1、4.5 Heat Transfer to Fluids with Phase Change Processes of heat transfer accompanied by phase change are more complex than simple heat exchange between fluids.A phase change involves the addition or subtraction of considerable quantities of heat at constant or nearly constant temperature.The rate of
2、 phase change may be governed by the rate of heat transfer,but it is often influenced by the rate of nucleation of bubbles,drops,or crystals and by the behavior of the new phase after it is formed.The condensing vapor may consist of a single substance,a mixture of condensable and noncondensable subs
3、tances,or a mixture of two or more condensable vapors.Friction losses in a condenser are normally small,so that condensation is essentially a constant-pressure process.The condensing temperature of a single pure substance depends only on the pressure,and therefore the process of condensation of a pu
4、re substance is isothermal.Also,the condensate is a pure liquid.Mixed vapors,condensing at constant pressure,condense over a temperature range and yield a condensate of variable composition until the entire vapor stream is condensed,The condensation of mixed vapors is complicated and beyond the scop
5、e this text.Dropwise and film-type condensation A vapor may condense on a cold surface in one of two ways,which are well described by the terms dropwise and film-type.In film condensation the liquid condensate forms a film of liquid that flows over the surface of the tube under the action of gravity
6、.It is the layer of liquid interposed between the vapor and the wall of the tube which provides the resistance to heat flow and therefore which fixes the value of the heat-transfer coefficient.In dropwise condensation the condensate begins to form at microscopic nucleation sites.Typical sites are ti
7、ny pits,scratches,and dust specks.The drops grow and coalesce with their neighbors to form visible fine drops.The fine drops,in turn,coalesce into rivulets,which flow down the tube under the action of gravity,sweep away condensate,and clear the surface for more droplets.Because of this the heat-tran
8、sfer coefficient at these areas is very high;the average coefficient for dropwise condensation may be 5 to 8 times that for film-type condensation.The average coefficient obtainable in pure dropwise condensation is as high as 114kW/m2.C.Although attempts are sometimes made to realize practical benef
9、its from these large coefficients by artificially inducing dropwise condensation.This type of condensation is so unstable and the difficulty of maintaining it so great that the method is not common.Also the resistance of the layer of condensate even in film-type condensation is ordinarily small in c
10、omparison with the resistance inside the condenser tube,and increase in the overall coefficient is relatively small when dropwise condensation is achieved.Coefficients for film-type condensation The basic equation for the rate of heat transfer in film-type condensation were first derived by Nusselt
11、Two forces remaining acting on the control volume are shear force and gravity in the direction of flow.dyygdudyduldxglydxyy或Integration of the equation between limits uy=0,y=0 gives the velocity distribution221yyguy321112020gdyyygdyuuyaverage velocity across entire film flowrate of the condensate pa
12、ssing through the cross section at x 3132gumdgdm22andThe rate of heat-transferdgdm22The rate of the heat transfers from a fluid to the wall by the conductionwsttdxkdg1224124gtkxIntegrating between limits =0 for x=0,=for x=x The local heat-transfer coefficient across the condensate film can be derive
13、d,based on the Newtonian law of cooling and the thermal conduction41324txgkkhx(4.5-3)(13-12)so413204341tLgkdxhLhLxThe local heat-transfer coefficient varies with the position from the entrance.The mean individual coefficient is attainable4132943.0tLgkhHowever,for laminar flow,experimental data are a
14、bout 20%above Eq.(4.5-12)(4.5-12)orHence,the final recommended expression for vertical surfaces in laminar flow is413213.1TLkghHorizontal tubes The following equation applies to single horizontal tubes(4.5-14)The equation can be used as they stand for calculating heat-transfer coefficients for film-
15、type condensation on a single horizontal tubes.4132725.0tdgkho For film-type condensation on a vertical stack of horizontal tubes,where the condensate falls cumulatively from tube to tube and the total condensate from the entire stack finally drops from the bottom tube.It is more accurate to use the
16、 equation below 4132725.0tdNgkho(4.5-16)For vertical tubes,the equations were derived on the assumption that the condensate flow was laminar.For long tubes,the condensate film becomes sufficiently thick and its velocity sufficiently large to cause turbulence in the low portions of the tube.Also,even
17、 when the flow remains laminar throughout,coefficients measured experimentally are about 20 percent larger than those calculated from the equation.This attributed to the effect of ripples on the surface of the falling film.In general,the coefficient of a film condensing on a horizontal tube is consi
18、derably larger than that on a vertical tube under similar conditions unless the tubes are very short or there are many horizontal tubes in the stack.Vertical tubes are preferred when the condensate must be appreciably subcooled below its condensation temperature.effect of Noncondensible gases When a
19、 multicomponent mixture contains a noncondensing gas,the rate of condensation is seriously reduced.As in the condensation of a mixture of condensable vapors,the condensing molecules must diffuse through a film of noncondensing gas which does not move toward the condensate surface.As condensation pro
20、ceeds,the relative amount of this inert gas in the vapor phase increases significantly.The presence of even small amounts of noncondensing gas in a condensing vapor seriously reduces the rate of condensation.Problem A vapor may condense on a cold surface in two ways:()and()the average coefficient fo
21、r dropwise condensation is()than that for film-type condensation.In general,the coefficient of a film condensing on a horizontal tube is()than that on a vertical tube under similar conditionsIt is difficulty to benefit practically from a dropwise condensation because this type of condensation is(),a
22、nd increase in the coefficient of dropwise condensation()the overall coefficient.the presence of even small amounts of noncondensing gas in a condensing vapor()the rate of condensation.In general,the coefficient of a film condensing on a single horizontal tube is()than that on a stack of horizontal
23、tubes under similar conditionsProblem 1 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 directions.The oil enters at 420 K and
24、 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.What would the length of the tubes become if the flow rate of oil was increased to
25、 2 times.(keep the outlet temperature of the oil unchanging)2.117 vapor is condensing on the outside of tubes to warm 500kg/h of air from 20 to 80,air is passed through tubes of 191mm forming a bank at 15m/s.the individual coefficients of the tube-side and shell-side are 80 W/m2 and 1104 W/m2,respec
26、tively.how many tubes will be needed and what is the overall coefficient?How would the outlet temperature and overall coefficient change if the mass flowrate were increased by 20%?Properties of the air:density=1.1kg/m3;specific heat=1.0 kJ/kg;viscosity=210-5Pas.The conductivity of metal wall=45W/m N
27、eglecting the heat loss and thermal resistance of scaleProblem 3 7.5kg/s of pure isobutane are to be condensed at a temperature of 331.7 K in the shell-side of a vertical tubular exchanger using a water inlet temperature of 301 K and flow rate of 36.7kg/s.It is to use 19 mm outside diameter tubes of
28、 1.6 mm wall and these may be 4.88m in length.Under these conditions the resistance of the scale may be taken as 0.0005m2 K/W.assuming the individual heat transfer coefficient of inside tubes is 4.2kW/m2 K.(1)it is required to determine the number of the tubes;(2)if two tube-side pass may be used,what is the outlet temperature of the water.The latent heat of vaporization of isobutane is 286kJ/kg;the temperature drop across the condensate film is 2 K;the physical properties of the condensate film:k=0.13W/m K,=508kg/m3,=0.000136N.s/m2.412313.1fffTLgkh
