Temperature-Driving Force for Heat Transfer

When streams on both sides of a heat exchanger are considered in process design with a simulation program, a two-sided heat exchanger model is used. The model applies Eq. (13.1) to each side under conditions of equal heat transfer rates, assuming that the exchanger is well insulated such that heat losses are negligible. Thus, all of the heat released by one side is taken up by the other side. In addition, a transport equation is applied  

The optimal minimum approach temperature is a function maiidy of the temperature levels of the two streams as indicated in Heuristic 25 of Chapter 5, and the lost work analysis in 

Toluene is converted to benzene by hydrodealkylation. Typically, a 75% conversion is used in the reactor, which necessitates the recovery and recycle of unreacted toluene. In addition, a side reaction occurs that produces a small amount of a biphenyl byproduct, which is separated from the toluene. A hydrodealkylation process is being designed that includes a distillation column for separating toluene from biphenyl. The feed to the column is 3.4 Ibmoiyhr of benzene, 84.6 IbmoVhr of toluene, and 5.1 Ibmol/hr of biphenyl at 264°F and 37.1 psia. The distillate is to contain 99.5% of the toluene and 2% of the biphenyl. If the column operates at a bottoms pressure of 38.2 psia, determine the bottoms temperature and select a suitable heat source for the reboiler. Steam is available at pressures of 60, 160, and 445 psig. The barometer reads 14 psia. 

Assume that no benzene is present in the bottoms because it has a much higher vapor pressure than toluene, and a sharp separation between toluene and biphenyl is specified. By material balance, the bottoms contains 0.423 Ibmol/hr of toluene and 4.998 Ibmol/hr of biphenyl. A bubble-point calculation for 

A mixture of 62.5 mol% ethylene and 37.5 mol% ethane is separated by distillation to obtain a vapor distillate of 99 mol% ethylene with 98% recovery of ethylene. When the pressure in the reflux drum is 200 psia, determine the distillate temperature and select a coolant for the condenser. What pressure is required to permit the use of cooling water in the condenser  

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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... 

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... 

Figure 3.18b shows the same streams plotted with a lower value of AT in- The amount of heat exchanged is increased and the utility requirements have been reduced. The temperature driving force for heat transfer has also been reduced, so the heat exchanger has both a larger duty and a smaller log-mean temperature difference. This leads to an increase in the heat transfer area required and in the capital cost of the exchanger. The capital cost increase is partially offset by capital cost savings in the heater and cooler, which both become smaller, as well as by savings in the costs of hot and cold utilities. In general, there will be an optimum value of ATmin, as illustrated in Figure 3.19. This optimum is usually rather flat over the range 10°C to 30°C.

Be familiar with the major types of heat exchange equipment and how they differ in flow directions of the two fluids exchanging heat, and the corresponding effect on the temperature-driving force for heat transfer. 

Chapter 13 Heat Exchanger Design Temperature-Driving Force for Heat Transfer... 

With the one-tube-pass exchangers of Figures 13.8a and 13.8b, efficient countercurrent flow between the tube-side and shell-side fluids is closely approximated. This is not the case with the 1-2 exchangers of Figures 13.8c, 13.8d, and 13.8e because of the reversal of the tube-side-fluid flow direction. The flow is countercurrent in one tube pass and cocurrent (parallel) in the other. As shown later in this section, this limits heat recovery because of the reduction in the mean temperature-driving force for heat transfer. Note that a video of an... 

This represents 8.83/45.05 = 0.196, or 19.6% of the total lost work for the cycle. This lost work results because of a frictional pressure drop of 2 psi through the heat exchanger and the rather large temperature driving force for heat transfer. 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

The amount of heat actually taken up by the particles was an important quantity, as tubes operate under heat transfer limited conditions near the tube inlet. Fig. 30 shows a plot of Q against r, where Q was the total energy flow into the solid particles, for the entire segment. For inlet conditions, Q varied strongly at lower r, but was almost constant at higher values. As rcut/rp decreased from 0.95 to 0.0 and the effectiveness factor increased from nearly zero to one, the active solid volume increased by a factor of 7. If the solid temperature had remained the same, the heat sink would also have had to increase sevenfold. This could not be sustained by the heat transfer rate to the particles, so the particle temperature had to decrease. This reduced the heat sink and increased the driving force for heat transfer until a balance was found, which is represented by the curve for the inlet in Fig. 30. 

If an internal cooling coil is used, the cooling medium flows in plug flow through the coil. The temperature differential driving force for heat transfer is a log mean average of the differential temperatures at the two ends of the coil... 

The driving force for heat transfer is the temperature difference. What is the driving force for mass transfer ... 

In the simple evaporators we have dealt with so far, one of the product streams is water vapor — also known as steam. Why can t this vapor be used in place of steam The answer is simple if the vapor replaced the steam, there would be no driving force for heat transfer because the steam and the vapor would have the same temperature. To get a driving force in the right direction, we have to use steam with a higher pressure. One method of making use of the latent heat of the vapor is the compress it. We will look at that option below, but first let s examine another option. 

Multiple effects recover some of the latent heat of the overhead vapor by using it in place of steam to boil the liquor in downstream effects. Is there any way we can use the vapor in place of steam in a single-effect evaporator The problem with using the vapor in place of steam is that the temperature of the vapor is the same as the temperature of the liquor the liquor and vapor leaving the same effect are already in thermal equilibrium with each other. In other words, there is no driving force for heat transfer. 

Let s start by recalling the driving force for heat transfer across an interface. Suppose 1 contact a hot gas with a cold liquid. The temperature profile near the interface will look something like that show at right. There are two characteristics of this sketch which are important ... 

But the driving force for the overall coefficients look a little different. The overall driving force for heat transfer is just the difference between the temperature of the hot and cold fluid... 

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