HEAT EXCHANGERS-2. Associate Professor. IIT Delhi P.Talukdar/ Mech-IITD

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1 HEA EXHANGERS-2 Prabal alukdar Assoiate Professor Department of Mehanial Engineering II Delhi

2 Multipass and rossflow he subsripts 1 and 2 represent the inlet and outlet, respetively.. and t represent the shell- and tube-side temperatures, respetively

3 and t represent the shell- and tube-side temperatures, respetively

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5 Design with LMD LMD method is very suitable for determining the size of a heat exhanger to realize presribed outlet t temperatures t when the mass flow rates and the inlet and outlet temperatures of the hot and old fluids are speified. With the LMD method, the task is to selet a heat exhanger that will meet the presribed heat transfer requirements. he proedure to be followed by the seletion proess is: Selet-type of fheat Exhanger Determine- Inlet, Oulet temp, Heat transfer rate Using energy balane alulate Δ lm and F if neessary Obtain U alulate A s

6 Alternative of LMD A seond kind of problem enountered in heat exhanger analysis is the determination of the heat transfer rate and the outlet temperatures of the hot and old fluids for presribed fluid mass flow rates and inlet temperatures when the type and size of the heat exhanger are speified. he heat transfer surfae area A of the heat exhanger in this ase is known, but the outlet temperatures are not. Here the task is to determine the heat transfer performane of a speified heat exhanger or to determine if a heat exhanger available in storage will do the job. he LMD method ould still be used for this alternative problem, but the proedure would require tedious iterations, and thus it is not pratial. In an attempt to eliminate the iterations from the solution of suh problems, Kays and London ame up with a method in 1955 alled the effetiveness NU method, whih greatly simplified heat exhanger analysis

7 Effetiveness-NU method Effetiveness. Q ε Q max Atual heat transfer rate Maximum possible heat transfer rate Atual heat transfer rate. Q (,out,in ) h ( h,in h, out ) Maximum temperature differene that an ours Δ max h h,in,in Maximum possible heat transfer. Q max min ( h,in, in )

8 Maximum heat transfer he heat transfer in a heat exhanger will reah its maximum value when (1) the old fluid is heated to the inlet temperature of the hot fluid or (2) he hot fluid is ooled to the inlet temperature of the old fluid. hese two limiting onditions will not be reahed simultaneously unless the heat apaity rates of the hot and old fluids are idential (i.e., ) h ). When h, whih is usually the ase, the fluid with the smaller heat apaity rate will experiene a larger temperature hange, and thus it will be the first to experiene the maximum temperature, at whih point the heat transfer will ome to a halt. Maximum possible heat transfer. Q max min ( h, in, in )

9 Example

10 Example- ontd.

11 Example -ontd. he temperature rise of the old fluid in a heat exhanger will be equal to the temperature drop of the hot fluid when the mass flow rates and the speifi heats of the hot and old fluids are idential.

12 Effetiveness relation parallel-flow double-pipe heat exhanger. Q (,out,in ) h (h,in h, out ) h,out h,in h (,out, in ) ln h,out h,in,out,in UA s m& h 1 ph + m& 1 p ln h,out h,in,out,in UA s 1 + h and after adding and subtrating, in gives ln h,in,in +,in h,in,out,in (,out,in ) h UA s 1 + h simplifies to ln h,out h,in,in,in UA s 1 + h

13 Effetiveness relation We now manipulate the definition of effetiveness to obtain ε. Q. Q max ( min,out ( h,in,in,in ) ),out h,in,in,in ε min aking either or h to be min (both approahes give the same result), the relation above an be expressed more onveniently as ε parallel _ flow UAs min 1 exp 1 + min max 1+ min max ln ε h,out h,in results parallel_ flow,in,in UA s 1 + UA s 1 exp 1 + min 1 + h h h

14 NU Number of transfer units UA s UA NU s. min (m ) p min apaity ratio min max Note that NU is proportional to A s. herefore, for speified values of U and min, the value of NU is a measure of the heat transfer surfae area A s. hus, the larger the NU, the larger the heat exhanger. ε parallel_ flow UAs min 1 exp 1 + min max 1+ min max ε funtion(uas / min,min / max) funtion(nu, )

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16 Effetiveness for heat exhangers (from Kays and London, Ref. 5).

17 Effetiveness for heat exhangers (from Kays and London, Ref. 5).

18 Effetiveness for heat exhangers (from Kays and London, Ref. 5).

19 Disussions 1. he value of the effetiveness ranges from 0 to 1. It inreases rapidly with NU for small values (up to about NU 1.5) but rather slowly for larger values. herefore, the use of a heat exhanger with a large NU (usually larger than 3) and thus a large size annot be justified eonomially, sine a large inrease in NU in this ase orresponds to a small inrease in effetiveness. hus, a heat exhanger with a very high effetiveness may be highly desirable from a heat transfer point of view but rather undesirable from an eonomial point of view. 2. For a given NU and apaity ratio min / max, the ounter-flow heat exhanger has the highest effetiveness, followed losely by the ross-flow heat exhangers with both fluids unmixed.

20 Disussions 3. he effetiveness of a heat exhanger is independent of the apaity ratio for NU values of less than about he value of the apaity ratio ranges between 0 and 1. For a given NU, the effetiveness beomes a maximum for 0 and a minimum for 1. he ase min / max 0 orresponds to max, whih is realized during a phase-hange h proess in a ondenser or boiler. All effetiveness relations in this ase redue to ε ε max 1 - exp(nu) regardless of the type of heat exhanger. Note that the temperature of the ondensing or boiling fluid remains onstant in this ase. he effetiveness is the lowest in the other limiting ase of min / max 1, whih is realized ed when the heat apaity rates of the two fluids are equal.

21 onlusions Note that the analysis of heat exhangers with unknown outlet temperatures is a straight forward matter with the effetiveness NU method but requires rather tedious iterations with the LMD method. When all the inlet and outlet t temperatures t are speified, the size of the heat exhanger an easily be determined using the LMD method. Alternatively, it an also be determined from the effetiveness NU method by first evaluating the effetiveness from its definition and then the NU from the appropriate NU relation given in tabular form.

22 ompat heat exhangers

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