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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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 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,substances,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 pure 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 scope 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.,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 tiny 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-transfer 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/m,2,.,C.,Although attempts are sometimes made to realize practical benefits 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 comparison 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,Two forces remaining acting on the control volume are shear force and gravity in the direction of flow.,Integration of the equation between limits,u,y,=0,y,=0 gives the velocity distribution,average velocity across entire film,flow,rate,of the condensate passing through the cross section at,x,and,The rate of heat-transfer,The rate of the heat transfers from a fluid to,the wall by the conduction,Integrating between limits,=0 for,x,=0,=,for,x,=,x,The local heat-transfer coefficient across the condensate film can be derived,based on the Newtonian law of cooling and the thermal conduction,(4.5-3),(13-12),so,The local heat-transfer coefficient varies with the position from the entrance.The mean individual coefficient is attainable,However,for laminar flow,experimental data are about 20%above Eq,.(4.5-12),(4.5-12),or,Hence,the final recommended expression for vertical surfaces in laminar flow is,Horizontal 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-type condensation on a single horizontal tubes.,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 equation below,(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 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 horizo
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