Page 43 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

2.6 Design overview for recuperators 39

where E f is a function of fin dimensions e t f ; W f ; h f denoting the thickness, width and height of fin
and k f is the thermal conductivity of the fin material.

tan h mL f ;eq
(2.15)
E f ¼
mL f;eq
where
2h
2
for t f << W f (2.16)
m ¼
k f t f
Fins are usually made of metals with high thermal conductivity. For copper and aluminium fins, E f
is typically 0.9e0.95. L f;eq , the characteristic/equivalent fin height can be expressed as
t f
(2.17)
2
L f;eq ¼ h f þ
for longitudinal fin and

R fc
L f;eq ¼ðR fc R o Þ 1 þ 0:35 ln
R o
for radial fin of outer radius R f , attached to a tube exterior where the corrected radius is
t f
(2.18)
R fc ¼ R f þ
2
Depending upon the nature of the fluids, one or more resistances may dominate the RHS of
Eqn. 2.14. In case of gaseliquid exchanger, the controlling resistance will be
that of the gas, if the heat transfer surface areas are nearly equal for both sides.
Lowest overall thermal resistance in a heat exchanger is obtained when the hot-
Fouling
and cold-side thermal resistances are nearly same. Therefore, fins (extended
surfaces) are used on the gas side to achieve this.
Eqn. 2.13 is valid for a heat exchanger with clean heat transfer surfaces. A film of dirt or scale
eventually builds up on the heat transfer surface with time. This process, called fouling, adds to the
resistance to heat transfer and results in lowering the performance of the exchanger. Fouling in heat
exchangers is traditionally taken care of in the design by considering fouling resistance (R Di and R Do )
that represents the thermal resistances of the dirty films on the inside and outside of the inner pipe. This
resistance is added in series to obtain the overall heat transfer coefficient
1 1
¼ þ R di þ R do (2.19)
U
U D
where U (as U h or U c ) is estimated from Eqn. 2.14 and U D is the overall design heat transfer coefficient
considering fouling. Designing an exchange with U D leads to higher heat transfer area than is actually
required for a clean exchanger. The thermal load of new (clean) exchanger will therefore be higher
than its design value. Compared to the design conditions, the new exchanger may therefore show lower
and higher outlet temperatures for the hot and the cold fluid, respectively.
Fouling is a gradual process that not only decreases thermal efficiency but can also perceptibly in-
crease pressure drop due to scale or other deposit. The effect of increasing pressure drop may be more