Page 37 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

2.6 Design overview for recuperators 33

2.6.1 Thermal design
The thermal design is based on the heat balance and the heat transfer rate equation conceptualised
below:
(1) Heat balance equation, one for each of the two fluids, considering negligible heat loss from the
exchanger
For only sensible heat transfer with constant specific heat under isobaric conditions, the heat duty
(Q) can be defined as the heat gained by cold fluid which is equal to the heat lost of the hot fluid

Q ¼ðm c ÞC pc T c;out T c;in ¼ðm h ÞC ph T h;in T h;out (2.1)
In Eqn. 2.1, m is the mass flow rate of streams and C p is the specific heat capacity. Subscripts c and
h indicate the parameters related to cold and hot fluid and subscripts ‘in’ and ‘out’ refer to the inlet and
outlet condition of each fluid. The heat capacities are measured at average temperature (T av ) for any
fluid where
T av ¼ð T in þ T out Þ=2 (2.2)
In case of phase change, the heat load calculation should be based on enthalpy change/latent heat.
Also the exchanger may be considered as consisting of length sections where phase change and no
phase change occur.
(2) Rate equation which reflects a convectioneconduction heat transfer phenomenon in a two-fluid
heat exchanger and shows that the heat transfer rate across a surface is proportional to the heat
transfer area ðAÞ and mean temperature difference ðDT M Þ between the fluids.
(2.3)
Q ¼ UADT M
The overall heat transfer coefficient (U) is the coefficient of proportionality in Eqn. 2.3.
In a design problem, the prime objective is to estimate A (or UA) of an exchanger to satisfy the terminal
values of temperature (sizing problem). In sizing problem, in addition to (UA), one of the four terminal
temperatures or one of the two flow rates may also be unknown (details discussed in Chapters 3 and 4).
In the rating calculation, the inlet temperature, the exchanger geometry and size (A) are known and
the outputs are Q, U and the outlet temperatures.
It is clear from Fig. 2.7 that the temperature difference between the hot and cold fluid driving the
heat transfer is not constant and its value is different for
different flow arrangements for the same inlet and outlet
temperatures.
Log mean temperature difference For true co-current and countercurrent flow and linear
temperatureeenthalpy curves (U constant along the
exchanger) when DT 1 and DT 2 are the temperature difference
at the two ends of the exchanger, the log mean temperature
difference ðDT LMTD Þ is given by
ð DT 2 DT 1 Þ
(2.4)
DT LMTD ¼
DT 2
ln
DT 1