流體力學與傳熱 ：4-3 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4、he shell-side space surrounding the tubes, condensate is withdrawn through connection G, and any noncondensable gas that might be enter with the inlet vapor is removed through vent K.,connection G leads to a trap, which is a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.,Single-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 incre

6、ases 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-s

7、ide fluid.,t2,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 is required.,One fluid flows through the inside pipe and second fluid through the

8、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 enter at different ends of the exchanger and pass in opposite di

9、rections 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 end, the flow is called parallel.,The temperature -length curv

10、es 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 the exit temperature of one fluid nearly to the entrance te

11、mperature 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:,In special situation where it is necessary to limit the maximum temperature of the cooler fluid;,Where it is important to change the t

12、emperature 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 by suitable insulation.,It is customary to neglect it in comparison with the heat trans

13、fer 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),Neglecting the heat transfer with the 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),(11-5),If constant s

14、pecific heats are assumed, the overall enthalpy balance for a heat exchanger becomes,(4.3-5),Enthalpy balances in total condensers,For a condenser,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

15、 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-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 va

16、por, Eq. (4.3-7) must be written,(4.3-7),4.3.3 Heat Flux and Heat-Transfer Coefficients,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

17、 stream,The temperature so defined is called the average temperature.,Because the 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 h

18、eat-transfer coefficient,It is reasonable to expect the heat flux to be proportional 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

19、, and, therefore, the flux also varies with tube length.,The local flux dq/dA is related to the local value of t by the equation,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 c

20、oefficient 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 difference,To apply Eq.(4.3-9) to the entire area of a exchanger, certain simplifying assumptions are accepted. (1)the overall

21、 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 these assumption is that of a constant overall coefficient.,(3)heat exchange with the ambient is negligible;,The coefficien

22、t 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 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

23、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) gives,If U is constant, the equation can be integrated over the limits A and 0 for A and t1 and t2 for t,(4.3-13),Equation (4.3-13) can be written,Equation (4.3-15) defines the logarithmic mean temper

24、ature difference, When t1 and t2 are nearly equal, their arithmetic average can be used.,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(4.3-15) applies to all of them.,The LMTD is no

25、t 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 point in the double-tube exchanger shown in Figur

26、e.,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.,The temperature profile is divided into three

27、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, small in the turbulent core, and rapidly chang

28、e 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 eddies in the core are effective in equalizing the

29、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 overall coefficient is best studied by analyzing

30、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,(4.3-18 ),Equation(4.3-18), when applied to the two fluids of Fig.4-10,for the cold side (outside of

31、 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 by,The rate of heat flow through the series of resistances are the ratio of the overall temperature drop to the overall r

32、esistance,the overall resistance in series are the sum of individual resistances,If both sides of the resulting equation are multiplied by dA,P241,equation(11-28),If that the surface is arbitrarily based on the outside area dAo,(4.3-32 ),P242,(4.3-33),If that the surface is arbitrarily based on the

33、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 flow, and reduce the overall coefficient.,Special cases of the overall coefficient,One i

34、ndividual 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 representing the resistance of the metal wall is small in comparison with 1/ho, the rat

35、ios 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 corresponds to the largest resistance, or the lowest value of h.,(4.3-39),For thin-wa

36、lled 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 both b/k and the other coefficient hi.,The larger resistance is called the controlling resistance, and i

37、t is sufficiently accurate to equate the overall coefficient to the small individual coefficient.,problem,A trap is a device that allows ( ) but ( ).,Parallel flow is rarely used in a single-pass exchanger because it is ( ) with this method of flow to bring the exit temperature of one fluid nearly t

38、o 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 countercurrent flow is always larger than that of parallel-current flow without phase change,( ) If the inlet a

39、nd outlet temperatures of fluids are fixed, the LMTD of countercurrent flow is always larger than that of parallel-current flow,If ho is very small in comparison with both k/b and the other coefficient hi，the correlation between the overall coefficient and individual coefficient will be（ ）. A）U= ho

40、B) U= hi C) U= b/k D）U ho,Heat transfer by two fluids，if one of the fluids is at constant temperature, difference exists between countercurrent flow and parallel flow.( ),ho is a film coefficient of shell side and hi is a film coefficient of tube side, if ho is much larger than hi the temperature of

41、 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 vapor C) increase air velocity. D) set up the baffle in the shell.,Problem