国外热力学经典教材之换热器heat exchangers

H E AT E X C H A N G E R S H eat exchangers are devices that facilitate the exchange of heat betweentwo fluids that are at different temperatures while keeping them frommixing with each other. Heat exchangers are commonly used in prac- tice in a wide range of applications, from heating and air-conditioning systems in a household, to chemical processing and power production in large plants. Heat exchangers differ from mixing chambers in that they do not allow the two fluids involved to mix. In a car radiator, for example, heat is transferred from the hot water flowing through the radiator tubes to the air flowing through the closely spaced thin plates outside attached to the tubes. Heat transfer in a heat exchanger usually involves convection in each fluid and conduction through the wall separating the two fluids. In the analysis of heat exchangers, it is convenient to work with an overall heat transfer coeffi- cient U that accounts for the contribution of all these effects on heat transfer. The rate of heat transfer between the two fluids at a location in a heat ex- changer depends on the magnitude of the temperature difference at that location, which varies along the heat exchanger. In the analysis of heat ex- changers, it is usually convenient to work with the logarithmic mean temper- ature difference LMTD, which is an equivalent mean temperature difference between the two fluids for the entire heat exchanger. Heat exchangers are manufactured in a variety of types, and thus we start this chapter with the classification of heat exchangers. We then discuss the de- termination of the overall heat transfer coefficient in heat exchangers, and the LMTD for some configurations. We then introduce the correction factor F to account for the deviation of the mean temperature difference from the LMTD in complex configurations. Next we discuss the effectiveness–NTU method, which enables us to analyze heat exchangers when the outlet temperatures of the fluids are not known. Finally, we discuss the selection of heat exchangers. 667 CHAPTER 13 CONTENTS 13–1 Types of Heat Exchangers 668 13–2 The Overall Heat Transfer Coefficient 671 13–3 Analysis of Heat Exchangers 678 13–4 The Log Mean Temperature Difference Method 680 13–5 The Effectiveness–NTU Method 690 13–6 Selection of Heat Exchangers 700 cen58933_ch13.qxd 9/9/2002 9:57 AM Page 667 13–1 TYPES OF HEAT EXCHANGERS Different heat transfer applications require different types of hardware and different configurations of heat transfer equipment. The attempt to match the heat transfer hardware to the heat transfer requirements within the specified constraints has resulted in numerous types of innovative heat exchanger designs. The simplest type of heat exchanger consists of two concentric pipes of dif- ferent diameters, as shown in Figure 13–1, called the double-pipe heat exchanger. One fluid in a double-pipe heat exchanger flows through the smaller pipe while the other fluid flows through the annular space between the two pipes. Two types of flow arrangement are possible in a double-pipe heat exchanger: in parallel flow, both the hot and cold fluids enter the heat exchanger at the same end and move in the same direction. In counter flow, on the other hand, the hot and cold fluids enter the heat exchanger at opposite ends and flow in opposite directions. Another type of heat exchanger, which is specifically designed to realize a large heat transfer surface area per unit volume, is the compact heat ex- changer. The ratio of the heat transfer surface area of a heat exchanger to its volume is called the area density �. A heat exchanger with � � 700 m2/m3 (or 200 ft2/ft3) is classified as being compact. Examples of compact heat exchangers are car radiators (� � 1000 m2/m3), glass ceramic gas turbine heat exchangers (� � 6000 m2/m3), the regenerator of a Stirling engine (� � 15,000 m2/m3), and the human lung (� � 20,000 m2/m3). Compact heat exchangers enable us to achieve high heat transfer rates between two fluids in � 668 HEAT TRANSFER FIGURE 13–1 Different flow regimes and associated temperature profiles in a double-pipe heat exchanger. Hot in Hot out Cold in Cold out (a) Parallel flow Hot in Hot out Cold out Cold in (b) Counter flow Cold fluid Hot fluid Hot fluid Cold fluid T T cen58933_ch13.qxd 9/9/2002 9:57 AM Page 668 a small volume, and they are commonly used in applications with strict limi- tations on the weight and volume of heat exchangers (Fig. 13–2). The large surface area in compact heat exchangers is obtained by attaching closely spaced thin plate or corrugated fins to the walls separating the two flu- ids. Compact heat exchangers are commonly used in gas-to-gas and gas-to- liquid (or liquid-to-gas) heat exchangers to counteract the low heat transfer coefficient associated with gas flow with increased surface area. In a car radi- ator, which is a water-to-air compact heat exchanger, for example, it is no sur- prise that fins are attached to the air side of the tube surface. In compact heat exchangers, the two fluids usually move perpendicular to each other, and such flow configuration is called cross-flow. The cross-flow is further classified as unmixed and mixed flow, depending on the flow con- figuration, as shown in Figure 13–3. In (a) the cross-flow is said to be un- mixed since the plate fins force the fluid to flow through a particular interfin spacing and prevent it from moving in the transverse direction (i.e., parallel to the tubes). The cross-flow in (b) is said to be mixed since the fluid now is free to move in the transverse direction. Both fluids are unmixed in a car radiator. The presence of mixing in the fluid can have a significant effect on the heat transfer characteristics of the heat exchanger. CHAPTER 13 669 FIGURE 13–2 A gas-to-liquid compact heat exchanger for a residential air- conditioning system. FIGURE 13–3 Different flow configurations in cross-flow heat exchangers. Cross-flow (mixed) Cross-flow (unmixed) Tube flow (unmixed) (b) One fluid mixed, one fluid unmixed(a) Both fluids unmixed Tube flow (unmixed) cen58933_ch13.qxd 9/9/2002 9:57 AM Page 669 Perhaps the most common type of heat exchanger in industrial applications is the shell-and-tube heat exchanger, shown in Figure 13–4. Shell-and-tube heat exchangers contain a large number of tubes (sometimes several hundred) packed in a shell with their axes parallel to that of the shell. Heat transfer takes place as one fluid flows inside the tubes while the other fluid flows outside the tubes through the shell. Baffles are commonly placed in the shell to force the shell-side fluid to flow across the shell to enhance heat transfer and to main- tain uniform spacing between the tubes. Despite their widespread use, shell- and-tube heat exchangers are not suitable for use in automotive and aircraft applications because of their relatively large size and weight. Note that the tubes in a shell-and-tube heat exchanger open to some large flow areas called headers at both ends of the shell, where the tube-side fluid accumulates before entering the tubes and after leaving them. Shell-and-tube heat exchangers are further classified according to the num- ber of shell and tube passes involved. Heat exchangers in which all the tubes make one U-turn in the shell, for example, are called one-shell-pass and two- tube-passes heat exchangers. Likewise, a heat exchanger that involves two passes in the shell and four passes in the tubes is called a two-shell-passes and four-tube-passes heat exchanger (Fig. 13–5). An innovative type of heat exchanger that has found widespread use is the plate and frame (or just plate) heat exchanger, which consists of a series of plates with corrugated flat flow passages (Fig. 13–6). The hot and cold fluids flow in alternate passages, and thus each cold fluid stream is surrounded by two hot fluid streams, resulting in very effective heat transfer. Also, plate heat exchangers can grow with increasing demand for heat transfer by simply mounting more plates. They are well suited for liquid-to-liquid heat exchange applications, provided that the hot and cold fluid streams are at about the same pressure. Another type of heat exchanger that involves the alternate passage of the hot and cold fluid streams through the same flow area is the regenerative heat ex- changer. The static-type regenerative heat exchanger is basically a porous mass that has a large heat storage capacity, such as a ceramic wire mesh. Hot and cold fluids flow through this porous mass alternatively. Heat is transferred from the hot fluid to the matrix of the regenerator during the flow of the hot fluid, and from the matrix to the cold fluid during the flow of the cold fluid. Thus, the matrix serves as a temporary heat storage medium. 670 HEAT TRANSFER FIGURE 13–4 The schematic of a shell-and-tube heat exchanger (one-shell pass and one-tube pass). Tube outlet Shell inlet Baffles Front-end header Tube inlet Shell outlet ShellTubes Rear-end header Out Shell-side fluid Out In Out In Shell-side fluid In Tube-side fluid Out (a) One-shell pass and two-tube passes (b) Two-shell passes and four-tube passes In Tube- side fluid FIGURE 13–5 Multipass flow arrangements in shell- and-tube heat exchangers. cen58933_ch13.qxd 9/9/2002 9:57 AM Page 670 The dynamic-type regenerator involves a rotating drum and continuous flow of the hot and cold fluid through different portions of the drum so that any portion of the drum passes periodically through the hot stream, storing heat, and then through the cold stream, rejecting this stored heat. Again the drum serves as the medium to transport the heat from the hot to the cold fluid stream. Heat exchangers are often given specific names to reflect the specific appli- cation for which they are used. For example, a condenser is a heat exchanger in which one of the fluids is cooled and condenses as it flows through the heat exchanger. A boiler is another heat exchanger in which one of the fluids ab- sorbs heat and vaporizes. A space radiator is a heat exchanger that transfers heat from the hot fluid to the surrounding space by radiation. 13–2 THE OVERALL HEAT TRANSFER COEFFICIENT A heat exchanger typically involves two flowing fluids separated by a solid wall. Heat is first transferred from the hot fluid to the wall by convection, through the wall by conduction, and from the wall to the cold fluid again by convection. Any radiation effects are usually included in the convection heat transfer coefficients. The thermal resistance network associated with this heat transfer process involves two convection and one conduction resistances, as shown in Figure 13–7. Here the subscripts i and o represent the inner and outer surfaces of the � CHAPTER 13 671 Hot fluid Cold fluid Ti Ri = ––– Ti To Rwall Wall Cold fluid 1 hi Ai Ro = ––– 1 hoAo Ao ho Ai hi Hot fluid Heat transfer FIGURE 13–7 Thermal resistance network associated with heat transfer in a double-pipe heat exchanger. FIGURE 13–6 A plate-and-frame liquid-to-liquid heat exchanger (courtesy of Trante Corp.). cen58933_ch13.qxd 9/9/2002 9:57 AM Page 671 inner tube. For a double-pipe heat exchanger, we have Ai � �DiL and Ao � �DoL, and the thermal resistance of the tube wall in this case is Rwall � (13-1) where k is the thermal conductivity of the wall material and L is the length of the tube. Then the total thermal resistance becomes R � Rtotal � Ri � Rwall � Ro � (13-2) The Ai is the area of the inner surface of the wall that separates the two fluids, and Ao is the area of the outer surface of the wall. In other words, Ai and Ao are surface areas of the separating wall wetted by the inner and the outer fluids, respectively. When one fluid flows inside a circular tube and the other outside of it, we have Ai � �DiL and Ao � �DoL (Fig. 13–8). In the analysis of heat exchangers, it is convenient to combine all the ther- mal resistances in the path of heat flow from the hot fluid to the cold one into a single resistance R, and to express the rate of heat transfer between the two fluids as Q· � � UA �T � Ui Ai �T � Uo Ao �T (13-3) where U is the overall heat transfer coefficient, whose unit is W/m2 · °C, which is identical to the unit of the ordinary convection coefficient h. Cancel- ing �T, Eq. 13-3 reduces to � R � � Rwall � (13-4) Perhaps you are wondering why we have two overall heat transfer coefficients Ui and Uo for a heat exchanger. The reason is that every heat exchanger has two heat transfer surface areas Ai and Ao, which, in general, are not equal to each other. Note that Ui Ai � Uo Ao, but Ui � Uo unless Ai � Ao. Therefore, the overall heat transfer coefficient U of a heat exchanger is meaningless unless the area on which it is based is specified. This is especially the case when one side of the tube wall is finned and the other side is not, since the surface area of the finned side is several times that of the unfinned side. When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, as is usually the case, the thermal resistance of the tube is negligible (Rwall � 0) and the inner and outer surfaces of the tube are almost identical (Ai � Ao � As). Then Eq. 13-4 for the overall heat transfer co- efficient simplifies to � (13-5) where U � Ui � Uo. The individual convection heat transfer coefficients inside and outside the tube, hi and ho, are determined using the convection relations discussed in earlier chapters. 1 hi � 1 ho 1 U 1 ho Ao 1 hi Ai 1 UAs � 1 Ui Ai � 1 Uo Ao �T R 1 hi Ai � ln (Do /Di) 2�kL � 1 ho Ao ln (Do /Di) 2�kL 672 HEAT TRANSFER Heat transfer Outer fluid Outer tube L Inner tubeInner fluid Ao = πDoL Ai = πDiL Do Di FIGURE 13–8 The two heat transfer surface areas associated with a double-pipe heat exchanger (for thin tubes, Di � Do and thus Ai � Ao). cen58933_ch13.qxd 9/9/2002 9:57 AM Page 672 The overall heat transfer coefficient U in Eq. 13-5 is dominated by the smaller convection coefficient, since the inverse of a large number is small. When one of the convection coefficients is much smaller than the other (say, hi ho), we have 1/hi 1/ho, and thus U � hi. Therefore, the smaller heat transfer coefficient creates a bottleneck on the path of heat flow and seriously impedes heat transfer. This situation arises frequently when one of the fluids is a gas and the other is a liquid. In such cases, fins are commonly used on the gas side to enhance the product UAs and thus the heat transfer on that side. Representative values of the overall heat transfer coefficient U are given in Table 13–1. Note that the overall heat transfer coefficient ranges from about 10 W/m2 · °C for gas-to-gas heat exchangers to about 10,000 W/m2 · °C for heat exchangers that involve phase changes. This is not surprising, since gases have very low thermal conductivities, and phase-change processes involve very high heat transfer coefficients. When the tube is finned on one side to enhance heat transfer, the total heat transfer surface area on the finned side becomes As � Atotal � Afin � Aunfinned (13-6) where Afin is the surface area of the fins and Aunfinned is the area of the unfinned portion of the tube surface. For short fins of high thermal conductivity, we can use this total area in the convection resistance relation Rconv � 1/hAs since the fins in this case will be very nearly isothermal. Otherwise, we should deter- mine the effective surface area A from As � Aunfinned � �fin Afin (13-7) CHAPTER 13 673 TABLE 13–1 Representative values of the overall heat transfer coefficients in heat exchangers Type of heat exchanger U, W/m2 · °C* Water-to-water 850–1700 Water-to-oil 100–350 Water-to-gasoline or kerosene 300–1000 Feedwater heaters 1000–8500 Steam-to-light fuel oil 200–400 Steam-to-heavy fuel oil 50–200 Steam condenser 1000–6000 Freon condenser (water cooled) 300–1000 Ammonia condenser (water cooled) 800–1400 Alcohol condensers (water cooled) 250–700 Gas-to-gas 10–40 Water-to-air in finned tubes (water in tubes) 30–60† 400–850† Steam-to-air in finned tubes (steam in tubes) 30–300† 400–4000‡ *Multiply the listed values by 0.176 to convert them to Btu/h · ft2 · °F. †Based on air-side surface area. ‡Based on water- or steam-side surface area. cen58933_ch13.qxd 9/9/2002 9:57 AM Page 673 where �fin is the fin efficiency. This way, the temperature drop along the fins is accounted for. Note that �fin � 1 for isothermal fins, and thus Eq. 13-7 reduces to Eq. 13-6 in that case. Fouling Factor The performance of heat exchangers usually deteriorates with time as a result of accumulation of deposits on heat transfer surfaces. The layer of deposits represents additional resistance to heat transfer and causes the rate of heat transfer in a heat exchanger to decrease. The net effect of these accumulations on heat transfer is represented by a fouling factor Rf , which is a measure of the thermal resistance introduced by fouling. The most common type of fouling is the precipitation of solid deposits in a fluid on the heat transfer surfaces. You can observe this type of fouling even in your house. If you check the inner surfaces of your teapot after prolonged use, you will probably notice a layer of calcium-based deposits on the surfaces at which boiling occurs. This is especially the case in areas where the water is hard. The scales of such deposits come off by scratching, and the surfaces can be cleaned of such deposits by chemical treatment. Now imagine those min- eral deposits forming on the inner surfaces of fine tubes in a heat exchanger (Fig. 13–9) and the detrimental effect it may have on the flow passage area and the heat transfer. To avoid this potential problem, water in power and process plants is extensively treated and its solid contents are removed before it is allowed to circulate through the system. The solid ash particles in the flue gases accumulating on the surfaces of air preheaters create similar problems. Another form of fouling, which is common in the chemical process indus- try, is corrosion and other chemical fouling. In this case, the surfaces are fouled by the accumulation of the products of chemical reactions on the sur- faces. This form of fouling can be avoided by coating metal pipes with glass or using plastic pipes instead of metal ones. Heat exchangers may also be fouled by the growth of algae in warm fluids. This type of fouling is called biological fouling and can be prevented by chemical treatment. In applications where it is likely to occur, fouling should be considered in the design and selection of heat exchangers. In such applications, it may be 674 HEAT TRANSFER FIGURE 13–9 Precipitation fouling of ash particles on superheater tubes (from Steam, Its Generation, and Use, Babcock and Wilcox Co., 1978). cen58933_ch13.qxd 9/9/2002 9:57 AM Page 674 necessary to select a larger and thus more expensive heat exchanger to ensure that it meets the design heat transfer requirements even after fouling occurs. The periodic cleaning of heat exchangers and the resulting down time are ad- ditional penalties associated with fouling. The fouling factor is obviously zero for a new heat exchanger and increases with time as the solid deposits build up on the heat exchanger surface. The fouling factor depends on the operating temperature and the velocity of the fluids, as well as the length of service. Fouling increases with increasing tem- perature and decreasing velocity. The overall heat transfer coefficient relation given above is valid for clean surfaces and needs to be modified to account for the effects of fouling on both the inner and the outer surfaces of the tube. For an unfinned shell-and-tube heat exchanger, it can be expressed as � R � (13-8) where Ai � �Di L and Ao � �Do L are th