Analogy With Heat Transfer

Chilton and Colburn (1934), based on experimental data, defined the j-factor for mass transfer and established the analogy with heat transfer ... 

Thus far, we have considered mass-transfer correlations developed from analogies with heat transfer. In this section, we present a few of the correlations developed directly from experimental mass-transfer data in the literature. Others more appropriate to particular types of mass-transfer equipment will be introduced as needed. 

Calculating higher-order terms in L6v que s series for finite Graetz number when Da -> 0 or Da - 00 (analogy with heat transfer)... 

By analogy with heat transfer, the mass transfer is controlled either by diffusion through the solid or by convection through the solid-fluid interface. Following this, diffusion takes place through solids in perfect contact. Finally, the equations for the one-directional mass transfers, are ... 

Pcm is evaluated in analogy with heat transfer through the bed, since the same molecular mechanism is used for the transport due to the highly turbulent flow and the parabolic temperature profile. 

The mass transfer situation involving flow over a solid sphere was obtained by analogy with heat transfer (8, 9) ... 

Fig. 9.4-1. The Graetz-Nusselt problem. In this case, a pure solvent flowing laminarly in a cylindrical tube suddenly enters a section where the tube s walls are dissolving. The problem is to calculate the wall s dissolution rate and hence the mass transfer coefficient. The problem s solutions, based on analogies with heat transfer, are useful for designing artificial kidneys and blood oxygenators.

Potentiostatic measurements are analogous to heat-transfer experiments in which the wall temperature is controlled, whereas galvanostatic measurements are similar in character to those in which the heat flux is controlled. However, whereas heat transfer may be measured readily with a uniform flux generated at the surface, there is no assurance that a known current applied to an extended electrode will yield a uniform current distribution over the surface, unless the surface is divided into electrically insulated segments and identical current densities are imposed externally on these... 

Electrochemical and non-electrochemical mass transfer phenomena can be correlated using analogies to heat transfer systems for both natural and forced flow convection, with reasonable success. 

Models Based on a Desorption-Dissolution-Diffusion Mechanism in a Porous Sphere. The precursor of these models was the application by Bartle et. al [20] of the Pick s law of diflusion (or the heat conduction equation, i.e. the Fourier equation) to SFE of spherical particles. In doing so they had to assume an initial uniform distribution of the material extracted (in this specific case 1-8 cineole) from rosemary particles. Since Pick s law of difiusion from a sphere is analogous to a cooling hot ball (Crank [21] vs Carslaw and Jaeger [22]), this type of models have been considered to be analogous to heat transfer. This model was also used by Reverchon and his co-workers [23] and [24] to SFE of basil, rosemary and marjoram with some degree of success. 

Steady-state heat transfer Unsteady-state heat transfer Convective heat transfer (heat transfer coefficient) Convective heat transfer (heat transfer coefficient) Radiative heat transfer (not analogous with other transfer processes) Steady-state molecular diffusion Unsteady-state molecular diffusion Convective mass transfer (mass transfer coefficients) Equilibrium staged operations (convective mass transfer using departure from equilibrium as a driving force) Mechanical separations (not analogous with other transfer processes) ... 

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