 ञर्ँपकट after the lecture आज�你知道, में दिनी स्पार कर of I'm Ganesh Baghlaw working as a assistant professor in क्नाप्ली के उंसष्टर। clearing the जोक सेटाcontrol At the end of Volume. यह तत्शाच्दरी आपतार औं है Yesiseesheesheesheesheesheesheeshees आप टकेण प्र के लेके अगलाग strand各 Auf deriving of the equation. we required to know about the NTU so if we don't know the outlet temperatures of the heat exchanger then we can adopt the NTU approach in the NTU approach the NTU term is there which is the long form of NTU is number of transfer units it is a dimensionless parameter and it is expressed as NTU is the ratio of heat capacity rate of heat exchanger to capacity rate of fluid which is equal to UA by C minimum so if we will see this relation we will come to know that NTU is directly proportionate to area so with more and more NTU number the size of the heat exchanger will be now we will do the analysis of heat exchanger by using the NTU approach for parallel flow. Theta O by Theta I is equal to minus UA into bracket 1 by CH plus 1 by CC now we will take this as a reference equation for deriving the NTU approach equation now I will substitute for Theta relation so ln THO minus TCO divided by THI minus TCI which is equal to minus UA into bracket 1 by CH plus 1 by CC now here we will try to get the relations for THO and TCO since we know the effectiveness equation which is equal to actual heat transfer to the maximum heat transfer so we will consider CC cold fluid cold fluid outlet temperature inlet temperature divided by C minimum into bracket THI minus TCI we can simplify this relation for TCO so TCO will become effectiveness into C minimum by CC into bracket THI minus TCI plus TCI similarly we can write the effectiveness equation for hot fluid so it will be CH into bracket THI minus THO divided by C minimum into bracket THI minus TCI since heat transfer for hot fluid and cold fluid is same which is nothing but actual heat transfer actually heat transfer now if this is simplified then if we will simplify this relation we may get for THO so that we can substitute TCO and THO in the equation third in the equation third so simplifying this the THO will be equal to THI minus epsilon C minimum by CH into bracket THI minus TCI now substituting the values of TCO and THO in equation third the equation will be THI minus epsilon C minimum by CH into bracket THI minus TCI so here it is ln so we have substituted it for THO now for TCO it is minus epsilon C minimum by CC into bracket THI minus TCI plus TCI so this is for TCO total divided by THI minus TCI which is equal to minus UA into bracket 1 by CH minus 1 by CC now we can simplify this as THI minus TCI minus epsilon C minimum by CH THI minus TCI minus epsilon C minimum by CC THI minus TCI divided by THI minus TCI which is equal to e to the power minus UA into bracket 1 by CH minus 1 by CC so this can be written as now 1 minus epsilon C minimum by CH minus epsilon C minimum by CC which is equal to e to the power minus UA by here we can take CC common 1 plus CH 1 plus CC by CH so after simplifying we get epsilon C minimum by CC into bracket 1 plus CC by CH is equal to 1 minus e raise to minus UA by CC into bracket 1 plus CC by CH so effectiveness is equal to 1 minus e to the power minus UA by CC into bracket 1 plus CC by CH total divided by C minimum by CC into bracket 1 plus CC by CH now let capital C is equal to C minimum by C maximum in this equation we can assume CC is equal to C minimum then effectiveness will be equal to 1 minus e to the power minus UA by C minimum here we assume capacity rate of cold fluid as C minimum into bracket 1 plus C minimum by CH will be C maximum divided by C minimum by CC is C minimum into bracket 1 plus C minimum by C maximum instead of CC we can assume CH also for both the cases the equation will be same the derivation will be same so 1 minus e to the power minus now as we know this ratio as NTU UA by C minimum is NTU into bracket 1 plus capital C divided by this will be 1 so 1 plus capital C so this is the relation for NTU so for effectiveness of heat exchanger effectiveness of heat exchanger we got NTU relation we got NTU relation so this case is to be adopted if the temperatures all temperatures are not known we can measure the inlet temperature and outlet temperature in that case we can adopt the NTU approach for further study you can refer fundamentals of heat and mass transfer by INCROPERA DEVILD thank you