 

Since D/6 is the mass-transfer coefficient. For the portion of the operating cui ve in which flux is invariant, the wall concentration is apparently invariant. The mechanism governing why and how that occurs is the subject of a continuing debate in the hterature. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

The convective and nucleate boiling heat transfer coefficient was the subject of experiments by Grohmann (2005). The measurements were performed in microtubes of 250 and 500 pm in diameter. The nucleate boiling metastable flow regimes were observed. Heat transfer characteristics at the nucleate and convective boiling in micro-channels with different cross-sections were studied by Yen et al. (2006). Two types of micro-channels were tested a circular micro-tube with a 210 pm diameter, and a square micro-channel with a 214 pm hydraulic diameter. The heat transfer coefficient was higher for the square micro-channel because the corners acted as effective nucleation sites. 

The differential equation describing the temperature distribution as a function of time and space is subject to several constraints that control the final temperature function. Heat loss from the exterior of the barrel was by natural convection, so a heat transfer coefficient correlation (2) was used for convection from horizontal cylinders. The ends of the cylinder were assumed to be insulated. The equations describing these conditions are ... 

Example 15.1 A hot stream is to be cooled from 300 to 100°C by exchange with a cold stream being heated from 60 to 200°C in a single unit. 1-2 shell-and-tube heat exchangers are to be used subject to IP =0.9. The duty for the exchanger is 3.5 MW and the overall heat transfer coefficient is estimated to be 100 W-m 2-K 1. Calculate ... 

In retrofit situations, existing heat exchangers might be subjected to changes in flowrate, heat transfer duty, temperature differences or fouling characteristics. Heat transfer coefficients and pressure drops can be approximated from... 

Instead of using a 1-1 design in Example 7, a 1-2 design is to be used subject to Xp = 0.9. Assume that the overall heat transfer coefficient is unchanged. (In practice, it would be expected to increase). Calculate... 

The convective mass transfer coefficient hm can be obtained from correlations similar to those of heat transfer, i.e. Equation (1.12). The Nusselt number has the counterpart Sherwood number, Sh = hml/Di, and the counterpart of the Prandtl number is the Schmidt number, Sc = p/pD. Since Pr k Sc k 0.7 for combustion gases, the Lewis number, Le = Pr/Sc = k/pDcp is approximately 1, and it can be shown that hm = hc/cp. This is a convenient way to compute the mass transfer coefficient from heat transfer results. It comes from the Reynolds analogy, which shows the equivalence of heat transfer with its corresponding mass transfer configuration for Le = 1. Fire involves both simultaneous heat and mass transfer, and therefore these relationships are important to have a complete understanding of the subject. 

A study of mass transfer between a liquid and a particle forming part of an assemblage of particles was made by Mulun and Treleaven1116, who subjected a sphere of benzoic acid to the action of a stream of water. For a fixed sphere, or a sphere free to circulate in the liquid, the mass transfer coefficient was given, for 50 < Re c < 700, by ... 

This is simply the definition of the mass transfer coefficient km, the subject of mass transfer courses is to find suitable correlations in order to estimate k A (units of lengthAime). The mass transfer coefficient is in turn defined through the Sherwood number,... 

At high Re and Ma in the free-molecule regime, transfer rates for spheres have been calculated by Sauer (S4). These results, together with others for cylinders and plates, have been summarized by Schaaf and Chambre (Sll). The particles are subject to aerodynamic heating and the heat transfer coefficients are based upon the difference between the particle surface temperature and the recovery temperature (see standard aerodynamics texts). In the transitional region, the semiempirical result of Kavanau (K2),... 

The mass transfer between phases is, of course, the very basis for most of the diffusional operations of chemical engineering. A considerable amount of experimental and empirical work has been done in connection with interphase mass transfer because of its practical importance an excellent and complete survey of this subject may be found in the text book of Sherwood and Pigford (S9, Chap. Ill), where dimensionless correlations for mass transfer coefficients in systems of various shapes are assembled. 

But suppose we are operating a heat exchanger subject to rapid rates of initial fouling. The start-of-run heat-transfer coefficient U is 120 Btu/[(h)(ft2(°F)]. Four months later, the U value has lined out at 38. The calculated clean tube-side velocity is lV2 ft/s. This is too low, but what can be done ... 

It is not often that proper estimates can be made of uncertainties of all the parameters that influence the performance or required size of particular equipment, but sometimes one particular parameter is dominant. All experimental data scatter to some extent, for example, heat transfer coefficients and various correlations of particular phenomena disagree, for example, equations of state of liquids and gases. The sensitivity of equipment sizing to uncertainties in such data has been the subject of some published information, of which a review article is by Zudkevich Encycl. Chem. Proc. Des. 14, 431-483 (1982)] some of his cases are ... 

The basis of the method was stated by Silver (1947). A numerical solution of a condenser for mixed hydrocarbons was carried out by Webb and McNaught (in Chisholm, 1980, p. 98) comparison of the Silver-Bell-Ghaly result with a Colburn-Hougen calculation showed close agreement in this case. Bell and Ghaly (1973) claim only that their method predicts values from 0 to 100% over the correct values, always conservative. A solution with constant heat transfer coefficients is made in Example 8.11 A recent review of the subject has been presented by McNaught (in Taborek et al., 1983, p. 35). 

When the ultimate objective of these operations is the carrying out of a chemical reaction, the achieved specific rate is a suitable measure of the quality of the mixing. Similarly the achieved heat transfer or mass transfer coefficients are measures of their respective operations. These aspects of the subject are covered in other appropriate sections of this book. Here other criteria will be considered. 

Some numerical examples are given. For a semi-infinite copper melt initially at the fusion temperature, losing heat with an over-all heat transfer coefficient of 0.5 B.t.u./(hr.)(ft.2)(°F.) to the surroundings at ambient temperature, after 4 hr. 771 = 0.98, and the estimated thickness of solidified copper is 44 in. with a 12% error. A second example is a steel sheet subjected to a slowly flowing stream of very hot gas, such that a uniform heat flux of 105 B.t.u./(hr,)(ft.2)(°F.) is imposed at the surface with negligible motion of the melt. After 200 sec., 771 = 0.68, and the melt thickness is estimated to be 1.26 in., with a possible error of 8.6%. 

Mass transfer coefficients are frequently regarded as a difficult subject, not because the subject is inherently difficult, but because of different definitions and because of complexities for mass transfer from one solution into a second solution. These differences merit further discussion. 

In most of the industrial applications, several DLCs are connected either in series or in series/ parallel. They are generally subjected to very high currents. Consequently, the heat produced by Joule effect must be dissipated with cooling systems like fans or air distribution channels. The choice of the cooling system depends on the level of the heat transfer coefficient and the maximum allowed operating temperature. The chosen cooling system should be sufficient to keep the DLC temperature at a tolerable temperature level which leads to a longer lifetime. 

The actual value of k a was measured by absorption of carbondiox-ide from air into a buffer solution of potassium-carbonate and bicarbonate. Care was taken that the mass transfer coefficient itself was not enhanced by the chemical reaction, although the composition of the buffers used guaranteed a substantial driving force for mass transfer over the whole length of the column. Literature about the subject is abundant and here referred to (11, 12, 13). 

To use the various criteria given in the previous section, some experimental data on the reacting system are necessary. These are the effective diffusivity of the key species in the pores of the catalyst, the heat and mass transfer coefficients at the fluid-solid interface, and the effective thermal conductivity of the catalyst. The accuracy of some of these parameters, which are usually obtained from known correlations, may sometimes be subject to question. For example, under labo-... 

More experimental work on this subject is needed. The above relation implies strong dependence of the heat transfer coefficient on the gas velocity and the liquid properties (pL, pL, AL, and CP). 

Direct evaluation of the convective heat transfer coefficient (h ) of subjects clothed in undergarments and socks (normal ventilated environment) was achieved by observing the sublimation rate of naphthalene balls uniformly positioned three centimeters from the body surface. Equations were developed for prediction of h as a function of metabolic activity and posture, calculation o average skin temperature, and estimation of maximum evaporative heat losses from the body (U2 ). In another approach, the coefficients of dry heat transfer at varying wind speeds for nude and clothed sectional mannequins were determined (U3). At air flow rates above 2 m/sec, percentage contributions of individual body sections to total heat transfer remain constant for the nude and clothed mannequin, yet increased for normally uncovered units such as the face and hands. Generally, the ratio of total heat flow for the nude to clothed mannequin increased with air flow. 

Rework Prob. 2-29 assuming that the plate is subjected to a convection environment on both sides of temperature T. with a heat-transfer coefficient h. Tw is now some reference temperature not necessarily the same as the surface temperature. 

A 12-mm-diameter aluminum sphere is heated to a uniform temperature of 400°C and then suddenly subjected to room air at 20°C with a convection heat-transfer coefficient of 10 W/m2 °C. Calculate the time for the center temperature of the sphere to reach 200°C. 

A thick concrete wall having a uniform temperature of 54°C is suddenly subjected to an airstream at 10°C. The heat-transfer coefficient is 2.6 W/m2 °C. Calculate the temperature in the concrete slab at a deptii of 7 cm after 30 min. 

A long steel bar 5 by 10 cm is initially maintained at a uniform temperature of 250°C. It is suddenly subjected to a change such that the environment temperature is lowered to 35°C. Assuming a heat-transfer coefficient of 23 W/m2 °C, use a numerical method to estimate the time required for the center temperature to reach 90°C. Check this result with a calculation, using the Heisler charts. 

A steel rod 12.5 mm in diameter and 20 cm long has one end attached to a heat reservoir at 250°C. The bar is initially maintained at this temperature throughout. It is then subjected to an airstream at 30°C such that the convection heat-transfer coefficient is 35 W/m2 °C. Estimate the time required for the temperature midway along the length of the rod to attain a value of 190°C. 

Water flows in a 2.5-cm-diameter pipe so that the Reynolds number based on diameter is 1500 (laminar flow is assumed). The average bulk temperature is 35°C. Calculate the maximum water velocity in the tube. (Recall that u, = 0.5wo.) What would the heat-transfer coefficient be for such a system if the tube wall was subjected to a constant heat flux and the velocity and temperature profiles were completely developed Evaluate properties at bulk temperature. 

If the vapor to be condensed is superheated, the preceding equations may be used to calculate the heat-transfer coefficient, provided the heat flow is calculated on the basis of the temperature difference between the surface and the saturation temperature corresponding to the system pressure. When a noncondensable gas is present along with the vapor, there may be an impediment of the heat transfer since the vapor must diffuse through the gas before it can condense on the surface. The reader should consult Refs. 3 and 4 for more information on this subject. 

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