MASS TRANSFER CLASS NOTES FOR ENGINEERING
MASS TRANSFER CLASS
NOTES FOR ENGINEERING
Before discussing convective mass
transfer, it is necessary to compare
convective heat transfer and convective
mass transfer since there is a similarity
between these two. In heat transfer,
there is convective heat transfer
coefficient ‘ h’. Similarly there is mass
transfer coefficient in mass transfer.
Prandtl number (Pr = ν / α) is replaced
by Schmidt number (Sc = ν / DAB) and
the Nusselt number (Nu = hL/kf) is
replaced by Sherwood number
(Sh = kc L / DAB) and T_{f} is mean film
temperature. Mass transfer may occur in a gas mixture.
Further mass transfer may occur in a liquid
solution. Also, mass transfer may occur in a
solid. The basic mechanisms of mass
transfer are the same whether the phase is
a gas, or a liquid, or a solid. Driving force
for mass transfer is concentration gradient
of species. Mass transfer due to
concentration gradient is diffusion which is
very analogous to heat transfer by
conduction.
Table: Mass transfer coefficients in Forced Convection Mass Transfer
Sr.No. 
Empiricalequation 
Object 
Type offlow 
local oraveragetemp 
Range ofdimensionless number 
1. 
Sh_{x}= 0.332 Re_{x}^{1/2} Sc ^{1/3} 
Flat plate 
Laminar 
Local 
0.6≤Sc ≤50 
2. 
Sh_{av}= 0.664 Re_{x}^{1/2} Sc ^{1/3} 
Flat plate 
Laminar 
Average 
0.6 ≤Sc ≤50 
3. 
Sh= 0.0296 Re_{x}^{4/5} Sc ^{1/3} 
Flat plate 
Turbulent 
local 
Re_{x}≤105, 0.6 ≤Sc ≤50 
4. 
Sh= (0.037 Re_{x}^{4/5} −871) Sc ^{1/3} 
Flat plate 
Transition 
Local 
5×10^{5}< Re_{x} ≤10^{7}, 0.6≤Sc ≤50 
5. 
Sh = 0.3+ [0.62Re_{D}^{1/2}Sc^{1/3} ×[1 + (0.4/Sc)^{2/3}]^{1/4}] ×[1 + (Re_{D}/282,000)^{5/8}]^{4/5} 
Cylinder 
Cross flow 
Average 
Re_{D }Sc > 0.2 
6. 
Sh= 2 + (0.4 Re_{D}^{1/2}+ 0.060 Re_{D}^{2/3}) Sc^{0.4} ×(μ/μ_{s})^{1/2} 
Sphere 
Cross flow 
Average 
3.5 < Re_{D}< 7.6×10^{4},0.71 < Sc < 380 and 1.0 < (μ/μs) < 3.2 
For an ideal gas
p_{A}V =n_{A} RT
C_{A}=n_{A} / V Normally in gases, there is equimolar counter diffusion which gives J*_{AZ} = — D_{AB} dC_{A}/dz = — J*_{BZ} = –(–) D_{BA} dC_{B}/dz = D_{BA} dC_{B}/dz D_{AB} = D_{BA} For a binary gas mixture of A and B, the diffusivity coefficient D_{AB}=D_{BA} in counter molar diffusion of gases. Other parameters of equimolar counter diffusion are J*_{AZ} = — J*_{BZ} or J* is constant in a steady state dc_{A} = –dC_{B} C= C_{A} + C_{B} D_{AB} = D_{BA}
Mass transfer Coefficients
These empirical correlations are valid for low mass transfer rate (or equimolar mass transfer) where the mole fraction of species ‘A’ is less than about 0.05. For higher mass transfer rate, corrected mass transfer coefficients, using the log mean concentration difference, must be used. Hence k_{c} is replaced by k_{c}/(1 − y_{A})lm
Where lm is logarithmic mean and is given by
(1 − y_{A})lm = [(1–y_{A}) –(1–y_{Ai})] /[ ln((1–y_{A}) / (1–y_{Ai}))] y_{A} is gas mole fraction of species A = p_{A} / p_{t} y_{Ai} is gas mole fraction of species A at the interface = p_{Ai} / p_{t} p_{A} is the partial pressure of species A p_{Ai} is the partial pressure of species A at the interface
Mass transfer coefficients at Macro level
When a fluid flowing outside a solid surface in forced convection motion, rate of convective molar flux is given by:
N_{A} = k_{c} (c_{L1}— c_{Li})
N_{A}=molar flux of species A = kmol/s m^{2} k_{c} = mass transfer coefficient (m/s) c_{L1} = bulk fluid concentration, kmol/m^{3} c_{Li} = concentration of fluid near the solid surface, k mol/m^{3} k_{c} depends on the following factors: 1. System geometry—pipe or flat plate or channel 2. Flow velocity—laminar, transition or turbulent flow 3. Fluid properties—density, viscosity, specific heat etc. From the empirical equation of Sherwood number applicable, first mass transfer coefficient is calculated. Only then, mass flux can be known. These calculations are very similar to convective heat transfer calculations i.e.
Convective heat flux = h Δt
Where h is the convective heat transfer coefficient
Δt is the temperature difference
MASS TRANSFER
Four terms frequently used in mass transfer

Molar concentration or Mole concentration or 3.5 < ReD< 7.6×104,
0.71 < Sc < 380
1.0 < (μ/μs) < 3.2
or volume concentration, ’ C_{A}’
ii. Mass concentration, ‘ ρ_{A’}
iii. Mole fraction ‘ x_{A’}
iv. Mass fraction ‘m_{A}*’
Definition of Mole concentration’ C_{A}’ of Species A in a mixture
Number of molecules of species A present per unit volume of the mixture (atoms/m^{3} or molecules/m^{3} or moles/m^{3 }or kmol/m^{3})
Definition of mass concentration, ‘ρ_{A}’_{,} of Species A in a mixture
Mass concentration of species A = Mass of species A per unit volume of the mixture ( kg of species A / m^{3} mixture)
Definition of Mole fraction’ x_{A}’ of Species A in a mixture
It is a ratio of molar concentration of A to the total molar concentration
x_{A } = C_{A}/C = C_{A}/(C_{A} + C_{B})
It has no units.
Definition of mass fraction ‘m_{A}*’ of Species A in a mixture
It is a ratio of mass concentration of A to the total mass concentration
m_{A}* = ρ_{A}/( ρ_{A}+ ρ_{B})
It has no unit.
Diffusion
It is the movement of particles in a medium from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance.
Diffusion in gases >> diffusion in liquids>>diffusion in solids.
Types of Diffusion
(a) Concentration diffusion: Concentration diffusion is due to concentration gradient. Fick’s law gives a linear relation between the rate of diffusion of chemical species and the concentration gradient of that species. (b) Thermal diffusion: Diffusion due to a temperature gradient. Usually negligible unless the temperature gradient is very large. (c) Pressure diffusion: Diffusion due to a pressure gradient. Usually negligible unless the pressure gradient is very large.
Diffusion in solids Knudsen diffusion: Diffusion phenomena in porous solids is called Knudsen diffusion.
Cause Of Diffusion Concentration difference—Whenever there is concentration difference in a medium, there is mass transfer by natural flow from the high concentration to the low concentration region.
Practical Examples Of Mass Transfer (Diffusion)
1. There is a tank which is divided into two equal parts by a partition. Initially, the left half of the tank contains oxygen O2 gas while the right half contains N2 gas at the same temperature and pressure. As soon as the partition is removed, the O2 molecules will start diffusing into the N2 while the N2 molecules will diffuse into O2. Over the passage of time, there will have a homogeneous mixture of N2 and O2 in the tank. It is mass transfer due to concentration gradients either way.
2. A drop of red liquid dye when added to a cup of water, the dye molecules will diffuse slowly by molecular diffusion in all directions in the remaining water till a homogeneous color is established. 3. Water evaporates from an open pan into air because of the difference in concentration of water vapor at the water surface and the surrounding air. 4. Evaporation of water from an open tray 5. Mass transfer is there in any open thermodynamic system i.e. suction, compression and discharge by a compressor is mass transfer.
6. Mass transfer in extraction
7. Mass transfer in distillation
8. Mass transfer in absorption
9. Mass transfer in separation
10. Mass transfer in purification