Mass convection analogy between coefficients

Rai (Rl) has presented experimental data for convective mass transfer from flat and cylindrical surfaces in axisyimnetric flow. Based on the analogy between mass- and heat-transfer processes, Rai s experimental values may be employed in estimating heat-transfer coefficients. 

We start this chapter with a general physical description of the convection mechanism. We then discuss (he velocity and thermal botmdary layers, and laminar and turbitlent flows. Wc continue with the discussion of the dimensionless Reynolds, Prandtl, and Nusselt nuinbers, and their physical significance. Next we derive the convection equations on the basis of mass, momentiim, and energy conservation, and obtain solutions for flow over a flat plate. We then nondimeiisionalizc Ihc convection equations, and obtain functional foiinis of friction and convection coefficients. Finally, we present analogies between momentum and heat transfer. 

Because of the analogy between simulated and true counter-current flow, TMB models are also used to design SMB processes. As an example, the transport dispersive model for batch columns can be extended to a TM B model by adding an adsorbent volume flow Vad (Fig. 6.38), which results in a convection term in the mass balance with the velocity uads. Dispersion in the adsorbent phase is neglected because the goal here is to describe a fictitious process and transfer the results to SMB operation. For the same reason, the mass transfer coefficient feeff as well as the fluid dispersion Dax are set equal to values that are valid for fixed beds. 

Ernst Schmidt (1892—1975), the German scientist, is known for his pioneering works in the fields of thermodynamics and heat and mass transfer. Some of his noteworthy contributions to heat and mass transfer were developing the analogy between heat and mass transfer, first measurement of velocity and temperature fields in natural convection boundary layer and heat transfer coefficient in droplet condensation, introduction of aluminum foil radiation shielding, and solution of... 

Cairncross et al. (1995). Parrouffe (1992) has demonstrated on the basis of extensive experimental data that one may, within engineering accuracy, use analogy between heat and mass nans-fer to estimate the convective heat or mass transfer coefficients even in the presence of intense radiative heat flux on the evaporating surface. Appropriate corrections must be employed, however, for the high evaporative mass flux at the surface. 

The heat-transfer coefficient for convection around a sphere is well established, and by invoking the analogy between convective heat and mass transfer, the following mass-transfer coefficient is obtained [60] ... 

Ernst Schmidt (1892-1975) a German scientist in the field of heat and mass transfer who measured the radiation properties of solids and developed the use of aluminum foils as radiation shields. He was the first to measure velocity and temperature fields in free convection boundary layers and discovered the large heat transfer coefficients occurring in condensation. A paper on the analogy between heat and mass transfer caused the dimensionless quantity involved to be called the Sc number. 

Jaturonglumlert and Kiatsiriroat (2010) considered heat and mass transfer for the combined convective and FIR drying of fruit leather, and found that the ratio between the heat and mass transfer coefficients for the combination technique could not be obtained from the heat-mass transfer analogy. Hence, modified correlations for predicting the ratio of heat and mass transfer coefficients in term of the heat transfer Nusselt number were developed. 

In this section the analogy between heat and mass transfer is introduced and used to solve problems. The specific estimation relationships for permeants in polymers are discussed in Section 4.2 with the emphasis placed on gas-polymer systems. This section provides the necessary formulas for a first approximation of the diffusivity, solubility, and permeability, and their dependence on temperature. Non-Fickian transport, which is frequently present in high activity permeants in glassy polymers, is introduced in Section 4.3. Convective mass transfer coefficients are discussed in Section 4.4, and the analogies between mass and heat transfer are used to solve problems involving convective mass transfer. Finally, in Section 4.5 the solution to Design Problem III is presented. 

To model convection drying both the heat transfer to the coated web and the mass transfer (qv) from the coatiag must be considered. The heat-transfer coefficient can be taken as proportional to the 0.78 power of the air velocity or to the 0.39 power of the pressure difference between the air in the plenum and the ambient pressure at the coatiag. The improvement in heat-transfer coefficients in dryers since the 1900s is shown in Figure 20. The mass-transfer coefficient for solvent to the air stream is proportional to the heat-transfer coefficient and is related to it by the Clulton-Colbum analogy... 

Heat transfer between a fluid and pellet in a fixed bed occurs by the same combination of molecular and convective processes as describe mass transfer.t The experimental data for heat-transfer coefficients can be correlated by an expression analogous to Eq. (10-10). Thus the heat-transfer correlation is... 

In Equations (26.78a,b), the subscripts F and N refer to forced and natural convection stirring. In Equations (26.79a-d), L is a characteristic electtode dimension, D is the diffusion coefficient, v is velocity, g is the gravity acceleration constant, p is viscosity, is bulk solution density, and Ap is the difference in density between the bulk solution and the solution at the electrode surface. Once a Sh or expression has been found/generated, it is combined with Equation (26.70) (or the analogous equation for a supporting electrolyte system) to obtain an / relationship. Examples of mass transfer correlations follow. 

Heat and mass transfer are analogous processes. Molecular diffusion in homogeneous materials or phases is similar to heat transfer. Convective diffusion or convection in homogeneous materials or phases corresponds to heat transfer by convection. Mass transfer at the phase boundary corresponds to heat conduction. Mass transfer between phases occurs like heat transfer in several chronological steps. The slowest step controls the rate of the entire process. Thus the mathematical descriptions of heat and mass transfer operations are analogous. Calculation methods and approaches to calculate the heat transfer coefficients may similarly be used to calculate mass transfer coefficients. (See Table 1-18 in Chapter 1.7.2 for the analogy of heat and mass transfer.)... 

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