Page 199 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 179

takes place in a constant-volume, jacketed CSTR.

a) Show that the conservation equations for chemical species A and energy take
the form

where Tm is a weighted mean temperature defined by

in which (h) is the average heat transfer coefficient, Tc is the cooling fluid temper-
ature, AH is the heat transfer area.
b) Show that the elimination of CA between Eqs. (1) and (2) leads to

c) In terms of the following dimensionless quantities

,g=-
A - A~-E/RT~
na-
+
[Q (CP)~, A~(h)lTm
X=

show that Eq. (4) takes the form

d) To determine the roots of Eq. (5) for given values of and p, it is more
convenient to rearrange Eq. (5) in the form

Examine the behavior of the function in Eq. (6) and conclude that
At least one steady-state solution exists when p 2 0.25,