Effect of scale formation
In most heat exchangers some scale formation will take place on both sides of the heat transfer surface after the heat exchanger has been in use for some time (unless scale inhibition mechanism is in place). This introduces two additional resistances in the heat flow path. Thus the total thermal resistance becomes:
ΣR = Ri + Rsi +Rw + Rso + Ro (eq. 1.27)
Where Rsi = thermal resistance due to scale formation on inside surface of inner pipe, m2 C/W
Rso = thermal resistance due to scale formation on outside surface of inner pipe, m2 C/W
(We can here consider no scaling on outside surface of inner pipe)
Since it is difficult to ascertain accurately the thickness and thermal conductivity of the scale formed, the effect of scale deposit on heat flow is generally taken into account by specifying an equivalent scale heat transfer coefficient, hs.
The reciprocal of the scale heat transfer coefficient is called the fouling factor. If hsi and hso denote the heat transfer coefficient for the scale formed on the inside and outside surface of he inner pipe, then:
Rsi = 1/Aihsi (eq. 1.29)
Rso = 1/Aohso (eq. 1.30)
And q = . (ti – to) (eq. 1.31)
1/Aihi + 1/Aihsi + ln (ro/ri) +1/Aohso + 1/Aoho
2πLKw
Ui = . 1 (eq. 1.32)
1/hi + 1/hsi + Ai ln (ro/ri) + [Ai/Ao]. 1/hso + [Ai/Ao]. 1/ho
2πLKw
or
Ui = 1 (eq. 1.33)
1/hi + 1/hsi + [ri/kw] ln (ro/ri) + [ri/ro]. 1/hso + [ri/ro]. 1/ho
The fouling factor (1/hs) for some representative applications are listed in following table:
| Fluid | Fouling factor (1/hs) (m2/K/W) |
| Distilled water | 0.000086 |
| Sea water | 0.000172 |
| Well water | 0.000344 |
| Treated boiler feed water | 0.000172 |
| Fuel oil and crude oil | 0.00086 |
| Steam, non-oil bearing | 0.00009 |