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32 Computational Modeling in Biomedical Engineering and Medical Physics
convection flux condition. The mathematical model of this mass transfer problem, in nondi-
mensional form is as follows:
1 2
ð ~ uUrÞ~u 52r~p 1 r ~u; rU~u 5 0; ð1:38Þ
Re d
B B 2 B
1
u Ur c 5 r c ; ð1:39Þ
Pe d
where the following definitions are used: ~u 5 U 0 ,P 0 5 ρU , ~ 5 c max 2 c 0 ,Re d 5 U 0 d ,
u
2
c
c 2 c 0
η
0
Pe d 5 U 0 d 5 Re d Sc, and Sc 5 ν is Schmidt number: viscous diffusion rate/molecular
D D
(mass) diffusion rate (Bejan, 1984). Here Re d 5 200 and Pe d 5 {0.08, 8, 80}.
Fig. 1.4 shows the mass transfer process seen through isoconcentration lines (thin,
~
21
black curves) and mass function, M f 5 ~u~c 2 Pe r~c, field lines (thicker black lines).
d
Figure 1.4 Isoconcentration lines and mass function field lines in forced convection mass
transfer in laminar, stationary, incompressible, fully developed channel flow of a Newtonian
fluid: (A) Pe d 5 0.08; (B) Pe d 5 8; and (C) Pe d 5 80.
