Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 41

vp
vs þ

v v 2 u

v 2 u
vq 2

y vu

w
r

vu
vq þ

u ð y sin q þ w cos q Þ
R

1
r

R 1

r 2

u

vr þ r sin q ¼ vr 2 þ þ R þ r sin q R þ r sin q

(2.92)

sin q vu

1
r

vu
vr þ

1 cos q

r

vu
vq

þ

vr þ R þ r sin q

FIGURE 2.15

Solution of Lorenz's equations for different Rayleigh numbers (Pr ¼ 10 and b ¼ 8/3): (a) Ra/Ra c ¼ 10; (b) Ra/

Ra c ¼ 20; (c) Ra/Ra c ¼ 30; and (d) Ra/Ra c ¼ 40.