Page 38 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

34 Chapter 2 Heat transfer processes in industrial scale

For a counterflow exchanger,
DT 1 ¼ T h;in T c;out ; DT 2 ¼ T h;out T c;in (2.5a)
and for a parallel flow exchanger,

DT 1 ¼ T h;in T c;in ; DT 2 ¼ T h;out T c;out (2.5b)
Eqn. 2.4 is applicable for sensible heat transfer when the heat capacities of both streams are
substantially independent of temperature over the range of the process and there is no phase change. It
is also applicable in case of phase chnage at constant pressure for either or both streams containing a
single component.
A few important points:
(i) When both fluids change phase and are pure components (not mixture),

DT 1 ¼ DT 2 ; and DT LMTD ¼ DT 1 ¼ DT 2

DT 1
2, DT LMTD can be substituted by arithmetic mean temperature difference
(ii) For 1
DT 2
!
DT 1 þ DT 2
DT AMTD ¼ with less than 4% error.
2
DT LMTD is lower than the arithmetic mean DT AMTD and both have the same value in the limiting
case of (i).
(iii) DT LMTD ¼ 0 for DT 1 ¼ 0or DT 2 ¼ 0.
(iv) A quick check of the thermodynamic feasibility of the process can be made by ensuring 2T h;out

T c;in þT c;out for hot fluid on the shell side and 2T c;out T h;in þT h;out for cold fluid on the
shell side. This eliminates the possibility of a temperature cross, i.e., the cold fluid outlet
temperature being higher than the hot stream outlet. If these limits are approached, it is
necessary to use multiple 1e2n shells in series.
(iv) If physical properties and overall heat transfer coefficient (U) vary and/or fluid temperature
profile is not smooth along the tube length, a simple and conservative practice is to evaluate the
heat transfer coefficients at the stream inlet and outlet temperatures and use the lower of the two
values. Alternatively, Eqns. (2.1) and (2.3) can be combined to give

A½U 2 DT 2 U 1 DT 1 Š
(2.6a)

Q ¼
U 2 DT 2
ln
U 1 DT 1
If the variation in physical property over the temperature range is too large, the entire heat ex-
change length is divided into a number of small lengths ðDzÞ and the basic heat transfer equation(s) are
applied to each length element. The results are then summed up, viz.
X X
U j A j DT LMTD;j (2.6b)
Q ¼ Q j ¼
where j refers to the jth element and DT LMTD;j is the log mean temperature difference in the jth
element.