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Mass transfer is the net movement of mass from one location (usually meaning stream, ... Mass transfer finds extensive application in chemical engineering problems ...
The heat and mass analogy allows solutions for mass transfer problems to be obtained from known solutions to heat transfer problems. Its arises from similar non-dimensional governing equations between heat and mass transfer.
mass transfer (advection–diffusion problems; total momentum transfer to diffusive mass transfer) Prandtl number: Pr = = heat transfer (ratio of viscous diffusion rate over thermal diffusion rate) Pressure coefficient: C P
The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy, Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
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
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
It is related to the turbulent Prandtl number, which is concerned with turbulent heat transfer rather than turbulent mass transfer. It is useful for solving the mass transfer problem of turbulent boundary layer flows. The simplest model for Sct is the Reynolds analogy, which yields a turbulent Schmidt number of 1.
is the Fourier number for mass transport; is the mass diffusivity (m 2 /s) is the time (s) is the length scale of interest (m) The mass-transfer Fourier number can be applied to the study of certain time-dependent mass diffusion problems.