Heat transfer coefficients, interfacial

Dukler (D12), 1959 Theoretical analysis of turbulent film flow (with and without downward cocurrent gas stream) with extension to film heat transfer. Interfacial disturbances are neglected basic equations are solved by computer giving film thicknesses, velocity profiles, local and mean heat transfer coefficients. Interfacial shear is shown to be of great importance. 

Equations (13-115) to (13-117) contain terms, for rates of heat transfer from the vapor phase to the hquid phase. These rates are estimated from convective and bulk-flow contributions, where the former are based on interfacial area, average-temperature driving forces, and convective heat-transfer coefficients, which are determined from the Chilton-Colburn analogy for the vapor phase and from the penetration theoiy for the liquid phase. 

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. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

Dukler and Taitel, 1991b). The simplest configuration of annular flow is a vertical falling film with concurrent downward flow. Given information on interfacial shear and considering the film to be smooth, the film thickness and heat transfer coefficient between the wall and the liquid film can be predicted from the following basic equations (Dukler, 1960) ... 

The final dimensionless group to be evaluated is the interfacial heat-transfer number, and therefore the interfacial heat-transfer coefficient and the interfacial area must be determined. The interface is easily described for this regime, and, with a knowledge of the holdup and the tube geometry, the interfacial area can be calculated. The interfacial heat trasfer coefficient is not readily evaluated, since experimental values for U are not available. A conservative estimate for U is found by treating the interface as a stationary wall and calculating U from the relationship... 

The design of devices to promote cocurrent drop flows for heating or cooling a two-phase system, or for direct-contact heat transfer between two liquids, is difficult. The study by Wilke et al. (W7) is typical of the approach frequently used to analyze these processes. Wilke et al. described the direct-contact heat transfer between Aroclor (a heavy organic liquid) and seawater in a 3-in. pipe. No attempt was made to describe the flow pattern that existed in the system. The interfacial heat-transfer coefficient was defined by... 

The interfacial heat transfer coefficient can be evaluated by using the correlations described by Sideman (S5), and then the dimensionless parameter Ni can be calculated. If the Peclet numbers are assumed to be infinite, Eqs. (30) can be applied to the design of adiabatic cocurrent systems. For nonadiabatic systems, the wall heat flux must also be evaluated. The wall heat flux is described by Eqs. (32) and the wall heat-transfer coefficient can be estimated by Eq. (33) with... 

From this discussion of parameter evaluation, it can be seen that more research must be done on the prediction of the flow patterns in liquid-liquid systems and on the development of methods for calculating the resulting holdups, pressure drop, interfacial area, and drop size. Future heat-transfer studies must be based on an understanding of the fluid mechanics so that more accurate correlations can be formulated for evaluating the interfacial and wall heat-transfer coefficients and the Peclet numbers. Equations (30) should provide a basis for analyzing the heat-transfer processes in Regime IV. 

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

The correlations for the mass and heat transfer coefficients and interfacial also take into account packing or tray geometries for the actual column. The total mass and energy rates are calculated from intergrating the mass and energy fluxes across the total surface area, a.j. 

Power or energy dissipated in the aerated suspension has to be large enough (a) to suspend all solid particles and (b) to disperse the gas phase into small enough bubbles. It is essential to determine the power consumption of the stirrer in agitated slurry reactors, as this quantity is required in the prediction of parameters such as gas holdup, gas-liquid interfacial area, and mass- and heat-transfer coefficients. In the absence of gas bubbling, the power number Po, is defined as... 

In the packed-bed reactor, the molar concentrations and temperature at the exterior of the catalyst particle are coupled to the respective fluid-phase concentrations and temperature through the interfacial fluxes given in Eqs. (3.3-1) and (3.3-2). Overall mass and heat transfer coefficients are often used to describe these interfacial fluxes, similar in structure to Eqs. (3.2-1) and (3.2-2). Complete solution of the packed-bed reactor model... 

In this paper, we now report measurements of heat transfer coefficients for three systems at a variety of compositions near their lower consolute points. The first two, n-pentane--CO2 and n-decane--C02 are supercritical. The third is a liquid--liquid mixture, triethylamine (TEA)--H20, at atmospheric pressure. It seems to be quite analogous and exhibits similar behavior. All measurements were made using an electrically heated, horizontal copper cylinder in free convection. An attempt to interpret the results is given based on a scale analysis. This leads us to the conclusion that no attempt at modeling the observed condensation behavior will be possible without taking into account the possibility of interfacial tension-driven flows. However, other factors, which have so far eluded definition, appear to be involved. 

In Table II, we list the various dimensionless groups defined above and the two criteria for enhancement of the heat transfer coefficient by interfacial tension-driven flow. Calculated values are given for the three mixtures for which we presented experimental data. All values pertain to a temperature difference AT of 10 K. 

Whilst heat transfer in convection can be described by physical quantities such as viscosity, density, thermal conductivity, thermal expansion coefficients and by geometric quantities, in boiling processes additional important variables are those linked with the phase change. These include the enthalpy of vaporization, the boiling point, the density of the vapour and the interfacial tension. In addition to these, the microstructure and the material of the heating surface also play a role. Due to the multiplicity of variables, it is much more difficult to find equations for the calculation of heat transfer coefficients than in other heat transfer problems. An explicit theory is still a long way off because the physical phenomena are too complex and have not been sufficiently researched. 

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