Heat 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. 

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... 

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),... 

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). 

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%. 

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. 

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. 

Determination of appropriate coefficients of heat transfer is required for design calculations on heat-transfer operations. These coefficients can sometimes be estimated on the basis of past experience, or they can be calculated from empirical or theoretical equations developed by other workers in the field. Many semiempirical equations for the evaluation of heat-transfer coefficients have been published. Each of these equations has its limitations, and the engineer must recognize the fact that these limitations exist. A summary of useful and reliable design equations for estimating heat-transfer coefficients under various conditions is presented in this chapter. Additional relations and discussion of special types of heat-transfer equipment and calculation methods are presented in the numerous books and articles that have been published on the general subject of heat transfer. 

With the measurements subject to fluctuations of 20 or 30%, no accurate description of the profile is possible. All that can be said is that with moderate ratios of tube to particle diameter, the maximum velocity is about twice the minimum, and that when the particles are relatively small, the profile is relatively flat near the axis. It is fairly well established that the ratio of the velocity at a given radial position to the average velocity is independent of the average velocity over a wide range. Another observation that is not so easy to understand is that the velocity reaches a maximum one or two particle diameters from the wall. Since the wall does not contribute any more than the packing to the surface per unit volume in the region within one-half particle diameter from the wall, there is no obvious reason for the velocity to drop off farther than some small fraction of a particle diameter from the wall. In any case, all the variations that affect heat transfer close to the wall can be lumped together and accounted for by an effective heat-transfer coefficient. Material transport close to the wall is not very important, because the diffusion barrier at the wall makes the radial variation of concentration small. 

Little is known about the fluid wall heat transfer in the case of gas -liquid flow in a fixed-bed reactor. Some research on this subject, however, has been carried out for the specific case of cocurrent downflow over a fixed-bed reactor. This is summarized in Chap. 6. Some work on the slurry-wall heat-transfer rate for a three-phase fluidized bed has also been reported. The heat-transfer rate is characterized by the convective heat-transfer coefficient between the slurry and the reactor wall. Some correlations for the heat-transfer coefficient in a three-phase slurry reactor are discussed in Chap. 9. 

Consider a long pipe of inner radius r, outer radius r2> and thermal conductivity k. The outer surface of the pipe is subjected to convection to a medium at T. with a heat transfer coefficient of h, but the direction of heat transfer is not known. Express the convection boundary condition on the outer surface of the pipe. 

Consider a short cyUnder of radius r<, and height H in which heat is generated at a constant rate of Heat is lost from the cylindrical surface at r = r by convection to the surrounding medium at temperature with a heat transfer coefficient of /i. The bottom surface of the cylinder at z = 0 is insulated, while the top surface at z — is subjected to uniform heat flux Assuming constant thermal conductivity and steady two-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem. Do not. solve. 

A 1000-W iron is left on Ihe iron board with its base exposed to ambient air at 26°C. The base plate of the iron has a thickness ofL= 0.5 cm, base area of A = 150 cm, and thermal conductivity of k = 18 W/m C.The inner surface of the base platens subjected to uniform heat flux generated by the resistance heaters inside. The outer surface of the base plate whose emissivity is k = 0.7, loses he4l by convection to ambient air with an average heat transfer coefficient of A = 30 W/pi °C as well as by radiation to the surrounding... 

A plane wall of lliickness L is subjected to convection at both surfaces with ambient temperature and heat transfer coefficient at inner surface, and corresponding and values at the outer surface. Taking the positive direction of x to be from the inner surface to the outer surface, the correct expression for the convection boundary condition is... 

The corrected length approximation gives very good results when the variation of temperature near the fin tip is small (which is the case when mL 1) and the heat transfer coefficient at the fin tip is about the same as that tit the lateral surface of the fin. Tlierefore.yins subjected to convection at their tips can be treated as fins with insulated tips by replacing the actual fi length by the corrected length in Eqs. 3-64 and 3-65. 

C Consider a short cylinder whose top and bottom surfaces are insulated. The cylinder is initially at a uniform tern perature T, and is subjected to convection from its side surface to a medium at temperature 71, with a heat transfer coefficient of /i. Is the heat transfer in this short cylinder one- or two dimensional Explain. 

Varialioii of lemperalure will) position and lime in a semi-infinite solid initially at temperature Tj subjected to convection to an environment at 7 with a convection heat transfer coefficient of h (plotted using EES). 

The soil temperature in the upper layers of the earth varies with the variations in the atmospheric condiliuns. Before a cold front moves in, the earth at a location is initially at a uniform temperature of 10°C. Then the area is subjected to a tem-peialure of 10°C and high winds that resulted in a convection heat transfer coefficient of 40 W/m - "C on Ihe earth .s surface for a period of 10 h. Taking the properties of the soil at that location to be /r = 0.9 W/m C and a = 1.6 X 10 m /s, determine the soil temperature at distances 0, 10, 20, and 50 cm from the earth s surface at the end of this lO-h period. 

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