Page 48 - Modelling in Transport Phenomena A Conceptual Approach
P. 48
2.4. TOTAL FLUX 29
The general flux expressions for momentum, energy and mass transport in dif-
ferent coordinate systems are given in Appendix C.
From Eq. (2.42), the ratio of the convective flux to the molecular flux is given
bY
Convective flux (Quantity/Volume) (Characteristic velocity)
-
Molecular flux - (Diffusivity) (Gradient of Quantity/Volume) (2.43)
Since the gradient of a quantity represents the variation of that particular quantity
over a characteristic length, the “Gradient of Quantity/Volume” can be expressed
as
Difference in Quantity/Volume
Gradient of Quantity/Volume = (2.4-4)
Characteristic length
The use of Eq. (2.44) in Eq. (2.43) gives
Convective flux - (Characteristic velocity)(Characteristic length) (2.45)
-
Molecular flux Diffusivity
The ratio of the convective flux to the molecular flux is known as the Peclet number,
Pe. Therefore, Peclet numbers for heat and mass transfers are
(2.46)
PeM = - (2.47)
VchLch
DAB
Hence, the total flux of any quantity is given by
Molecular flux Pe << 1
Molecular flux + Convective flux Pe N 1 (2.48)
Convective flux Pe >> 1
2.4.1 Rate of Mass Entering and/or Leaving the System
The mass flow rate of species i entering and/or leaving the system, mi, is expressed
as
Gradient of
-
Mass of i/Volume
L Molecular mass flux of species i
1
+ ,( Volume ) ( Characteristic ) I ( Flow ) (2,49)
Mass of i
area
velocity
/
7- J
Convectivemass flux of specie=
In general, the mass of species i may enter and/or leave the system by two means:
