Estimation of Heat- and Mass-Transfer Coefficients

Heat or Mass Transfer on the Surface of Drying Material 

Forced Heat Convection in Laminar Flow of a Fluid Parallel to a Surface 

Pohlhausen (P4) in 1921 presented the direct solutions of the convection equations for the laminar boundary layer on the upstream portion of a flat 

This equation is in good agreement with the result of direct measurements on air by Jakob and Dow (J2). 

Mass transfer j-factors jm can be obtained by replacing the Prandtl number (p/wt) by the Schmidt number (p/Dy), where Dy is the diffusivity of vapor. 

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Maroulis, Z.B., Kiranoudis, C.T., and Marinos-Kouris, D., Simultaneous estimation of heat and mass transfer coefficients in externally controlled drying, / Food Eng., 14(3) 241-255,1991. 

The advantage of using P is that it is approximately constant over normal ranges of temperature and pressure for any given pair of vapor and gas values. This avoids having to estimate values of heat- and mass-transfer coefficients a and ky from uncertain correlations. For the air-water system, considering convective heat transfer alone, P-l.l. In practice, there is an additional contribution from radiation, and P is very close to 1. As a result, the wet-bulb and adiabatic saturation temperatures differ by less than 1°C for the air-water system at near-ambient conditions (0 to 100°C, Y < 0.1 kg/kg) and can be taken as equal for normal calculation purposes. Indeed, t ically the T b measured by a practical psychrometer or at a wetted solid surface is closer to Tjs than to the pure convective value of T b. 

No theory is available for estimating the heat and mass transfer coefficients using basic thermophysical properties. The analogy of heat and mass transfer can be used to obtain mass transfer data from heat transfer data and vice versa. For this purpose, the Chilton-Colburn analogies can be used [129]... 

Estimation of parameters. Model parameters in the selected model are then estimated. If available, some model parameters (e.g. thermodynamic properties, heat- and mass-transfer coefficient, etc.) are taken from literature. This is usually not possible for kinetic parameters. These should be estimated based on data obtained from laboratory expieriments, if possible carried out isothermal ly and not falsified by heat- and mass-transport phenomena. The methods for parameter estimation, also the kinetic parameters in complex organic systems, and for discrimination between models are discussed in more detail in Section 5.4.4. More information on parameter estimation the reader will find in review papers by Kittrell (1970), or Froment and Hosten (1981) or in the book by Froment and Bischoff (1990). 

Because of the very small fluid channels (Re is very small), the flows in microreactor systems are always laminar. Thus, mass and heat transfers occur solely by molecular diffusion and conduction, respectively. However, due to the very small transfer distances, the coefficients of mass and heat transfer are large. Usually, film coefficients of heat and mass transfer can be estimated using Equations 5.9b and 6.26b, respectively. 

Methods of estimating numbers and/or heights of transfer units and mass-transfer coefficients and interfacial areas in packed columns are reviewed by Ponter and Au Yeung (in Handbook of Heat and Mass Transfer, Gulf Pub., 1986), by Wang et al. [Ind, Eng, Chem. Res., 44, 8715 (2005)], and in Sec. 5 of this handbook one such method is illustrated below. 

Correlations to estimate heat and mass transfer coefficients in gas-solid fluidized beds operating in the controversial low Reynolds numbers zone are proposed.The correlations incorporate the influence of particle diameter to bed length and particle diameter to bed diameter ratios and gas flowrate. Also, the experimental data are used to analyse the models proposed by Kato and Wen, and Nelson and Galloway in order to explain the behaviour of fluid bed systems operating at low Reynolds numbers. 

In spite of the amount of research effort directed towards the determination of the fluid to particle heat and mass transfer coefficients in fluidized beds of fine particles,there is a wide spread in the correlations proposed to estimate them. 

Literature correlations to estimate heat and mass transfer coefficients are generally of the form Sh=a Re 0).ln general, they do not take into account the scale factors dp/D and dp/L which should be important, especially in the case of fluidized beds, given the complex hydrodynamics of these systems. 

This overlapping will in fact reduce the available area for heat and mass transfer. During the present work, some boundary layer thicknesses were estimated for the experimental conditions of this work. As a result, the boundary layers only overlap for Reynolds numbers below 0.826. For the case of Reynolds numbers of 1.74 and 3.05 using the particle diameter of 0.035 cm., the boundary layers do not overlap.Table III shows some of the values obtained.Clearly, this effect cannot explain completely the low heat and mass transfer coefficients at low Reynolds numbers. 

It seems clear that a two phase model will be able to predict low values of the heat and mass transfer coefficients as Kunii has done O). The trouble with this approach will be an accurate estimate of the equivalent bubble bed diameter. Thus, improved empirical correlations are still useful for design purposes, when one looks for estimates of gas-solid heat and mass transfer coefficients. 

Ponter, A. B. and Au-Yeung, P. H., Estimating Liquid Film Mass Transfer Coefficients in Randomly Packed Columns, in Handbook of Heat and Mass Transfer, Cheremisinoff, N. P. (Ed.), Gulf Publishing Corp., Houston, TX, Chap. 20, Vol. II, pp. 903-952, 1986. 

Heat transfer coefficients for pneumatic dryers have been reviewed in Ref [6]. The majority of authors examined and use an equation similar to Equations T9.13 and T9.14 of Table 4.9 for spray dryers. For immobile particles, the exponent of the Re number is close to 0.5 and for free-falling particles, it is 0.8. Equation T9.17 of Table 4.9 is proposed. The mass transfer coefficient could be estimated by the analogy Sh = Nu [6]. In extensive reviews [133-135], correlations for estimating heat and mass transfer coefficients in impingement drying under various configurations are discussed. 

These figures can be used to estimate approximately the heat and mass transfer coefficients for various dryers. The simplifications made for the construction of these figures concern the drying air and material conditions. For instance, the air temperature is taken as 80°C, the air humidity as 0.010 kg/kg db, and the particle size as 10 mm (typical drying conditions). For other conditions, the equations of Table 4.9 should be used. 

Despite the small gap size, transverse temperature and concentration gradients may exist in microchannels. These gradients depend on the rates of heat and mass transfer versus the rate of reaction. Da, as discussed above, provides an estimate of transport effects but cannot be used for quantitative modeling. The Nusselt number (Nu) and Sherwood number (Sh) provide the heat and mass transfer coefficients, respectively, between a surface and the bulk gas, in the direction perpendicular to the flow. They are defined as ratios of heat or mass flux at the boundary to the net flux between the bulk and the surface ... 

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