化工原理英文課件：chapter 4-2 Principles of Heat Flow in Fluids

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 equipment Single-pass shell-and-tube condenser It consists

3、essentially of a bundle of parallel tubes 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 t

4、he shell-side space surrounding the tubes, condensate is withdrawn through connection G, and any noncondensable gas that might be enter with the inlet vapor is removed through vent K. connection G leads to a trap, which is a device that allows flow of liquid but holds back vapor. The fluid to be hea

5、ted is pumped through connection H into channel D2. lSingle-pass shell-and-tube condenser If the vapor entering the condenser is not superheated and the condensate is not subcooled, the temperature throughout the shell-side of the condenser is constant. The temperature of the fluid in the tubes incr

6、eases continuously 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-

7、side fluid. t1 t2 Temperature C Length of tube L t Temp of condensing vapor T Temp of cool fluid Double-tube heat exchanger It is assembled of standard metal pipe and standarized return bends and return heads. shown in figure. Double-pipe exchanger are useful when not more than 9 to 14 m2 of surface

8、 is required. One fluid 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 f

9、lows The two fluids enter 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 d

10、irection to the other end, 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

11、 is not possible to bring 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 li

12、mit the maximum temperature 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 exchangers Heat transfer to or from the ambient is not desired in practice, and it is usually reduced to a small magnitude

13、by suitable insulation. It is 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 heat q=mc(Hc2 - Hc1) Neglecting the heat transfer with t

14、he ambient. The heat lost by the warm fluid is gained by the cold fluid, therefore q=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 con

15、densers For a condenser )( 12 ttcmm pcch Equation (4.3-7) 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,

16、it must be accounted for by an added term in the left-hand 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 )()( 12 ttcmtTcm pccphh (4.3-7) 4.3.3 Heat Flux and Heat- Transfer Coeffi

17、cients Heat flux In many types of heat-transfer equipment the transfer surfaces are constructed from tubes. Heat flux may be based either on the inside area or the outside area of the tubes. Average temperature of fluid stream The temperature so defined is called the average temperature. Because the

18、 temperature gradients throughout the cross section of the stream, it is necessary to state what is meant by the temperature of the stream. The temperature plotted figure above are average stream temperatures. Overall heat-transfer coefficient It is reasonable to expect the heat flux to be proportio

19、nal to a driving force. The driving force is taken as t=T-t,which is the overall local temperature 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

20、related to the local value of t by the equation dq U Tt dA The quantity U is called the local overall 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 insi

21、de area Ai is chosen, the coefficient is also based on that area and is denoted by Ui. Mean temperature 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

22、fluids are constant; (4)the flow is steady and either parallel or countercurrent. The most questionable of 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 chang

23、es with temperature is gradual, so that when the temperature ranges are moderate, the assumption of constant 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 21 t dttt dqq (4.3-11 ) 21 t dttt U t

24、dAq (4.3-12) Elimination of dq from Eqs.(4.3-9) and (4.3-11) gives If U is constant, the equation can be integrated over the limits A and 0 for A and t1 and t2 for t 21 2 1 ln t Uttt A tq (4.3-13) Equation (4.3-13) can be written 21 2 1 ln tm tt qUAUA t t t Equation (4.3-15) defines the logarithmic

25、mean temperature difference, When t1 and t2 are nearly equal, their arithmetic average can be used. 21 2 1 ln m tt t t t (4.3-15) Where If one of the fluids is at constant temperature, as in a condenser, no difference exists between countercurrent flow, parallel flow, or multipass flow, and equation

26、(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 depends upon many variables. Consider the local overall coefficient at a specific po

27、int in the double-tube exchanger shown in Figure. 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 turbulent flow and that both surfaces of the inside tube are clear of dirt or scale.

28、 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 temperature gradient is large at the wall and through the viscous sublayer,

29、 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 fluids because of the low thermal conductivity, whereas the rapidly moving edd

30、ies 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 series. The wall resistance is small in comparison with that of the fluids. The o

31、verall 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 generally by the equation w dq dA h TT (4.3-18 ) Equation(4.3-18), when applie

32、d to the two fluids of Fig.4-10 for the cold side (outside of tube) o o w dq dA h tt i i w dq dA h TT (11-24) for the warm side Heat transfers from warm fluid to cold fluid across a wall of metal. for the warm side wwww w m TtTt dq b R dA The rates of heat transfer in three zones can be represent by

33、 1 ww iwi i ii TTTT dqh TTdA R hdA wwww w m TtTt dq b R dA The rate of heat flow through the series of resistances are the ratio of the overall temperature drop to the overall resistance 1 ww owo o oo tttt dqhtt dA R h dA 1 11 wwww iioo m TTTtttTt dq b UdA hdAh dA dA the overall resistance in series

34、 are the sum of individual resistances 111 iimoo b UdAhdAkdAh dA 1 iimoo dAdAdA UhdAkdAh dA If both sides of the resulting equation are multiplied by dA P241 equation(11-28) oooo iimm dAddAd and dAddAd If that the surface is arbitrarily based on the outside area dAo 11 oo oiimo dbd Uhdkdh (4.3-32 )

35、P242 11 ii iimoo bdd Uhkdh d (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 additional resistances to heat fl

36、ow, and reduce the overall coefficient. Special cases of the overall coefficient One individual coefficient , hi , is large numerically in comparison with the other , ho , and that fouling effects are negligible. Sometimes one particular area is more convenient than others. Also, assuming the term r

37、epresenting 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 coefficient on that area which

38、 corresponds to the largest resistance, or the lowest value of h. 111 oio b Uhkh (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 bot

39、h 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. problem l A trap is a device that allows ( ) but ( ). l Parallel flow is rarely used in a single-pass

40、 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 counte

41、rcurrent 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 co

42、efficient hi，the correlation between the overall coefficient and individual coefficient will be（ ）. A）U= ho B) U= hi C) U= b/k D）U ho lHeat 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 coeff

43、icient 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 practice as follows. A）increase vapor velocity; B) employ superheated vap