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In engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration change as driving force: [1] = ˙ Where: is the mass transfer coefficient [mol/(s·m 2)/(mol/m 3)], or m/s
turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients) Damkohler number: Da = chemistry (reaction time scales vs. residence time) Darcy friction factor: C f or f D: fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor) Dean number: D
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 higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm 2 /s, and in water its diffusion coefficient is 0.0016 mm 2 /s. [1] [2]
Where q” is the heat flux, is the thermal conductivity, is the heat transfer coefficient, and the subscripts and compare the surface and bulk values respectively. For mass transfer at an interface, we can equate Fick's law with Newton's law for convection, yielding:
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 ...
Here, is the diffusion coefficient matrix, () is the thermal diffusion coefficient, is the body force per unit mass acting on the ith species, = / is the partial pressure fraction of the ith species (and is the partial pressure), = / is the mass fraction of the ith species, and = =
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 ...