Coefficients mass heat transfer

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. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass transfer, and therefore turbulence is often purposely induced by this method. 

Inside diameter of tube Velocity Mass velocity Film coefficient of heat transfer h ... 

Taking the coefficients of heat transfer on the water side as 4.0, and on the steam side as 8.5 kW/m2 K, caleulaic the outlet water temperature and the total mass of steam condensed per second. The latent heat of steam at 372 K is 2250 kJ/kg. The density of water is 1000 kg/nr. 

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 solution containing 23 per cent by mass of sodium phosphate is cooled from 313 to 298 K in a Swenson-Walker crystalliser to form crystals of Na3P04.12H20. The solubility of Na3P04 at 298 K is 15.5 kg/100 kg water, and the required product rate of crystals is 0.063 kg/s. The mean heat capacity of the solution is 3.2 kJ/kg deg K and the heat of crystallisation is 146.5 kJ/kg. If cooling water enters and leaves at 288 and 293 K, respectively, and the overall coefficient of heat transfer is 140 W/m2 deg K, what length of crystalliser is required ... 

The film (individual) coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. A few different driving potentials are used today to define the film coefficients of mass transfer. Some investigators use the mole fraction or molar ratio, but often the concentration difference AC (kg or kmol m ) is used to define the liquid phase coefficient (m while the partial pressure difference A/i (atm) is used to define the gas film coefficient (kmolh m 2 atm ). However, using and A gp of different dimensions is not very convenient. In this book, except for Chapter 15, we shall use the gas phase coefficient (m h" ) and the liquid phase coefficient ki (m h ), both of which are based on the molar concentration difference AC (kmol m ). With such practice, the mass transfer coefficients for both phases have the same simple dimension (L T" ). Conversion between k and is easy, as can be seen from Example 2.4. 

As mentioned in Chapter 2, close analogies exist between the film coefficients of heat transfer and those of mass transfer. Indeed, the same type of dimensionless equations can often be used to correlate the film coefficients of heat and mass transfer. 

A condenser consists of 30 rows of parallel pipes of outer diameter 230 mm and thickness 1.3 mm with 40 pipes, each 2 m long in each row. Water, at an inlet temperature of 283 K, flows through the pipes at 1 m/s and steam at 372 K condenses on the outside of the pipes. There is a layer of scale 0.25 mm thick of thermal conductivity 2.1 W/m K on the inside of the pipes. Taking the coefficients of heat transfer on the water side as 4.0 and on the steam side as 8.5 kW/m2 K, calculate the water outlet temperature and the total mass flow of steam condensed. The latent heat of steam at 372 K is 2250 kJ/kg. The density of water is 1000 kg/m3. 

Heat and mass transfer are taking place simultaneously to a surface under conditions where the Reynolds analogy between momentum, heat and mass transfer may be applied. The mass transfer is of a single component at a high concentration in a binary mixture, the other component of which undergoes no net transfer. Using the Reynolds analogy, obtain a relation between the coefficients for heat transfer and for mass transfer. 

The solution to this problem is presented in Sections 12.8.1 and 12.8.2 and the relation between the coefficients for heat transfer and mass transfer is ... 

Coefficient of heat transfer Diffusion coefficient Flux of a quantity x Heat flow rate Kinematic viscosity Mass flow rate Mass-transfer coefficient Thermal conductivity Thermal diffusion coefficient Thermal diffusivity Viscosity Volume flow rate... 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

Gs = shell-side mass velocity across tubes based on the minimum free area between baffles across the shell axis, lb/(hXft2) h = film coefficient of heat transfer, Btu/(hXft2X°F) subscript c indicates convection subscript d represents dirt or fouling subscript co indicates conduction... 

Determine the overall heat-transfer coefficient The heat-transfer coefficient on the tube side is proportional to G0 8. The mass velocity G will be doubled because the exchanger is to be converted to two passes on the tube side. Therefore, = 178.6(2)0 8 = 310.9 Btu/(h)(ft2)(°F) [1764 W/(m2)(K)]. The new overall heat-transfer coefficient can now be calculated ... 

Nomenclature (Use consistent units.) A = heat-transfer surface C,c = specific heats of hot and cold fluids respectively Lq = How rate of liquid added to tank M = mass of fluid in tank T, t = temperature of hot and cold fluids respectively Ti, ti = temperatures at beginning of heating or cooling period or at inlet T, h = temperature at end of period or at outlet To, to = temperature of liquid added to tank U = coefficient of heat transfer and W,w = flow rate through external exchanger of hot and cold fluids respectively. 

The treatment is divided into four sections. Section II deals with estimation of coefficients of heat transfer and of mass transfer. Because most, or all, of the latent heat of evaporation of the moisture is normally derived from the sensible heat of the carrier gas, our knowledge of the pertinent coefficients of heat transfer from the gas to the surface of the drying solid is summarized. A summary of the analogous mass-transfer coefficients records in condensed form gives our current knowledge of the means of estimating the rate of transport from the solid to the gas of the vapor evolved. 

FLUIDS FLOWING NORMALLY TO A SINGLE TUBE. The variables affecting the coefficient of heat transfer to a fluid in forced convection outside a tube are D , the outside diameter of the tube Cp, /r, and k, the specific heat at constant pressure, the viscosity, and the thermal conductivity, respectively, of the fluid and G, the mass velocity of the fluid approaching the tube, Dimensional analysis gives, then, an equation of the type of Eq, (12,27) ... 

At larger temperature drops, lying between 5 and 25°C (9 and 45°F) in the case shown in Fig. 13.5, the rate of bubble production is large enough for the stream of bubbles moving up through the liquid to increase the velocity of the circulation currents in the mass of liquid, and the coefficient of heat transfer becomes greater than that in undisturbed natural convection. As A F is increased, the rate of bubble formation increases and the coefficient increases rapidly. 

Hohne (145) pointed out that the function principle of DSC can give rise to calibration errors in case of phase transitions disturbing the steady-state conditions. The cause of this problem is the temperature dependence of the coefficients of heat transfer, leading to weak nonlinearity of the calorimeter. This results in a dependence of the calibration factor on parameters such as mass and thermal conductivity of the sample, heating rate, peak shape, and temperature. By theoretical considerations and calculations, the uncertainty of the calibration factor due to the variation of sample parameters can be 1-5%, depending on the temperature and the instrument involved. 

The Sieder and Tate relation involving coefficient of heat transfer, mass velocity, physical properties of a fluid and inside tube diameter is shown in Figure 2-25 in terms of dimensionless groups with Reynolds number as abscissa. It will be seen from Figure 2-25 that there are three distinct zones of flow. The first is the streamline region for values of Reynolds number of 2,100 and less. The series of parallel lines is expressed by the equation shown in Figure 2-25. 

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