The rate equation for heat transfer is: Q = U × A × MTD where:…
Single-phase Convective Heat Transfer
This section discusses single-phase convective heat transfer inside tubes and outside bare tube bundles.
Analysis of heat transfer in commercial heat exchangers can be extremely complex. For in-tube flow, local tube side heat transfer coefficients vary along the length of the tube as the flow structure develops, may include both natural and force convection components, and may involve significant fluid property variation in both radial and axial directions.
Shell side flow involves similar effects, but is much more complicated. The various flow paths that exist on the shell side of an exchanger are illustrated in Figure 200-3.
Each flow fraction has a different heat transfer effect and may vary along the length of the exchanger. “B-stream” flow dominates overall shell side heat transfer. It is most effective in the cross flow region between baffle tips and somewhat less effective in the window region around the end of the baffle. “A-stream” is effective, but applies only to the short section of tube in the baffle hole. “C,” “E,” and “F” streams are relatively ineffective and are usually minimized by the use of seal bars, dummy tubes, and small clearances. “C,” “E,” and “F” should each be less than 0.1.
Rigorous computer simulation is required to analyze all of the complexities that exist on shell and tube sides of a heat exchanger. Good designs, however, fall within narrow limits where design and evaluation procedures can be greatly simplified. For example, a typical shell and tube heat exchanger for pumped liquids is a TEMA “AEU” with 3/4-inch, 14 BWG (minimum wall) carbon steel tubes on 1-inch square pitch, 45 degree tube layout angle, 20% cut segmental baffles, TEMA standard clearances, and about 0.25 psi/ft tube side pressure gradient and 0.5 psi/ft (axial) shell side pressure gradient. This is near optimum for most pumped liquid cases as discussed in Section 220. Rigorous computer generated heat transfer coefficients for this case are shown in Figure 200-4. These curves may be used for initial estimates and scoping studies. Final designs should be checked using the HTRI ST computer program.
Figure 200-4 applies to water and to hydrocarbons. The difference between the water and hydrocarbon curves reflects the difference in fluid properties. Hydrocarbon luid properties also vary widely; however, they vary with each other and with temperature in such a way that heat transfer can be correlated to viscosity and density. Figure 200-4 applies to hydrocarbons extending from naphtha to residuum and for temperatures from ambient to 650°F. Overall accuracy of the curves is about 15%.
Heat transfer film coefficients in Figure 200-4 are presented in the conventional way. Tube side coefficients, hi, are referred to the inside tube surface area. Shell side coefficients, ho, are referred to the outside tube surface area. The overall heat transfer coefficient, referred to the outside surface, is:
U = 1/[ 1/ho + Rw + (1/hi)/(Ai/Ao) ]
where the wall resistance, Rw, is 0.0003 hr × °F × ft2/Btu and the area ratio, Ai/Ao, is 3/4.
To compare shell and tube side film coefficients, both coefficients should be referred to the same surface area, usually the outside surface. That is, the shell side coefficient should be compared to 0.75 times the tube side coefficient in Figure 200-4.
From Figure 200-4, 75% of the tube side coefficient is approximately equal to the shell side coefficient for both water and hydrocarbon in the turbulent regime (viscosity < 2 centipoise). This is as it should be. Equal expenditure of pumping power per unit of heat transfer surface and equally efficient conversion of pressure drop to heat transfer result in equal heat transfer coefficients in the turbulent regime. In the laminar regime (viscosities > 10 centipoise), the shell side coefficient is about seven times the tube side coefficient when referred to the same surface area.
In-tube laminar flow heat exchange is never economical, sometimes leads to “viscosity plugging” (see Section 610), and should be avoided.
The pumping power expended per unit of heat transfer surface is the controlling factor influencing heat transfer in turbulent flow. Where expensive alloys are needed, it is usually economical to spend more on pumping power to save on
exchanger costs. Film coefficients vary at about the 0.4 power of the pressure gradient.
General heat transfer correlations for liquids and gases are given in Appendix B. Most of this information is taken from the HTRI Design Manual and is proprietary. Equation B-1 in Appendix B applies to turbulent flow of liquids or gases in tubes and is accurate within about 15%. This is a Dittus-Boelter type correlation and is similar to those found in general heat transfer text books. Corresponding text book correlations are based on open literature data with accuracy in the 20% to 30% range.
Appendix B also gives approximate methods to estimate laminar and transition flow heat transfer in tubes. This information may be off by a factor of two. When accurate laminar flow heat transfer information is needed, the HTRI ST simulation programs should be used. Simple shell side heat transfer correlations for liquids and gases are included in Appendix B. They apply to well proportioned shell and tube exchangers with turbulent flow only. Extreme geometries or low shell side velocities require computer analysis.
The best conversion of pressure drop to heat transfer occurs with rotated square tube layout (45 degrees) in liquid service. Inline square tube layout (90 degrees) is slightly better in gas service where Reynolds numbers are typically very high.
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