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The process represented in
the above figure (1.1) is one in which hot fluid is cooled by water, which
itself heated without any loss of exchanged heat. Industrial heat exchangers
consist of a number of tubes enclose in a shell. Exchangers with cooling water
in the tubes, and hot product in the shell are the most satisfactory. Fouling
often occurs if water is circulated through the shell, because the velocity of
the water stream is lower in this design. Tubes are much easier to clean than
the shell. Matters are also so arranged that the pressure of the product being
cooled is higher than that of cooling water, so that the water cannot leak into
the hot product, and damage the equipment.
In
the figure (t1) temperature of CW inlet; (t2) temperature of CW outlet; (T1)
temperature of process inlet; (T2) Temperature of process outlet. Here we will
consider CW as cooling water and Process as P.
Now
U = ΔHp/ΔtmA
(eq-1.0)
Where: U = net effective overall heat transfer coefficient (Kcal/0C-h-m2)
ΔH = difference in enthalpy of P at T1 and T2 (Kcal/kg)
P = flow rate of the product (m3/h)
A = area of heat transfer surface (m2)
Δtm = the average of the temperature
differences at both ends of the exchanger (0C)
Δtm = (T1-t2) +(T2-t1)
(eq – 1.5)
2
Here
it is assumed that the temperature of the fluid is in the shell falls
continuously and uniformly from T1 to T2, while that of the water inside the
tubes rises similarly from t1 to t2. With this assumption it is permissible to
use the average of the terminal differences for the mean temperature difference.
In more complicated heat exchangers, however, it is necessary to use the log
mean temperature difference, and when calculation the value for multipass
exchangers correction factors also must be applied to (Δtm).
(Δt)log
e = (Δt)max - (Δt)min = (T2-t1)
– (T1 – t2) (eq – 1.6)
log e [(Δt)max/(Δt)min]
log e [(T2-t1)/(T1-t2)]
(see
topic LMTD for detailed description)
In a water-tube exchanger U
is likely to decrease gradually because of accumulating deposits, or because of
scale formation on the tubes. Referring to the figure, the effect of these
events on the heat transfer coefficient can be predicted qualitatively. If a
thin layer of insulating scale forms on either side of the tube T2 rises and t2
falls as less heat passes from P to CW through the insulating layer. Thus ΔH
decreases, and as both t1 and T1 are unaffected by conditions within the heat
exchanger, Δtm increases. The net result is that the heat transfer
coefficient becomes smaller.
If deposits slow the flow of
water, t2 and T2 both rise. In this event, however, Δtm may
increase and ΔH may decrease by such small amounts that the effect on U may not
be significant.
The reciprocal of the heat
transfer coefficient is called the “fouling resistance,” this number multiplied
by one thousand is the “fouling factor.” Except in unusual circumstances the
effect of fouling resistances can never be exactly known, as fouling within an
actual heat exchanger is seldom uniform, and also the net effect is a
combination of conditions on both sides of the heat transfer surface.
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Introduction |
Combined heat transfer process |
Heat transfer in cooling tower |
Variables affecting performance of CT heat transfer |
Heat transfer within
cooling system (heat exchanger) |
Types of heat exchanger |
Basic design
procedure and theory |
Designing a test heat exchanger |
Log Mean Temperature
difference | L.M.T.D. Correction factors |
Overall heat transfer coefficient |
Elaborated method for calculating U values |
Effect of scale formation |
Condensation of steam |
Condenser, where the hot fluid temperature varies |
Significance of pressure |
Significance of flow rate |
Methods of checking steam
condenser performance |
Common conversion factors
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