Page 200 - Chemical Process Equipment - Selection and Design

172 HEAT TRANSFER AND HEAT EXCHANGERS

EXAMPLE 8.&(continued) Total cost:
D U c2 c1 + c
---- 2 C = C, + C2-+ minimum. (5)
c1
.498 ,354 6.66 3.56 18.2147
.494 ,349 6.57 3.65 16t.2118 Substitute Eqs. (2)-(4) into Eq. (5). The outside diameter is the
,495 ,347 6.54 3.67 18.2117-w key unknown.
.496 ,346 6.52 3.63 10.2118 The cost curve is fairly flat, with a minimum at d = 0.50 ft,
.588 .341 6.43 3.78 18.214:3 corresponding to 1.25 in. thickness of insulation. Some trials are
Insulation cost: shown with the computer program. A more detailed analysis of
insulation optima is made by Happel and Jordan [Chem. Process,
C, = 1..51&/Ai Econ., 380 (1975)], although their prices are dated. Section 8.12
also discusses insulation.
-
- 1'5(d2 - o'm2), $/(yr)(sqft inside).
(0.2557)' (4)

Heat transfer coefficients are empirical data and derived T
correlations. They are in the form of overall coefficients U for
frequently occurring operations, or as individual film coefficients [hot
and fouling factors. (AT), (AT),
cold
,I
II
T
8.2. MEAN TEMPERATURE DIFFERENCE
Figure 8.2. Terminal temperatures and temperature differences of a
In a heat exchanger, heat is transferred between hot and cold fluids heat exchanger, with unidentified internal flow pattern.
through a solid wall. The fluids may be process streams or
independent sources of heat such as the fluids of Table 8.2 or
sources of refrigeration. Figure 8.2 shows such a process with inlet
and outlet streams, but with the internal flow pattern unidentified SINGLE PASS EXCHANGER
because it varies from case to case. At any cross section, the
differential rate of heat transfer is The simplest flow patterns are single pass of each fluid, in either the
same or opposite directions. Temperature profiles of the main kinds
dQ= U(T-T')dA=-mcdT=m'c'dT'. (8.23) of thermal behavior are indicated on Figure 8.3(a). When the
unbroken lines [cases (a)-(e)] are substantially straight, the mean
The overall heat transfer rate is represented formally by temperature is expressed in terms of the terminal differences by

Q = UA(AT),. (8.25)
-. ,_ . . __
The mean temperature difference (AT), depends on the terminal
temperatures, the thermal properties of the two fluids and on the This is called the logarithmic mean temperature difference. The
flow pattern through the exchanger. temperature profiles are straight when the heat capacities are

TABLE 8.2. Properties of Heat Transfer Media
atm,
Medium Trade Name Phase "F gage Remarks
- - -
Electricity 100-4500
Water - vapor 200-1 100 0-300 -
Water - liquid 300-400 6-15 -
Flue gas - gas 100-2000 0-7 -
Diphenyl-diphenyl oxide eutectic Dowtherm A liquid or 450-750 0-9 nontoxic, carbonizes at high temp
vapor
Di + triaryl cpds Dowtherm G liquid 20-700 0-3 sensitive to oxygen
Ethylene glycol, inhibited DOW SR-1 liquid -40-250 0 acceptable in food industry
Dimethyl silicones Dow Syltherm liquid -40-750 0 low toxicity
800
Mixed silanes Hydrotherm liquid -50-675 0 react with oxygen and moisture
Aromatic mineral oil Mobiltherm, liquid 100-600 0 not used with copper based materials
Mobil
Chlorinated biphenyls Therminol, liquid 50-600 0 toxic decomposition products
Monsanto
Molten nitrites and nitrates of K and Na Hi-Tec. DuPont liquid 300-1100 0 resistant alloys needed above 850°F
Sodium-potassium eutectic liquid 100-1400 0 stainless steel needed above 1000°F
Mercury vapor 600-1000 0-12 low pressure vapor, toxic, and expensive