Page 74 - Modelling in Transport Phenomena A Conceptual Approach

3.4. DIMENSIONLESS NUMBERS 55

Table 3.1 Transfer coefficient, diffusivity and flux ratio for the transport of
momentum, energy and mass.

Interphase Flux
Process Transfer Coefficient Diffusivity
Molecular Flux
1 P
Momentum 5 f vch -
P
h
k
Energy - -
P 6P P CP
kcLch
Mass DAB
DAB

The dimensionless terms representing the ratio of the interphase flux to the
molecular flux in Table 3.1 are defined in terms of the dimensionless numbers as

(3.410)
--
h Lch - Nu (3.4-11)
k
kcLch
-- - NUM = Sh (3.412)
DAB
where Nu is the heat transfer Nwselt number and NUM is the mass transfer Nusselt
number. The mass transfer Nusselt number is generally called the Sherwood num-
ber, Sh. Equations (3.410)-(3.412) indicate that the product (f Re/2) is more
closely analogous to the Nusselt and Sherwood numbers than f itself. A summary
of the analogous dimensionless numbers for energy and mass transfer covered so
far is given in Table 3.2.

Table 3.2 Analogous dimensionless numbers in energy and mass transfer.
Energy Mass

hLch
NU= -
k