Temperature cross

The final temperature of the hot stream is slightly lower than the final temperature of the cold stream, as illustrated in Fig. 7.86. This is called a temperature cross. This situation is also usually straightforward to design for, providing the temperature cross is small, because, again, it can probably be accommodated in a single shell. 

As the amount of temperature cross increases, however, problems are encountered, as illustrated in Fig. 7i8c. Local reversal of heat flow may be encountered, which is wasteful in heat transfer area. The design may even become infeasible. 

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. 

Figure 7.8 Designs with a temperature approach or small temperature cross can be accommodated in a single 1-2 shell, whereas designs with a large temperature cross become infeasible. (From Ahmad, Linnhoff, and Smith, Trans. ASME, J. Heat Transfer, 110 304, 1988 reproduced by permission of the American Society of Mechanical Engineers.)...

The best known use of the hairpin is its operation in true counter-current flow which yields the most efficient design for processes that have a close temperature approach or temperature cross. However, maintaining countercurrent flow in a tubular heat exchanger usually implies one tube pass for each shell pass. As recently as 30 years ago, the lack of inexpensive, multiple-tube pass capability often diluted me advantages gained from countercurrent flow. 

Type T is the spiraf-spiral flow pattern. It is used for all heating and cooling seiwices and can accommodate temperature crosses such as lean/rich seiwices in one unit. The removable covers on each end allow access to one side at a time to perform maintenance on that fluid side. Never remove a cover with one side under pressure as the unit will telescope out hke a collapsible cup. 

The most common form has both sides in helical flow patterns, pure countercurrent flow is followed and the LMTD correction factor approaches 1.0. Temperature crosses are possible in single units. Like the spiral-plate unit, different configurations are possible for special apphcations. 

One thing to be careful of in cross exchangers is a design having a so-called temperature cross. An example is shown in Figure 1. 

In Figure 1, the colder fluid being heated emerges hotter than the outlet temperature of the other fluid. For actual heat exchangers that deviate from true countercurrent flow the follow ing things can happen under temperature cross conditions ... 

Figure 1. Shown here is an example of a temperature cross.

The calculation procedure for temperature correction factors won t work for a temperature cross in a single shell pass, but this is an undesirable situation anyway. 

For counter-current flow of the fluids through the unit with sensible heat transfer only, this is the most efficient temperature driving force with the largest temperature cross in the unit. The temperature of the outlet of the hot stream can be cooler than the outlet temperature of the cold stream, see Figure 10-29 ... 

Find the minimum temperature that a hot fluid at 410°F can be cooled if the cold fluid is heated from an inlet temperature of 167°F to 257°F. Also And the theoretical temperature cross and theoretical minimum hot fluid shell-side outlet temperature, Tg. 

The theoretical maximum possible temperature cross in t/iAstyle exchanger = (tg — T2 ,i ) = 0.1715. 

Then, for the example the theoretical maximum possible temperature cross ... 

The cost of recovery will be reduced if the streams are located conveniently close. The amount of energy that can be recovered will depend on the temperature, flow, heat capacity, and temperature change possible, in each stream. A reasonable temperature driving force must be maintained to keep the exchanger area to a practical size. The most efficient exchanger will be the one in which the shell and tube flows are truly countercurrent. Multiple tube pass exchangers are usually used for practical reasons. With multiple tube passes the flow will be part counter-current and part co-current and temperature crosses can occur, which will reduce the efficiency of heat recovery (see Chapter 12). 

In most shell and tube exchangers the flow will be a mixture of co-current, counter-current and cross flow. Figures 12.186 and c show typical temperature profiles for an exchanger with one shell pass and two tube passes (a 1 2 exchanger). Figure 12.18c shows a temperature cross, where the outlet temperature of the cold stream is above that of the hot stream. 

Figure 12.18. Temperature profiles (a) Counter-current flow (/>) 1 2 exchanger (c) Temperature cross...

The value of F, will be close to one when the terminal temperature differences are large, but will appreciably reduce the logarithmic mean temperature difference when the temperatures of shell and tube fluids approach each other it will fall drastically when there is a temperature cross. A temperature cross will occur if the outlet temperature of the cold stream is greater than the inlet temperature of the hot stream, Figure 12.18c. 

An economic exchanger design cannot normally be achieved if the correction factor Ft falls below about 0.75. In these circumstances an alternative type of exchanger should be considered which gives a closer approach to true counter-current flow. The use of two or more shells in series, or multiple shell-side passes, will give a closer approach to true counter-current flow, and should be considered where a temperature cross is likely to occur. 

Although the result in Equation 15.45 applies to both countercurrent and cocurrent flow, in practice, cocurrent flow is almost never used as, given fixed fluid inlet and outlet temperatures, the logarithmic mean temperature difference for countercurrent flow is always larger. This in turn leads to smaller surface area requirements. Also, as shown in Figure 15.6a for countercurrent flow, the final temperature of the hot fluid can be lower than the final temperature of the cold fluid (sometimes known as temperature cross), whereas in Figure 15.6b, it is clear that there can never be a temperature cross. 

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