Chemical Engineering

Thermal conductivity is expressed as W/(m·K) in SI units, equivalent to J/(s·m·K). This represents heat flow rate per unit area per unit temperature gradient.

Sherwood number Sh = k_c·L/D_AB represents the ratio of convective mass transfer to diffusive mass transfer, analogous to Nusselt number in heat transfer.

Schmidt number Sc = ν/D_AB = (μ/ρ)/D_AB, representing the ratio of kinematic viscosity to mass diffusivity, analogous to Prandtl number in heat transfer.

In equimolar counter-diffusion, the molar fluxes of the two components are equal in magnitude but opposite in direction, hence N_A = -N_B.

The distribution coefficient K_D = C_solvent/C_aqueous at equilibrium, determining the driving force for extraction and the selectivity of the separation process.

For a spherical particle in creeping flow with negligible convection, the Sherwood number approaches the purely diffusive limit of Sh = 2, independent of Reynolds and Schmidt numbers.

Schmidt number Sc = ν/D_AB where ν is kinematic viscosity and D_AB is mass diffusivity. It represents the relative importance of momentum and mass transport.

The mass transfer coefficient k_c is defined as molar flux per unit concentration difference, having dimensions of velocity (Length/Time), commonly expressed in cm/s or m/s.

Mass transfer coefficient (k) has dimensions of velocity: m/s. It represents the driving force (concentration difference) per unit area per unit time.

Fick's second law: ∂C/∂t = D(∂²C/∂x²), where ∂C/∂t represents the temporal change in concentration.