Temperature-difference driving force, mean

At, = log-mean temperature-difference driving force over condenser, °F Hy = hours the condenser is operated per year, h/year Cw = cooling-water cost assumed as directly proportional to amount of water supplied, /lb... 

At = temperature-difference driving force (subscript lm designates log mean), °F... 

Evaluate the mean temperature-difference driving force. 

Estimate the log-mean temperature temperature-difference driving force. The formula is LMTD = (tg — ti)/ln(tg — ti), where LMTD is log-mean temperature difference, tg is the maximum temperature difference between steam and cooling water, and is the minimum temperature difference between them. The maximum difference is (212 — 80), or 132 the minimum is (212 — 115), or 97. Accordingly, LMTD = (132 - 97)/ln( 132/97) = 113.6°F. 

A = At designates temperature-difference driving force, F subscript / designates across film subscript m designates mean At subscript oa or no subscript designates overall At At, = At, = t[— AP... 

The outlet vapor stream has much less mass than the inlet stream, due to a large percentage of vapor condensation in the section. The heat load on the packed bed is greater than the heat removed by external pumparound coolers because the vacuum gas oil condensate normally is discharged from the system at the same temperature it is withdrawn from the column. The logarithmic mean temperature difference driving force for each packed bed is determined from Equation 6-24. 

If the condenser uses the flow rate of a cooling medium (typically cooling water) or if the reboiler uses the flow rate of a heating medium (hot oil), a model, using a log-mean temperature differential driving force (temperature differentials at outlet and inlet ends), can be used. The inlet medium temperature and the minimum approach temperature difference between the process and the medium are specified. Then Aspen calculates the required UA product (overall heat-transfer coefficient U and heat-transfer area A) and the required flow rate of the medium from the known heat-transfer rate. 

FIG. 2 Growth rates as a function of the driving force A//. Comparison of theory and computer simulation for different values of the diffusion length and at temperatures above and below the roughening temperature. The spinodal value corresponds to the metastability limit A//, of the mean-field theory [49]. The Wilson-Frenkel rate WF is the upper limit of the growth rate. 

In fully developed flow, equations 12.102 and 12.117 can be used, but it is preferable to work in terms of the mean velocity of flow and the ordinary pipe Reynolds number Re. Furthermore, the heat transfer coefficient is generally expressed in terms of a driving force equal to the difference between the bulk fluid temperature and the wall temperature. If the fluid is highly turbulent, however, the bulk temperature will be quite close to the temperature 6S at the axis. 

A Tm = the mean temperature difference, the temperature driving force, °C. 

Prior to discussions of the capital and operating costs, we need to define the temperature driving force for heat transfer. Examine the notation in Figure El 1.3c by definition the log mean temperature difference ATlm is... 

Logarithmic-mean driving force, packed column absorbers, 1 53 Logarithmic mean temperature difference (LMTD), 13 251, 252 Logic circuits, CMOS, 22 251-253 Logic gates, molecular-based, 17 61 Log-mean temperature difference (LMTD), 26 64... 

When one is dealing with direct contact heat transfer, the corresponding terms are hLa and hca. Here the driving force is the temperature difference. The L subscript means that we are dealing with a liquid-limited process such as condensing a pure liquid. How to convert kLa data to an hLa value is illustrated by Example 23. 

The supersaturation in condensers arises for two reasons. First, the condensable vapor is generally of higher molecular weight than the noncondensable gas. This means that the molecular diffusivity of the vapor will be much less than the thermal diffusivity of the gas. Restated, the ratio of NSc/Npr is greater than 1. The result is that a condenser yields more heat-transfer units dTg/(Tg — Tt) than mass-transfer units dYg/(Yg — Yt). Second, both transfer processes derive their driving force from the temperature difference between the gas Tg and the interface Tt. Each incremental decrease in interface temperature... 

The temperature driving force for heat transfer between the reaction liquid at temperature Tr and the coil is the log-mean temperature difference given in Eq. (2.19). The heat transfer rate is given by... 

LMTD. This mode is equivalent to an internal heat transfer coil where the temperature driving force is a log-mean average of the differences between the reactor temperature... 

Mean temperature difference Effective difference between the temperature of the hot stream and the temperature of the cold stream in a heat exchanger. This is the driving force for the heat transfer process. 

---