Page 442 - Modelling in Transport Phenomena A Conceptual Approach

422 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

9.13 Two large porous plates are separated by a distance B as shown in the
figure below. The temperatures of the lower and the upper plates are To and TI,
respectively, with TI > To. Air at a temperature of To is blown in the x-direction
with a velocity of V.

B
"t r TO I
,....*.
1 . 2
*
1 il I 1 1 1 I"
Air

a) Show that the inventory rate equation for energy becomes
dT d2T
p CpV - = k -
dx dx2
b) Show that the introduction of the dimensionless variables
T - To
e=-
Tl - To

(3)
pepVB
A= (4)
k
reduces Eq. (1) to
&e de
-- A-=O (5)
ax2 d4
c) Solve Eq. (5) and show that the velocity distribution is given as
e=-
1 - e'€
1-eX
d) Show that the heat flux at the lower plate is given by

9.14 Rework the problem given in Section 9.4.1 for a zeroth-order chemical reac-
tion, i.e., r = k,, and show that the concentration profile is given by