Convective mass transfer and analogies

Convective mass transfer coefficient

When a fluid flows over a surface from which species A is transferred, the flux is written in the form of Newton's law of cooling:

$$N_A = h_m\,(C_{As}-C_{A\infty})$$

$h_m$ (m/s) is the convective mass transfer coefficient, found from correlations just like $h$.

Dimensionless numbers

Analogy between momentum, heat and mass transfer

Because all three processes are carried by the same molecular and eddy motion in the boundary layer, their equations are similar. Reynolds analogy (for $Pr = Sc = 1$): $\dfrac{f}{2}=St=St_m$. For other fluids the Chilton-Colburn analogy applies ($0.6 < Pr < 60$, $0.6 < Sc < 3000$):

$$j_H = St\,Pr^{2/3}= \frac{f}{2}= j_M = St_m\,Sc^{2/3}$$

Hence, if $h$ is known, $h_m$ follows from

$$\frac{h}{h_m} = \rho c_p\,Le^{2/3}$$

Mass transfer can thus be predicted from heat transfer results by replacing $Nu \to Sh$ and $Pr \to Sc$.

Correlations

• Laminar flow over a flat plate: $Sh_L = 0.664\,Re_L^{1/2}\,Sc^{1/3}$.
• Turbulent flow in tubes (Gilliland-Sherwood): $Sh = 0.023\,Re^{0.83}\,Sc^{0.44}$. The Linton-Sherwood form $Sh = 0.023\,Re^{0.83}\,Sc^{1/3}$ is also used.
• Flow past a sphere (Frossling): $Sh = 2 + 0.552\,Re^{1/2}Sc^{1/3}$.