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1、4.3 Principles of Heat Flow in Fluids Heat transfer from a warmer fluid to a cooler fluid, usually through a solid wall separating the two fluids, is common in chemical engineering practice. The heat transferred may be latent heat accompanying a phase change such as condensation or vaporization, or
2、it may be sensible heat from the rise or fall in the temperature of a fluid without any phase change.Heat is transferred between warm and cool fluids by conduction and convection. 4.3.1 Typical Heat-Exchange Equipment Typical heat-exchange equipmentSingle-pass shell-and-tube condenserIt consists ess
3、entially of a bundle of paralleltubes A, the ends of which are expanded into tube sheets B1 and B2. The tube is inside a cylindrical shell C and is provided with two channels D1 and D2, one at each end, and two channel covers E1 and E2. Steam and other vapor is introduced through nozzle F into the s
4、hell-side space surrounding the tubes, condensate is withdrawn through connection G, and any noncondensable gas that might be enter with the inlet vapor is removed through vent K. connection G leads to a trap, which is adevice that allows flow of liquid but holds back vapor.The fluid to be heated is
5、 pumped through connection H into channel D2.lSingle-pass shell-and-tube condenserIf the vapor entering the condenser is notsuperheated and the condensate is not subcooled,the temperature throughout the shell-side of thecondenser is constant. The temperature of the fluid in the tubes increases conti
6、nuously as the fluid flows through the tubes. The temperatures of the condensing vapor and of the liquid are plotted against the tube length. The horizontal line represents the temperature of the condensing vapor, and the curved line below it represents the rising temperature of the tube-side fluid.
7、t1t2Temperature CLength of tube LtTemp of condensing vapor TTemp of cool fluid Double-tube heat exchangerIt is assembled of standard metal pipe and standarized return bends and return heads. shown in figure. Double-pipe exchanger are useful when notmore than 9 to 14 m2 of surface is required. One fl
8、uid flows through the inside pipe and second fluid through the annular space between the outside and inside pipes.For larger capacities , more elaborate shell-and-tube exchangers, containing up to thousand of square meter of area, are used.Countercurrent and parallel-current flows The two fluids ent
9、er at different ends of the exchanger and pass in opposite directions through the unit. It is called counterflow or countercurrent flow. The temperature-length curves for this case shown in figure.If the two fluids enter at the same end of the exchanger and flow in the same direction to the other en
10、d, the flow is called parallel. The temperature -length curves for parallel flow are shown in Figure The flow type with the counterflow is commonly used. Parallel flow is rarely used in a single-pass exchanger. As inspection of distribution of temperature show, Parallel flow is not possible to bring
11、 the exit temperature of one fluid nearly to the entrance temperature of the other， and the heat that can be transferred is less than that possible in countercurrent flow. The parallel flow may be used in following situation:lIn special situation where it is necessary to limit the maximum temperatur
12、e of the cooler fluid;lWhere it is important to change the temperature of at least one fluid rapidly.4.3.2 Energy Balances Enthalpy balances in heat exchangersHeat transfer to or from the ambient is notdesired in practice, and it is usually reduced to a small magnitude by suitable insulation. It is
13、customary to neglect it in comparison with the heat transfer through the wall of the tubes from the warm fluid to the cold fluid.For the warm fluid, it can lose heat. q=mh(Hh1-Hh2)For the cold fluid, it can gain heatq=mc(Hc2 - Hc1) Neglecting the heat transfer with the ambient. The heat lost by the
14、warm fluid is gained by the cold fluid, thereforeq=mh(Hh1-Hh2)= mc(Hc2 - Hc1)(4.3-3) q=mhCph (Th1-Th2)= mcCpc (tc2 - tc1)(11-5)If constant specific heats are assumed, the overall enthalpy balance for a heat exchanger becomes(4.3-5) Enthalpy balances in total condensers For a condenserEquation (4.3-7
15、) is based on the assumption that the vapor enters the condenser as saturated vapor (no superheat) and the condensate leaves at condensing temperature without being further cooled. (4.3-7) If either of these sensible-heat effects is important, it must be accounted for by an added term in the left-ha
16、nd side of Eq. (4.3-7). For example, if the condensate leaves at a temperature t that is less than T, the condensing temperature of the vapor, Eq. (4.3-7) must be written (4.3-7) 4.3.3 Heat Flux and Heat-Transfer Coefficients Heat fluxIn many types of heat-transfer equipment the transfer surfaces ar
17、e constructed from tubes. Heat flux may be based either on the inside area or the outside area of the tubes.Average temperature of fluid streamThe temperature so defined is called the average temperature.Because the temperature gradients throughout the cross section of the stream, it is necessary to
18、 state what is meant by the temperature of the stream.The temperature plotted figure above are average stream temperatures.Overall heat-transfer coefficientIt is reasonable to expect the heat flux to beproportional to a driving force. The drivingforce is taken as t=T-t,which is the overall local tem
19、perature difference. It is clear from distribution of temperature that t can vary considerably from point to point along the tube, and, therefore, the flux also varies with tube length. The local flux dq/dA is related to the local value of t by the equationThe quantity U is called the local overall
20、heat-transfer coefficient. (4.3-9) It is necessary to specify the area. If A is taken as the outside tube area Ao, U becomes a coefficient based on that area and is written Uo.Likewise, if the inside area Ai is chosen, the coefficient is also based on that area and is denoted by Ui.Mean temperature
21、difference To apply Eq.(4.3-9) to the entire area of a exchanger, certain simplifying assumptions are accepted. (1)the overall coefficient U is constant;(2)the specific heats of the hot and cold fluids are constant;(4)the flow is steady and either parallel or countercurrent.The most questionable of
22、these assumption is that of a constant overall coefficient. (3)heat exchange with the ambient is negligible;The coefficient does in fact vary with the temperatures of the fluids, but its changes with temperature is gradual, so that when the temperature ranges are moderate, the assumption of constant
23、 U is not seriously in error. If T and t are plotted against q,the straight lines are obtained. So the slope of the graph of t vs q is constant. Therefore(4.3-11 )(4.3-12)Elimination of dq from Eqs.(4.3-9) and (4.3-11) givesIf U is constant, the equation can be integrated over the limits A and 0 for
24、 A and t1 and t2 for t (4.3-13)Equation (4.3-13) can be writtenEquation (4.3-15) defines the logarithmic mean temperature difference, When t1 and t2 are nearly equal, their arithmetic average can be used.(4.3-15)WhereIf one of the fluids is at constant temperature, asin a condenser, no difference ex
25、ists between countercurrent flow, parallel flow, or multipassflow, and equation(4.3-15) applies to all of them.The LMTD is not always the correct mean temperature difference to use. It should not be used when U changes appreciably. Individual heat-transfer coefficients The overall coefficient depend
26、s upon many variables. Consider the local overall coefficient at a specific point in the double-tube exchanger shown inFigure. Metal wall of the tube separates the warm fluid on the right from the cold fluid.Assume that the Reynolds numbers of the two fluids are sufficiently large to ensure turbulen
27、t flow and that both surfaces of the inside tube are clear of dirt or scale. The temperature profile is divided into three separate parts, one through each of the two fluids and the other through the metal wall. The overall effect, therefore, should be studied in terms of these individual parts. The
28、 temperature gradient is large at the wall and through the viscous sublayer, small in the turbulent core, and rapidly change in the buffer zone. Basically, the reason for this is that heat must flow through the viscous sublayer by conduction, which call for a steep temperature gradient in most of fl
29、uids because of the low thermal conductivity, whereas the rapidly moving eddies in the core are effective in equalizing the temperature in the turbulent zone. The overall resistance to the flow of heat from the warm fluid to the cold fluid is a result of three separate resistances operating in serie
30、s. The wall resistance is small in comparison with that of the fluids.The overall coefficient is best studied by analyzing it in terms of the separate resistances. The separate resistances can then be combined to form the overall coefficient. The individual heat-transfer coefficient h is defined gen
31、erally by the equation(4.3-18 )Equation(4.3-18), when applied to the two fluids of Fig.4-10for the cold side (outside of tube)(11-24)for the warm side Heat transfers from warm fluid to cold fluid across a wall of metal. for the warm side The rates of heat transfer in three zones can be represent byT
32、he rate of heat flow through the series of resistances are the ratio of the overall temperature drop to the overall resistance the overall resistance in series are the sum of individual resistancesIf both sides of the resulting equation are multiplied by dA P241equation(11-28)If that the surface is
33、arbitrarily based on the outside area dAo(4.3-32 )P242(4.3-33)If that the surface is arbitrarily based on the inside area dAi. Fouling factor In actual service, heat transfer surfaces do not remain clean. Scale, dirt, and other solid deposits form on one or both sides of the tubes, provide additiona
34、l resistances to heat flow, and reduce the overall coefficient. Special cases of the overall coefficientOne individual coefficient , hi , is large numericallyin comparison with the other , ho , and that fouling effects are negligible. Sometimes one particular area is more convenient than others. Als
35、o, assuming the term representing the resistance of the metal wall is small in comparison with 1/ho, the ratios do/di and do/dm have so little significance that they can be disregarded, and Eq.(4.3-32) can be replaced by the simpler form In such a case it is advantageous to base the overall coeffici
36、ent on that area whichcorresponds to the largest resistance, or the lowest value of h.(4.3-39) For thin-walled tubes of large diameter, flat plates. Eq(4.3-39) can be used for the overall coefficient, and Ui and Uo are identical.Sometimes one coefficient, say, ho, is so very small in comparison with
37、 both b/k and the other coefficient hi. The larger resistance is called the controlling resistance, and it is sufficiently accurate to equate the overall coefficient to the small individual coefficient.probleml A trap is a device that allows ( ) but ( ).l Parallel flow is rarely used in a single-pas
38、s exchanger because it is ( ) with this method of flow to bring the exit temperature of one fluid nearly to the entrance temperature of the other and the heat transferred is ( ) than that possible in countercurrent flow. ( ) If the inlet and outlet temperatures of fluids are fixed, the LMTD of count
39、ercurrent flow is always larger than that of parallel-current flow without phase change( ) If the inlet and outlet temperatures of fluids are fixed, the LMTD of countercurrent flow is always larger than that of parallel-current flow lIf ho is very small in comparison with both k/b and the other coef
40、ficient hi，the correlation between the overall coefficient and individual coefficient will be（ ）. A）U= ho B) U= hi C) U= b/k D）U holHeat transfer by two fluids，if one of the fluids is at constant temperature, difference exists between countercurrent flow and parallel flow.( )l ho is a film coefficie
41、nt of shell side and hi is a film coefficient of tube side, if ho is much larger than hi the temperature of the metal wall will close to ( )Air flows along the tube and saturated vapor passes through the shell in a shell-tube exchanger. In order to enhance heat transfer, which way is feasible in pra
42、ctice as follows. A）increase vapor velocity; B) employ superheated vapor C) increase air velocity. D) set up the baffle in the shell.Problem 1 A cooling coil, consisting of a single length through which water is circulated, is provided in the reactor vessel, the contents of which are kept uniformly
43、at 360 K by means of stirrer. The inlet and outlet temperatures of the cooling water are 280 K and 320 K respectively. What would the outlet water temperature become if the length of the cooling coil were increased by 4 times ? Assume the overall heat transfer coefficient to be constant over the len
44、gth of the tube and independent of the water temperature. Problem 2 In an oil cooler, 60g/s of hot oil enters a thin metal pipe of diameter 25mm. An equal mass of cooling water flows through the annular space between the pipe and a larger concentric pipe, the oil and water moving in opposite directi
45、ons. The oil enters at 420 K and is to be cooled to 320 K. If the water enters at 290 K, what length of pipe will be required ? Take coefficients of 1.6kW/m2K on the oil side and 3.6kW/m2K on the water side and 2.0kJ/kgK for the specific heat of the oil.Problem 3 In order to warm 0.5kg/s of a heavy
46、oil from 311 K to 327 K, it is passed through tubes of inside diameter 19mm and length 1.5 m forming a bank, on the outside of which steam is condensing at 373 K. how many tubes will be needed? For condensing steam, ho=10000W/m2K; and for oil, hi=250W/m2K. the specific heat of oil may be taken as 2.1kJ/kg K.
