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NOTES ON VAPOR-COMPRESSION REFRIGERATION
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Introduction The purpose of this lecture is to review some of the background material required to undertake the refrigeratio at ion n la labor borat ator ory y. Th The e Th Ther ermod modyn ynam amic icss of th the e ba basi sicc re re-frigeration cycle will be reviwed and some aspects of of simple heat exchanger modelling will be discussed.
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A re refr frig iger erat ator or is a ma macchi hine ne th that at re remo mov ves he heat at fr from om a lo low w te temp mper erat atur ure e re regi gion on.. Si Sinc nce e en ener ergy gy ca cann nnot ot be de de-stroyed, the heat taken in at a low temperature must be dissipate dissi pated d to the surrou surroundin ndings. gs. The Second Law Law of Thermodyn mod ynam amic icss st stat ates es th that at he heat at wi will ll no nott pa pass ss fr from om a co cold ld regi re gio on to a war arm m on one e wi wittho hou ut th the e ai aid d of an “ex exte tern rnal al agent”. agen t”. There Therefore, fore, a refrig refrigerator erator will requi require re this “external agent”, or energy input, for its operation.
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A refrigeration system.
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The most common refrigeration system in use today involves the input of work (from a compressor) and uses the Vapor Com Compre pressi ssion on Cyc Cycle. le. The purpose of the these se not notes es is to introduce some important features of this type of refrigeration system and to discuss how such systems can be thermody the rmodynam namica ically lly mode modeled led.. In a vapor com compre pressi ssion on refrigeration system a gas is alternatively compressed and expa ex pand nded ed an and d goe goess fr from om th the e li liqu quid id to th the e vapo aporr st stat ate. e. The basic components of a vapor-compression refrigeration system are shown below.
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A vapor-compression refrigeration system..
The characteristics of this gas must be chosen to match the th e us use e to wh whic ich h th the e sy syst stem em is to be pu put. t. Th This is gas is re re-ferred to as the refrigerant.
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Coefficient of Performance The purpose of the refrigerator is to remove heat from the cold region while requiring as little external work as possible.. A measure possible measure of the efficiency efficiency of the device device is therefore: Coefficie Coeffi cien nt of Perform Performanc ance e (COP) = Q˙ Rate of heat removal from the cold region = ˙ Rate work is done W
The COP will here be given the symbol β. If q is the heat removed per unit mass and if w is the work done per unit masss the ma then n if if m ˙ is mass flow rate of the refrigerant, then mq q ˙ C OP (= β ) = = mw w ˙
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Vapor-Compression Cycle The Vapor Compression Cycle uses energy input to drive a compressor that increases the pressure and pressure of the refrigera refrigeran nt whi whicch is in the vapor vapor sta state. te. The refriger refriger-ant is then exposed to the hot section (termed the condenser) of the system, its temperature being higher than the temperature temperature of this section. section. As a result, heat is transtransferr fe rred ed from th the e re refri frige gera ran nt to th the e ho hott se sect ctio ion n (i (i.e .e.. he heat at is removed from the refrigerant) causing it to condense i.e. i. e. fo forr it itss st stat ate e to cha hang nge e fr from om th the e vapo aporr ph phas ase e to th the e liqu li quid id ph phas ase e (h (hen ence ce th the e te term rm co cond nden ense ser). r). Th The e re refri frige gerrant then passes through the expansion valve across which its pre pressu ssure re and tem temperat perature ure dro drop p con consid sidera erably bly.. The refrigerant temperature is now below that existing in the cold co ld or re refri frige gera rate ted d se sect ctio ion n (t (ter erme med d th the e ev evapo apora rato tor) r) of the th e sy syst stem em,, it itss te tempe mperat ratur ure e bei being ng lo low wer th than an th the e te temmperat per atur ure e in th this is se sect ctio ion. n. As a re resu sult lt,, he heat at is tr tran ansf sfer erre red d from fro m the refriger refrigerate ated d sec sectio tion n to the refrigera refrigeran nt (i. (i.e. e. hea heatt is absorbed by the refrigerant) causing it to pass from the liquid or near-liquid state to the vapor state again (hence the term ev evapora aporator tor). ). The refrigera refrigeran nt the then n aga again in pas passes ses to the compressor in which its pressure is again increased and the whole cycle is repeated.
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The basic processes in a vapor-compression refrigeration system are therefore as shown below.
Vapor-compression refrigeration cycle.
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The four basic components of the vapour compression refrigeration system are thus: 1. ev evapo apora rato torr - He Heat at is absor absorbed bed to boi boill th the e li liqu quid id at a low temperature, therefore a low pressure must be maintained in this section. 2. com compre presso ssorr - The compre compresso ssorr does work work on the system system increasing the pressure from that existing in the evaporator (drawing in low- pressure, low-temperature saturated vapour) and to that existing in the condenser (i.e., delivering high pressure and high temperature vapour to the condenser. 3. con conden denser ser - The high pressure pressure,, hig high h tem temperat perature ure (superheated or saturated) vapour that enters the condenser has heat removed from it and as a results it is condensed back into a liquid phase. 4. thr thrott ottle le valv alve e - The high pressure pressure liquid liquid from the condenser is expanded through this valve, allowing its pressure to drop to that existing in the evaporator. As alre already ady men mentio tioned ned,, Vaporapor-com compre pressi ssion on ref refrige rigeraration systems are the most common type of refrigerator in use today.
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Cycle Analysis If it is assumed that the system is operating at a steadystate and if it is assumed that kinetic and potential energy changes are negligible, the cycle can be analysed in the usual way way. The principal work and heat transf transfer er that occur occ urss in th the e sy syst stem em ar are e sh sho own bel belo ow, th thes ese e qu quan anti titi ties es being taken as positive in the directions indicated by the arrows arro ws in thi thiss figu figure. re. In the analyses analyses,, eac each h com compone ponen nt is first separately separately considered. considered. The evaporator, evaporator, in whic which h the desired refrigeration effect is achieved, will be considered first.
A vapor-compression refrigeration system.
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As the refrigerant passes through the evaporator, heat transfer from the refrigerated space results in the vaporizatio iza tion n of the refriger refrigeran ant. t. Con Consid sideri ering ng a con contro troll vo volum lume e enclos enc losing ing the ref refrig rigera eran nt sid side e of the ev evapora aporator tor,, con conser ser-vation of mass and energy applied to this control volume together give the rate of heat transfer per unit mass of refrigerant flow in the evaporator as: ˙ in Q m ˙
= h1 − h4
wher wh ere em ˙ is the mass flow rate of the refrigerant. The heat transfer rate to the refrigerant in the evaporator, Q˙ in, is referred to as the refrigeration capacity, it usually being express in kW or in Btu/hr or in tons of refrigeration, one ton of refrigeration being which is equal to 200 Btu/min or about 211 kJ/min.
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Next consider consider the comp compresso ressor. r. The refrigeran refrigerantt lea leaving ving the th e ev evapo apora rato torr is co comp mpre ress ssed ed to a re rela lati tiv vel ely y hi high gh pr pres es-sure su re an and d te temp mper erat atur ure e by th the e co comp mpre ress ssor or.. It is us usua uall lly y adequate to assume that there is no heat transfer to or from fro m th the e co comp mpre ress ssor or.. Co Cons nser erv vat atio ion n of ma mass ss an and d en ener ergy gy rate applied to a control volume enclosing the compressor then give: ˙ W
= h2 − h1
m ˙ ˙ /m where W ˙ is the work done per unit mass of refriger-
ant.
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Next Ne xt,, th the e re refr frig iger eran antt pa pass sses es th thro roug ugh h th the e co cond nden ense ser, r, where the refrigerant condenses and there is heat transfer from the refrig refrigeran erantt to the cooler co oler surroundings surroundings.. For a control volume enclosing the refrigerant side of the condenser, the rate of heat transfer from the refrigerant per unit mass of refrigerant is ˙ out Q m ˙
= h2 − h3
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Fina Fi nall lly y, th the e re refri frige geran rantt at st stat ate e 3 en ente ters rs th the e ex expa pannsion sio n valv alve e and exp expand andss to the ev evapora aporator tor pre pressu ssure. re. Thi Thiss process is usually modeled as a throttling process in which there is no heat transfer, i.e., for which h4 = h3
In this valve the refrigerant pressure decreases in an irreversible adiabatic process and there is an accompanying increa inc rease se in en entro trop py. The ref refrig rigera eran nt lea leav ves the valv alve e at state 4 as a two-phase liquid-vapor mixture.
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In the vapor-compression system, the net power input is eq equa uall to th the e co comp mpre ress ssor or po pow wer er,, th the e ex expa pans nsio ion n val alv ve inv in vol olvi ving ng no po pow wer in inpu putt or ou outp tput ut.. Us Usin ing g th the e qu quan anti ti-ties and expressions introduced above, the coefficient of performance, β, of the vapor- com compre pressi ssion on ref refrig rigera eratio tion n system is given by: Q˙ in/m h1 − h4 ˙ β = = ˙ W C h2 − h1 ˙ C /m
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Provided states 1 through 4 are prescribed, the above equations can be used to evaluate the principal work and heat he at tr tran ansf sfer er an and d th the e coe coeffic fficie ien nt of pe perf rfor orma manc nce e of th the e vapo aporr-co comp mpre ress ssio ion n sy syst stem em..
Sinc Si nce e th thes ese e eq equa uati tion onss ha hav ve
been developed by using conservation of mass and energy, they can be used to predict the actual performance of a real system when irreversibilities are present in the evaporator, compressor, and condenser and to predict the performance of an idealized system in which such effects are absent. absen t. Altho Although ugh irrev irreversib ersibilitie ilitiess in the evaporator, evaporator, compressor, and condenser can have a pronounced effect on overall ov erall performance performance of the system, much much is to be gained by considering an idealized cycle in which such irreversibilities are assumed assumed absent. absent. Suc Such h a cycle establish establishes es an upper limit on the performance of the vapor-compression refrigeration eratio n cycle cycle.. Suc Such h an ideal idealized ized cycle is considered considered in the next section.
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Ideal and Actual Vapor-Compression Cycles An id ide eal re refr frig iger erat atio ion n cyc ycle le is fir firsst co con nsi sid der ered ed..
In
this case irreversibilities within the evaporator, compressor, so r, an and d co cond nden ense serr are ignore ignored, d, it is as assu sume med d th that at fri fricction ti onal al pr pres essu sure re dr drop opss in th the e sy syst stem em ar are e ne negl glig igib ible le an and d that th at th the e re refri frige geran rantt flo flows ws at co cons nsta tan nt pr pres essu sure re th thro roug ugh h the two heat exchangers, i.e., through the condenser and through the evaporator and that all heat transfer to the surrou sur roundi ndings ngs is neg neglig ligibl ible. e. Wit With h the these se ass assump umptio tions, ns, the compre com pressi ssion on proce process ss wil willl be ise isen ntro tropic pic.. The ideal vaporcompression refrigeration cycle, labeled 1-2s-3-4-1, on the temperature-entropy temperature-entrop y, i.e. T-s, diagram is as shown before.
Vapor-compression refrigeration cycle.
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This cycle consists of the following series of processes: Process 1-2s: Isentropic compression of the refrigerant from state 1 at the exit of the evaporator to the condenser pressure at state 2s. Proce Pr ocess ss 2s 2s-3 -3:: He Heat at tr tran ansf sfer er fro from m th the e re refri frige gera ran nt occ occur urss as the refrigerant flows at constant pressure through the condenser. The refrigerant exits as a liquid at state 3. Proce Pr ocess ss 33-4: 4: Thr Throt ottl tlin ing g pr proce ocess ss fr from om st stat ate e 3 to a twophas ph ase e li liqu quid id-v -vapo aporr mi mixt xtur ure e at 4 occ occur urss at co cons nsta tan nt en en-thalpy. Process 4-1: Heat transfer to the refrigerant occurs as it flows at constant pressure through the evaporator to complete the cycle.
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All of the processes in the above cycle are internally reversib rev ersible le except throttling throttling process process.. Desp Despite ite the inclu inclusion sion of this irreversible process, the cycle is normally referred to as th the e id ide eal cyc ycle le.. Th The e id idea eall cy cyccle is of ofte ten n ta tak ken to involve a saturated vapor, state 1’, at the compressor inlet and a saturated liquid, state 3’, at the condenser exit, this cycle being shown in below.
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“Ideal”Vapor-compression refrigeration cycle.
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The operating temperatures of the vapor-compression refrigeration cycle are established by the temperature T C C to be maintained in the cold region and the temperature T H the e war arm m re regi gion on to wh whic ich h he heat at is di disc scha harg rged ed.. As H of th
pointed out earlier, refrigerant temperature in the evaporator must be less than T C C and the refrigerant temperature in the condenser must be greater than T H H .
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Shown in the following figure (same as given earlier)the actual cycle 1-2-3-4-1 differs in a key way from that of the ideal cycle.
Vapor-compression refrigeration cycle.
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This Th is di diffe ffere renc nce e is th the e de depa part rtur ure e fr from om an is isen entr trop opic ic process due to internal irreversibilities present during the actu ac tual al co comp mpre ress ssio ion n pr proce ocess ss.. Th The e ac actu tual al pr proce ocess ss is in indi di-cated schematically by the dashed line for the compressio si on pr proc oce ess fr from om sta tate te 1 to st stat ate e 2. Th This is da dasshe hed d li line ne shows the increase in specific entropy that would accompany pan y an adi adiaba abatic tic irr irrev evers ersibl ible e com compre pressi ssion. on. Ho How wev ever, er, if sufficient heat transfer occurred from the compressor to its surroundings, the specific entropy at state 2 could be less le ss th than an at st stat ate e 1. Co Comp mpari aring ng cy cycl cle e 11-22-33-44-1 1 wi with th th the e corresponding ideal cycle 1- 2s-3-4-1, it will be seen that the th e re refr frig iger erat atio ion n ca capa paci citty is th the e sa same me fo forr ea eacch, bu butt th the e work input is greater the case of irreversible compression than th an in th the e id idea eall cy cycl cle. e. Ac Acco cord rdin ingl gly y, th the e coe coeffic fficie ien nt of performance of cycle 1-2-3-4-1 is less than that of cycle 1-2s-3-4-1.
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The effect of irreversible compression can be accounted for by using the isentropic isentropic compressor efficiency, efficiency, ηC , which, for the refrigerant states indicated in the previous figure, is given by: ηC
˙ C (W ˙ )s h2s − h1 C /m = = ˙ h2 − h1 W C ˙ C /m
Addi Ad diti tion onal al de depa part rtur ures es fro from m id idea eall cy cycl cle e st stem em fr from om fri fricctional effects that result in pressure drops as the refrigeran era nt flo flows ws thr throug ough h the ev evapora aporator tor,, con conden denser ser,, and the piping connecting the various components in the system. These pressure drops are usually ignored.
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Refrigerant Properties The Th e te tempe mperat ratur ures es of th the e re refri frige geran rantt in th the e ev evapo apora ra-tor and condenser are the temperatures of the cold and warm regions, respectively, with which the system interacts ac ts th ther erma mall lly y.
This Th is,, in tu turn rn,, de dete term rmin ines es th the e ope opera ratt-
ing in g pr pres essu sure ress in th the e ev evapo aporat rator or an and d co cond nden ense ser. r. Co Cons nseequently, the selection of a refrigerant is based partly on the suitability of its pressure-temperature relationship in the range range of the par partic ticula ularr app applic licati ation. on. It is gen genera erally lly desirable to avoid excessively low pressures in the evaporator and exces excessiv sively ely hig high h pressur pressures es in the conden condenser ser.. Oth Other er consid con sidera eratio tions ns in ref refrig rigera eran nt sel select ection ion inc includ lude e chem hemica icall stab st abil ilit ity y, to toxi xici citty, co corro rrosi siv ven enes ess, s, an and d co cost st.. Th The e type of compresso compr essorr used also affects affects the choice choice of of refrigeran refrigerant. t. Centrif tr ifug ugal al co comp mpre ress ssor orss are bes bestt su suit ited ed fo forr lo low w ev evapo apora rato torr pressures and refrigerants with large specific volumes at low lo w pre pressu ssure. re. Rec Recipr iprocati ocating ng com compre presso ssors rs perfo perform rm bett better er over large pressure ranges and are better able to handle low lo w specific volume volume refrigerants. refrigerants. Other considerati considerations ons in refrigeran refrig erantt sele selection ction inclu include de ch chemic emical al stabi stabilit lity y, to toxicit xicity y, corrosiveness, and cost.
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A thermodynamic property diagram widely used in the refrigeration field is the pressure-enthalpy or p-h diagram. The Th e fo foll llo owi wing ng fig figur ure e sh sho ows th the e ma main in fe feat atur ures es of su succh a property diagram.
Pressure-Enthalpy (p-h) diagram. The principal states of the vapor-compression cycles discussed cuss ed before are indicated indicated on this p-h diagram. diagram. Propert Property y tables and p-h diagrams for many refrigerants are given in handbooks dealing with refrigeration.
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Overall Heat Transfer Coefficient In the evaporator and condenser, heat is transferred betw bet wee een n th the e re refr frig iger eran antt an and d th the e su surro rroun undi ding ng flu fluid id.. Th The e evaporator ev aporator and condenser condenser are examples examples of a heat exc exchange hangerr which is a device designed to transfer heat from one fluid to another fluid, the fluids both flowing through the heat exchanger and the fluid streams being separated by the solid sol id wall allss of the heat exchan exchanger ger.. The layout layout of a sim simple ple “shell-in-tube”is shown in the following figure.
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Shell-in-Tube heat exchanger.
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As th the e flu fluid idss pa pass ss th thro roug ugh h th the e he heat at ex exccha hang nger er th thei eirr temperatures change and it is usual to express the rate of heat transfer from the hot fluid to the cold fluid, Q˙ , by an equation of the form: Q˙ = U A (T hot hot − T cold cold )
Here U is termed the overall heat transfer coefficient, A is th the e ar area ea of th the e su surf rfac ace e se sepa para rati ting ng th the e flu fluid idss th thro roug ugh h which the heat transfer occurs and ( T hot hot − T cold cold ) is the mean me an di diffe ffere renc nces es bet betw wee een n th the e te tempe mpera ratu ture ress of th the e two fluids.
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It can be shown that if U is as assu sume med d co cons nsta tan nt, th the e mean mea n temperatu temperature re differenc difference e tha thatt should should be use used d is the socalled lo Cons nsid ider er the the log. g. me mean an temp temper eratur aturee differ differenc encee, θLM T . Co temperature variations of the fluids as they pass through the heat exchanger as shown schematically below:
Fluid temperature variation through heat exchanger.
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If θi is the difference between the temperatures of the hot and cold fluids at the inlet to the heat exchanger and if θo is the difference between the temperatures of the hot and cold fluids at the outlet to the heat exchanger the log mean temperature difference is given by: θLM T =
θi − θo
ln(θi /θo )
The heat transfer rate is then given by: Q˙ = U A θLM T
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It sh shou ould ld al also so be no notted tha hatt sin ince ce a st ste ead ady y sta tate te is being assumed: Q˙ = Ra Rate te of he heat at transf transfer er from from ho hott flu fluid id
= Ra Rate te of he heat at transf transfer er to co cold ld fluid = m ˙ H (hH i − hH o) = m ˙ C (hCo − hCi ) The subscripts H and C referring to the hot and cold fluid streams respectively and the subscripts i and o referring to inlet and outlet conditions respectively.
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Layout of experimental apparatus.
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The Th e sy syst stem em us uses es RR-14 141b 1b as a re refri frige gera ran nt. Pr Prope opert rtie iess of this refrigerant are given in the figures, one giving the relation between the saturation temperature and the saturation pressure while the other gives a p-h diagram.
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Saturation temperature and the saturation pressure diagram for R-141b.
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p-h diagram for R-141b.
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ASSIGNMENT Assume that a vapor-comp vapor-compression ression refrigeration refrigeration system system operates at a steady state and on an ideal refrigeration refrigeration o cycle using Refrigerant Refrigerant 134a as the working working fluid. Saturated Saturated vapor enters enters the compressor at -10 C and saturated o liquid leaves the condenser at 28 C. The mass flow rate of the refrigerant is 5 kg/min. Find: a. The compressor power in kW. b. The refrigerating refrigerating capacity capacity in tons. c. The coefficient of performance. 1.
Tables giving the properties of R134a are attached. 2. A vapor-compress vapor-compression ion refrigeration refrigeration system operates at a steady state and uses Refrigeran Refrigerantt 134a as the working fluid. fluid. The mass flow rate of the refriger refrigeran antt is 6 kg/min kg/min.. The vapor vapor enters enters the compresso compressorr at a tempera temperatur turee of o -10 C and a pressure of 1.4 bar and leaves at a pressure of 7 bar. The isentropic compressor efficiency is 67%. The refrigerant leaves the condenser at a temperature of 24o C and a pressure of 7 bar. Pressure drops in the condenser and evaporator and in the connecting piping can be neglected as can any heat transfer between the system and its surroundings. surroundings. Find: a. The refrigerating capacity in tons. b. The coefficient of perform p erformance. ance.
In finding the thermodynamic properties of the refrigerant, it can be assumed that the enthalpy of the subcooled liquid refrigerant depends only on the temperature, i.e. that h for the sub-cooled liquid is equal to h for the saturated liquid at the same temperature. A heat exchanger is used to heat air from an inlet temperature of 0 o C to an exit temperature of 30o C using water which enters the heat exchanger at a temperature of 60o C and leaves the heat exchanger at a temperature of 50oC, the process being shown in the following figure: 3.
The mass flow rate of air through the heat exchanger is 0.007 kg/s. Find: a. The mass flow rate of water. b. The log. mean temperature difference. c. The heat transfer area. In finding the required enthalpy changes it can be assumed for air that: (hb − T
J/kg J/kg = 1005 1005 (T b −
T a )
being in o C, and that for water: (hb −
T
ha )air
ha )water
J/kg J/kg = 4180 4180 (T b −
again being in o C. 11
T a )
