barcode reading in asp.net (THI - Tcz) + (THS - Ted in .NET framework

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The error approaches zero as the temperature differences at the ends of the exchanger approach each other, and is less than 10 percent with a 4 : 1 rat io of temperature difference. Each of the two fluids will be assigned a mass flow IV and a specific heat C. One of the flows ordinarily is wild and represents the load on the exchanger; the ot,her is often manipulated in some way to control t he exit temperature of the first. Temperature changes in both streams are interrelated :
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& = WHCH(THI - TII~) = IYcCc(Tcz
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(9.7)
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Equations (9.4), (9.6), and (9.7) contain four expressions with four They can be solved simultaneously unknowns, Q, AT,,, TH2, and Tm.
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FIG 9.3. Manipulation of flow has little effect on heat transfer at high flow rates.
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for any of the four unknowns. least complicated : Tm - TCI
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The solution for heat transfer rate is the
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Q = l/C A + ~~(l/W,CH + l/WcCc)
(9.8)
Heat transfer rate ran be normalized by dividing by its maximum possible value, which would occur with both streams at infinite flow such that THY = THY a n d Tcz = Tel:
Q max = CA(Tm - TcJ Q
(9.9) (9.10)
1 1 + (UA/2)(1/-W&I + l/WcCc) UA(Tm - Ted =
E igure 9.3 is a plot of normalized heat transfer rate vs. normalized flow -of cold fluid with the flow of hot fluid as a parameter. Observe the extreme nonlincnrity of the curves and how ineffective the manipulation of flow is over a wide operating range. Substitution of Eq. (9.7) into (9.10) yields the following formulas describing dimensionless temperatures as a function of flow rates:
1 T III - TCI = W~CH/UA + $$(I +
THI - THZ
(9.11)
wHcH/wCcC)
Tcz - TCI
THI - TCI =
WcCc/UA
1 >s(l
+ WCCC/WHCH)
(9.12)
To envision what effect flow rates have upon exit temperature, Eg. (9.11) is plot ted in Fig. 9.4 with the same abscissa and parameter that were used in Fig. 9.3.
1.0 N F c I I f f W,&/UA = 1 2 4 0.5 E 0 1 2 3 4 WC CJU.A
FIG 9.4. It is apparent that effective temperature control cannot be obtained over very wide ranges by manipulation of flow rate.
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Not only does the slope of the curves change with temperature, but it Any horizontal line drawn across Fig. 9.4 also changes with load WH. will present the conditions required for temperature control. Doubling of the load at any given temperature requires the manipulated variable WC to be much more than doubled. In practice, the overall heat transfer coefficient aIso varies with the flow rates, which improves the controllability somewhat. Although the film coefficient on each side of the heat transfer surface varies at about the 0.8 power of the fluid velocity, for simplification it will be assumed that the relationship is linear. Furthermore the reciprocal of the overall heat transfer coefficient mill be assumed to be the sum of the reciprocals of the individual film coefficients: 1 1 1 -= u W&H + W&c The terms kH and kc are the flow indices of their respective heat transfer coefficients. Combining with Eq. (9.11) yields:
THI - THZ THI - TCI = CH/AkH
-k 96 k ( WHCH/WCCC)(CC/A~C -k 35)
(9.13) A plot of Eq. (9.13) for conditions of CH/AkH = Cc/Akc = 1 is given in Fig. 9..5. Compare it with the curves of Fig. 9.4. The point of the foregoing analysis has been to demonstrate the nonlinear properties associated with heat transfer. Even under the most favorable conditions, manipulation of flow is far from sat isfactory for temperature control. There are practical considerations, too. Throttling of streams which may contain impurities (river water, for example) can cause deposits to accumulate, fouling the heat transfer surfaces. Furthermore, manipulation of flow causes variable loop gain through the variation of dead time. In the event that there is no alternative to the manipulation of flow, an equal-percentage valve characteristic should be chosen. Part of the stream whose temperature is to be controlled may be allowed to bypass the exchanger as shown in Fig. 9.6. But Fig. 9.3 indicates that
$1; 1 m1o FIG 9.5. h V a r i a t i o n f t e h e a t transfer coefficient with flow somewhat eases the nonlinearity of the process.
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