CONDENSER DESIGN Condensation on horizontal tubes (Nusselt theory) Heat transfer coefficient is obtained by h=0.728[kL3 ϸL(ϸL- ϸV)g ƛ /µL (Tv –TW) D] Where kL – thermal conductivity of liquid ϸL – density of liquid ϸV –density of vapour ƛ – latent heat of condensation of steam g- Gravitational acceleration =9.81m/s2 µL – viscosity of liquid TW – temperature of surface Tv –temperature of vapour D –diameter The above eqn applies for a single tube or single row of tubes. When tubes are stacked over each other the heat coefficient is calculated as H=h NR-1/6 Nr- no of rows of horizontal tubes
As the properties(kL, ϸL, µL) of the condensate changes with the temperature ,so some modifications are being done to compensate for that . Tf =βTw +(1- β)Tsat Where β-weight factor (recommended in the literature from 0.5 to 0.75) Condensate sub cooling The temp in the condensate film drops from Tsat at the liquid vapour interface to Tw at the wall. Therefore the avg condensate temperature, TL is less than Tsat, and hence the condensate leaving the surface is sub cooled. Accounting for sub cooling, the rate of heat transfer is Q=W ƛ +WCp,L (Tsat - TL)= Whfg*
Cp,L heat capacity of condensate W- condensation rate to account for both sub cooling and inertial effects h/hNu =(1+(0.683 -0.228 PrL-1)Ԑ)^0.25 hNu - heat transfer coeff by basic nusselt theory Ԑ- Cp,L (Tsat - Tw)/ƛ PrL - Cp,L µL/ kL above eqn is valid for Pr>0.6 Q=NhD0L∏(Tsat - Tw) Tw=…………… Then Tf can be obtained by the eqn given above Mass flow rate of water =ϸAu U –flow velocity A of tube can be calculated from the above eqn And the total area= N∏DL And the condensation rate –Q/hfg* Some FACTS to remember
In drop wise condensation Heat transfer coefficient is considerably high as compared to film condensation. The reason being the direct contact of vapor with the cooler surface. The effectiveness of a condenser can be calculated as (1 - eNTU) NTU=(UA/Cmin) Cmin=(mCp)min
References –process heat transfer principles and applications by ROBERT W SERTH Heat and mass transfer –cengel and ghajar
