Page 521 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.6 MuRiple Steady States 491
into Equation (8-64) give$

( - rA V)(-A.HRx) = FAOC,o (T - To) + UA( T - Tu) (8-65)

where

By letting

and

(8-66)

Equation (8-65) may be simplified to

The left-hand side is referred to as the heat-generated term:
G(T) = heat- (8-68)
generated term G( T) = ( -AH$)( - rAV/FAo)

The right-hand side of Equation (8-67) is referred to as the heat-removed term
(by flow and heat exchange) R(T):

Heat-removed term R(T) = Cpo (1 + K)( T - Tc) (8-69)

8.6.1 He,at-Removed Term, R( T)

From Equation (8-69) we see that R(T) increases linearly with tempera-
ture, with slope Cp0 (1 + K ). As the entering temperature To is increased, the line
retains the same slope but shifts to the right as shown in Figure 8- 18.
If one increases K by either decreasing the molar flow rate FA* or incireas-
ing the: heat-exchange area, the slope increases and the ordinate intercept moves
to the lleft as shown in Figure 8- 19, for conditions of T, < To :
K=O Tc=To

K=CC Tc = T,
If Tu > To, the intercept will move to the right as K increases.