Page 468 - Elements of Chemical Reaction Engineering Ebook

Sec. 0.2 The Energy Balance 439

rate of1 [ rate of 1
Energy balance on heattransfer = (8-35)
heat exchanger from exchanger
L to reactor 1

where Cpc is the heat capacity of the coolant fluid and TR is the reference
temperature. Simplifying gives us

Solving Equation (8-37) for the exit temperature of the coolant fluid yields
[;E) (8-38)
T,, = T-(T-T,,)exp -

From Equation (8-37)

Substituting for Ta2 in Equation (8-39), we obtain

(8-40)

For large values of the coolant flow rate, the exponent can be expanded
in a Taylor series where second-order terms are neglected in order to give

Heat transfer to a (8-41)
CSTR

Then
1 Q= UA(T,-T) 1 (8-42)

where TuI = TO2 = Tu.

fibular Reactors (PFR/PBR). When the heat flow vanes along the length
of the reactor, such as would be the case in a tubular flow reactor, we must
integrate the heat flux equation along the length of the reactor to obtain the
total heat added to the reactor,

A
Q = 1 U( T, - T) dA = (8-43)