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Elementary Mass Transfer
Published in Anthony F. Mills, Heat and Mass Transfer, 2018
which is valid for constant thermal properties and no internal heat generation. We see also that both the mass diffusivity ℐ12 and thermal diffusivity α have the same units [m2/s]. It follows that, when the various assumptions made hold true, the solution of a diffusion problem may be obtained directly from the corresponding heat conduction problem. In the mathematics literature both the heat conduction equation and Fick’s second law of diffusion are usually referred to as the diffusion equation, () ∂ϕ∂t=α∂2ϕ∂z2
Thermophysical and transport fundamentals
Published in S. Mostafa Ghiaasiaan, Convective Heat and Mass Transfer, 2018
For gas mixtures, the binary diffusion coefficients are insensitive to the magnitude of mass fractions (or concentrations). They also increase with temperature and vary inversely with pressure. For the diffusion of inert species in liquids, the mass diffusivity is sensitive to the concentration and increases with temperature.
Mass Transfer
Published in C. Anandharamakrishnan, S. Padma Ishwarya, Essentials and Applications of Food Engineering, 2019
C. Anandharamakrishnan, S. Padma Ishwarya
where JA is the molar flux of A which has units of amount of component diffused per unit area per unit time (kmol/m2 s), dCAdx is the concentration gradient (kmol/m3) in the x-direction (direction of flow), and DAB is the constant of proportionality, known as the binary diffusion coefficient or mass diffusivity of A in B (m2/s). The negative sign is to convert the flow in the direction of reducing concentration gradient into a positive quantity. This is justified as dCAdx is a negative quantity since concentration decreases in the flow direction. The mass diffusivity is a measure of the rate at which a component diffuses through an area in a given medium. The value of the diffusion coefficient for a component depends on the concentration and the medium. Further, the diffusion rate (D) depends directly on temperature and molecular spacing. As a result, diffusion in gases proceeds at a faster rate (5 cm/min) compared to liquids (0.05 cm/min) and solids (10−5 cm/min). In gases, mass diffusivity is inversely proportional to pressure. At low pressure, the concentration of molecules would be low thus leading to fewer collisions between them. A larger number of collisions per unit time hinder the molecular motion. This reduces the mean free path which is the distance traveled by a molecule in the gaseous phase between two subsequent collisions. On the other hand, diffusivity in liquids is inversely proportional to the concentration and viscosity of the solution. Also, from Eq. 6.1, the higher the mass diffusivity, the greater the mass transfer flux.
Computation of reactive thermosolutal micropolar nanofluid Sakiadis convection flow with gold/silver metallic nanoparticles
Published in Waves in Random and Complex Media, 2022
MD. Shamshuddin, M. Ferdows, O. Anwar Bég, Tasveer A. Bég, H. J. Leonard
Figure 16 visualizes the variation in nanoparticle concentration profiles for various Schmidt numbers variation and for gold, silver and copper-water micropolar nanofluids. No tangible modification in concentration values is computed for the different metallic nanoparticles. With increasing Schmidt number however, there is a substantial depletion in nanoparticle concentration and concentration boundary layer thickness is also reduced. This key parameter in convective mass transfer parameter symbolizes the ratio of the momentum to the mass diffusivity. It measures the relative effectiveness of momentum and mass transport by diffusion in the hydrodynamic (velocity) and concentration (nanoparticle species) boundary layers. corresponds to both momentum and species boundary layer thicknesses being the same. In the present investigation we consider , for species diffusivity exceeds momentum diffusivity and this range is appropriate for aqueous polymers. For momentum diffusion rate exceeds the species molecular diffusion rate. Mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Schmidt number therefore allows engineers an insight into the selection of different molecular diffusivities corresponding to different nanoparticles in nanofluid suspensions. Larger Schmidt numbers leads to a thinning in the concentration boundary layer. With thinner concentration boundary layers, the concentration gradients will be enhanced causing a decrease in concentration of species in the boundary layer. The implication for engineering designers is that in such a regime, a diffusing nanoparticle species with a lower Schmidt number is more amenable to achieving enhanced nanoparticle concentration distributions.