Effective wall heat transfer coefficient

Crider, J.E. and Foss, A.S. (1965) Effective wall heat transfer coefficients and thermal resistances in mathematical models of packed beds. AIChE J., 11,1012. 

Dimensionless effective radial thermal conductivity X and effective wall heat transfer coefficient h as function of Peclet-number (a measured under reacting conditions, b calculated according to /42/for nonreacting conditions)... 

Perhaps the simplest to determine is the effective wall heat transfer coefficient (based on tube wall temperature) used in conjunction with the one-dimensional model. A heat balance for a bed packed with inert pellets is given by ... 

Figure 14.5 Dependence of effective wall heat transfer coefficient on reactor length for various conditions. (De-wasch and Froment 1972 reprinted with permission from Chemical Engineering Science. Copyright by Pergamon Press, Inc.)...

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)... 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

The static contribution l. , incorporates heat transfer by conduction and radiation in the fluid present in the pores, conduction through particles, at the particle contact points and through stagnant fluid zones in the particles, and radiation from particle to particle. Figure 19-20 compares various literature correlations for the effective thermal conductivity and wall heat-transfer coefficient in fixed beds [Yagi and Kunii, AlC hE J. 3 373(1957)]. 

Eqns. (3) - (9) enable the effective radial thermal conductivity (kr>eff), the apparent wall heat transfer coefficient (hw>eff) and the overall heat transfer coefficient (U) to be predicted in terms of the physical properties p, kg and Cp of air, together with measurable parameters such as , 6, dt, kp, dp (A), dp>(v), dp>(V/A), e and T, the mean bed temperature. The predicted and observed values of U are compared in Figure 6. The averaged normalised standard error... 

For Rep < 100 and 0.05 < rp/r, < 0.2, wall Biot numbers range between 0.8 and 10 [28], so this means that wall effects cannot be neglected a priori [38]. Also this criterion contains procurable parameters. For the wall heat transfer coefficient hw and the effective heat conductivity in the bed Abc(r, the correlations in Table 2, eqs. 44-47 can be used [8, 39]. These variables are assumed to be composed of a static and a dynamic (i.e. dependent on the flow conditions) contribution. Thermal heat conductivities of gases at 1 bar range from 0.01 to 0.5 Js m l K l, depending on the nature of the gas and temperature. 

Along with wall heat transfer coefficient in non-adiabatic reactors, another effect frequently added in models is that of thermal conduction in the solid phase (27, 28, 29). One should be particularly careful here, since most of the correlations available in the literature (9 y 32) are for effective... 

The choice of a model to describe heat transfer in packed beds is one which has often been dictated by the requirement that the resulting model equations should be relatively easy to solve for the bed temperature profile. This consideration has led to the widespread use of the pseudo-homogeneous two-dimensional model, in which the tubular bed is modelled as though it consisted of one phase only. This phase is assumed to move in plug-flow, with superimposed axial and radial effective thermal conductivities, which are usually taken to be independent of the axial and radial spatial coordinates. In non-adiabatic beds, heat transfer from the wall is governed by an apparent wall heat transfer coefficient. ... 

Figure 17.37. Some measured and predicted values of heat transfer coefficients in fluidized beds. 1 Btu/hr(sgft)(°F) = 4.88 kcal/(hr)(m )(°C) = 5.678 W/(m )(°C). (a) C o mp arisen of correlations for heat transfer from silica sand with particle size 0.15 mm dia nuiaized in air. Conmtions are identified in Table 17.19 Leva, 1959). (b) Wall heat transfer coefficients as function of the superficial fluid velocity, data of Varygin and Martyushin. Particle sizes in microns (1) ferrosilicon, i 82.5 (2) hematite, d = 173 (3) Carborundum, d = 137 (4) quartz sand, d = 140 (5) quartz sand, d = 198 (6) quartz sand, d = 216 (7) quartz sand, d = 428 (8) quartz sand, d = 51.5 (9) quartz sand, d = 650 (10) quartz sand, d = 1110 (11) glass spheres, d= 1160. Zabrqdskystal, 1976,Fig. 10.17). (c) Effect of air velocity and particle physical properties on heat transfer between a fluidized bed and a submerged coil. Mean particle diameter 0.38 mm (I) BAV catalyst (II) iron-chromium catalyst (III) silica gel (IV) quartz (V) marble Zabrodsky et at, 1976, Fig. 10.20).

Figure 17.36. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = r/ G/jjL, dp = SVpjAp, s = poros-...

Figure 9.2 shows existing data for the effective thermal conductivity of packed beds. These data include both ceramic and metallic packings. More accurate results can be obtained from the semitheoretical predictions of Dixon and Cresswell (1979). Once Kr is known, the wall heat transfer coefficient can be calculated from... 

In liquid-solid fluidized beds, the bed-to-wall heat transfer coefficient increases with an increase in liquid flow rate due to the reduction in thermal boundary layer thickness. The heat transfer coefficient was also found to increase with the particle size. The effective thermal conductivity of liquid fluidized bed increases sharply with liquid velocity beyond minimum fluidization, passes through a maximum near a voidage of 0.7, and then gradually decreases. 

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