Page 39 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

2.6 Design overview for recuperators 35

For all flow arrangements other than true co-current and countercurrent flow, integration of
differential energy and rate equations
yields a complicated implicit or explicit
expression for DT M . For these flow ar-
rangements, it is customary to consider
Log mean temperature difference correction factor e F T
the heat exchanger as a hypothetical
counterflow unit operating at the same
heat capacity ratio and the same terminal temperatures and then incorporate a correction factor F T in
Eqn. 2.3,where F T is defined as the ratio of the true mean temperature difference for countercurrent
flow to the log mean temperature difference or ratio of the actual heat transfer rate in a given
exchanger to that in a counterflow exchanger having the same UA andfluidterminaltemperatures.
This gives
(2.7)
Q ¼ F T UADT LMTD;counterflow
where
DT M q
(2.8)
F T ¼ ¼
DT LMTD;counterflow UADT LMTD;counterflow
and DT LMTD;counterflow is calculated using Eqn. 2.5a for all exchangers except parallel flow exchangers
where the same is calculated using Eqn. 2.5b. F T is dimensionless and, in general, a function of the
thermal effectiveness (S), heat capacity ratio (R) and flow arrangement. The thermal effectiveness S is
defined as the ratio of the temperature range (rise or drop) of one fluid (irrespective of whether it is a
cold fluid or a hot fluid) and inlet temperature difference of the two fluids. It is thus different for each
fluid of a two-fluid exchanger.
For fluid 1
T 1;out T 1;in DT 1
(2.9a)
S 1 ¼ ¼
T 2;in T 1;in DT max
and for fluid 2
T 2;in T 2;out DT 2
(2.9b)
S 2 ¼ ¼
T 2;in T 1;in DT max
The heat capacity ratio (R) for each fluid is
m 1 C p1 T 2;in T 2;out
R 1 ¼ ¼
m 2 C p2 T 1;out T 1;in
m 2 C p2 T 1;out T 1;in
R 2 ¼ ¼
m 1 C p1 T 2;in T 2;out
Explicit expressions for F T in terms of R and S for 1e2 (TEMA E shell) exchanger (see Chapter 4
for TEMA classification) and cross-flow exchanger with one mixed and one unmixed flow are given in
Table 2.2. Further discussions on calculation of F T from terminal temperatures in case of shell and tube
exchanger are provided in Chapter 4.