Page 45 - Modelling in Transport Phenomena A Conceptual Approach

26 CHAPTER 2. MOLECULAR AND CONVECTIVE TRANSPORT

Table 2.1 Analogous terms in constitutive equations for momentum, energy, and
mass (or, mole) transfer in one-dimension.

Momentum Energy Mass Mole

Molecular flux TYX QY jA. J;.
Transport property CL IC DAB DAB
Gradient of driving force

Diffusivity v CY DAB DAB
Quantity/Volume PVX pcPT PA cA

(103)(10-5)
Pr = = 1 for gases
10-2
(103)(10-3)
Pr = = 10 for liquids
10-1
The Schmidt number is defined as the ratio of the momentum to mass difhsivities:
Schmidt number = Sc = - = - (2.2-7)
c1
Y
DAB PDAB
The order of magnitude of the Schmidt number for gases and liquids can be esti-
mated as
10-5
sc = (1)(10-5) = for gases

= lo3 for liquids
sc = ( lo3)(
Finally, the ratio of Q to 'DAB gives the Leu16 number, Le:
Lewis number = Le = - k -- (2.2-8)
Q
SC
-
=
DAB ~CPDAB Pr
2.3 CONVECTIVE TRANSPORT
Convective flux or bulk flux of a quantity is expressed as

( Coygtive Characteristic (2.3-1)
= (Quantity/Volume) velocity