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The same restrictions described in the heat transfer definition are applied to the mass transfer definition. The Sherwood number can be used to find an overall mass transfer coefficient and applied to Fick's law of diffusion to find concentration profiles and mass transfer fluxes.
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction, or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation. Mass transfer is used by different scientific disciplines for different processes ...
Some of the most common examples of transport analysis in engineering are seen in the fields of process, chemical, biological, [1] and mechanical engineering, but the subject is a fundamental component of the curriculum in all disciplines involved in any way with fluid mechanics, heat transfer, and mass transfer.
Quantifying mass transfer allows for design and manufacture of separation process equipment that can meet specified requirements, estimate what will happen in real life situations (chemical spill), etc. Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of ...
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate (convection + diffusion) to the rate of diffusive mass transport, [1] and is named in honor of Thomas Kilgore Sherwood. It is defined as follows
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
D is the mass diffusivity (m 2 /s). μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/m·s) ρ is the density of the fluid (kg/m 3) Pe is the Peclet Number; Re is the Reynolds Number. The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is the Lewis number ...
There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems. In the case of mass transfer, natural convection is caused by concentration gradients rather than temperature gradients. [2] = (,,) where
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