mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
Appendix B, Dimensionless Groups
Dimensionless groups were used extensively herein. The dimensionless groups are used in science and
engineering for correlations, comparisons, and determining transport coefficients based on system
physics. It is useful to think of dimensionless groups as ratios of forces or similar effects (Placeholder1).
A few examples illustrate this:
Reynolds number (Re):
2
v / D inertial forces
Re (58)
2
v / D viscous forces
v 2 / D inertial forces
Fr (59)
g
gravity forces
The author’s experience is based on deriving the dimensionless groups by non-dimensionalizing the
equations of motion, energy, and mass. For heat transfer within a single phase:
T
q k hi
T T
z
2
(60)
To non-dimensionalize, substitute:
Θ T
T
T
2
2
T
(61)
z
(62)
L
Θ
k / L h i
Θ
(63)
Isolating the dimensionless ordinary differential equation reveals the Nusselt number a ratio of heat
transferred by convection to that transferred by conduction:
Nu
hL
k
i
(64)
Similarly for mass transfer m :
m Assumes non-diffusing component B. Both these situations are highly simplified with many assumptions but demonstrate the
ideas.
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