Transcription of Heat Exchanger Effectiveness
1 1 heat Exchanger Effectiveness ()lmTmTFUATUAQ = =()()()()22112211lnTTTTTTTTTlm = To calculate Q, we need both inlet and outlet temperatures:1T 2T 2T1 TWhat if the outlet temperatures are unknown? calculate the performance of a given heat Exchanger . Faith A. Morrison, Michigan Tech :1. guess outlet temperatures2. calculate Tlm, FT3. calculate Q4. calculate Qfrom energy balance5. compare, adjust, calculate unknown outlet temperatures:This tedious procedure can be simplified by the definition of heat - Exchanger Effectiveness , . Faith A. Morrison, Michigan Tech Exchanger EffectivenessConsider a counter-currentdouble-pipe heat Exchanger :coTciT hoThiThiThoTciTcoTdistance along the Exchanger Faith A.
2 Morrison, Michigan Tech balance cold side:()()cicocoldpcoldinTTmCQQ ==,Energy balance hot side:()()hihohotphotinTTmCQQ = =,()()()()hchihocicocoldphotpTTTTTTmCmC = = Faith A. Morrison, Michigan Tech profile in a double-pipe heat Exchanger :xeTTTT011 = =mCmCRUpp 1 120 Faith A. Morrison, Michigan Tech U.** REVIEW OF LECTURE 7 ** REVIEW OF LECTURE 7 ** , T' (oC) TNote that the temperature curves are only approximately '2== == = LxLeTTTT011 11 TTTT Faith A. Morrison, Michigan Tech U. Faith A. Morrison, Michigan Tech U. =mCmCRLULpp 1 120 ** REVIEW OF LECTURE 7 ** REVIEW OF LECTURE 7 **4hiThoTciTcoTdistance along the exchangerhT cT Case 1:()()hccoldphotpTTmCmC > >cold fluid = minimum fluid Faith A.
3 Morrison, Michigan Tech want to compare the amount of heat transferred in this case to the amount of heat transferred in a PERFECT heat along the exchangerIf the heat Exchanger were perfect, Thi=Tco =A()()cihicoldpATTmCQ = =this temperature difference only depends on inlet temperaturescold side: Faith A. Morrison, Michigan Tech = AQQ heat Exchanger Effectiveness , ()()cihicoldpTTmCQ = cold fluid = minimum fluidif is known, we can calculate Q without iterations Faith A. Morrison, Michigan Tech along the exchangerhT cT Case 2:()()hccoldphotpTTmCmC < <hot fluid = minimum fluid Faith A.
4 Morrison, Michigan Tech the heat Exchanger were perfect, Thi=Tco =A()()cihihotpATTmCQ = =this temperature difference only depends on inlet temperatureshot side:hiTcihoTT=coTdistance along the Exchanger Faith A. Morrison, Michigan Tech U. = AQQ heat Exchanger Effectiveness , ()()cihihotpTTmCQ = hot fluid = minimum fluidif is known, we can calculate Q without iterations()()cihipTTmCQ =min in general, Faith A. Morrison, Michigan Tech where do we get ?The same equations we use in the trial-and-error solution can be combined algebraically to give as a function of (mCp)min, (mCp) relation is plotted in Geankoplis, as is the relation for co-current flow.
5 ()()()()()()()() = minminminmaxminmin1maxmin111ppppppmCmCmC UAppmCmCmCUAemCmCe counter-current flow: Faith A. Morrison, Michigan Tech 4thed., p299counter-currentco-currentnote: Geankoplis Cmin=(mCp)minHeat Exchanger Effectiveness forDouble-pipe or 1-1 shell -and-Tube heat Exchangers Faith A. Morrison, Michigan Tech ExamCM 310 November 16, 19983. (25 points) Water flowing at a rate of kg/s enters theinside of a countercurrent, double-pipe heat Exchanger at 300K andis heated by an oil stream that enters at 385K at a rate of heat capacity of the oil is kJ/kg K, and the average heatcapacity of water over the temperature range of interest is K.
6 The overall heat -transfer coefficient of the Exchanger is300 W/m2 K, and the area for heat transfer is m2. What is thetotal amount of heat transferred? Faith A. Morrison, Michigan Tech U.
