OPTIMAL ECOLOGICAL PERFORMANCE OF A GENERALIZED IRREVERSIBLE CARNOT HEAT PUMP WITH COMPLEX HEAT TRANSFER LAW

Transcription

1 OPTIMA COOGICA PRFORMANC OF A GNRAIZD IRRVRSIB CARNOT AT PUMP WIT COMPX AT TRANSFR AW Ju I, ige CN, Fegrui SUN NAVA UNIVRSITY OF NGINRING, WUAN, P. R. CINA Rezuat. The optial exergy-based ecological perforace of a irreversible Carot heat pup with the losses of heat-resistace, heat leakage ad iteral irreversibility, i which the trasfer betwee the workig fluid ad the heat reservoirs obeys a coplex heat trasfer law Q Δ ( T ), is derived by takig a ecological optiizatio criterio as the objective, which cosists of axiizig a fuctio represetig the best coproise betwee exergy output rate ad exergy loss rate (etropy productio rate) of the heat pup. Soe special exaples are discussed. The results ca provide soe theoretical guidelies for the desigs of practical heat pup. Cuvite cheie: fiite tie therodyaics, irreversible Carot heat pup, ecological optiizatio, heat trasfer law. Abstract. The optial exergy-based ecological perforace of a irreversible Carot heat pup with the losses of heat-resistace, heat leakage ad iteral irreversibility, i which the trasfer betwee the workig fluid ad the heat reservoirs obeys a coplex heat trasfer law Q Δ ( T ), is derived by takig a ecological optiizatio criterio as the objective, which cosists of axiizig a fuctio represetig the best coproise betwee exergy output rate ad exergy loss rate (etropy productio rate) of the heat pup. Soe special exaples are discussed. The results ca provide soe theoretical guidelies for the desigs of practical heat pup. Keywords: fiite tie therodyaics, irreversible Carot heat pup, ecological optiizatio, heat trasfer law.. INTRODUCTION Fiite tie therodyaics is a powerful tool for perforace aalysis ad optiizatio of various therodyaic processes ad cycles. I the aalysis ad optiizatio for heat pup cycles, various optiizatio objectives were adopted, icludig heatig load, coefficiet of perforace (COP), exergy output, exergy efficiecy, specific heatig load, heatig load desity, etc.. Agulo-Brow [] proved that the product of the etropy geeratio rate σ ad the teperature T of low-teperature heat reservoir reflects the dissipatio of the power output P of the heat egie. So he ivestigated the optial perforace of heat egie by takig ito accout the fuctio represetig best ' coproise betwee P ad T σ, = P T σ as the ' objective fuctio. Sice the objective fuctio is siilar to the ecological objective i soe sese, it is called ecological objective fuctio. owever, Ya [2] cosidered that fuctio is ot reasoable because, if the cold reservoir teperature T is ot equal to the eviroet teperature T ', i the defiitio of, two differet quatities, exergy output P ad o-exergy T σ, were copared. Ad he brought forward a fuctio = P T σ istead of '. This criterio fuctio is ore reasoable tha that preseted by Agulo- Brow []. The optiizatio of the ecological fuctio represet a coproise betwee the power output P ad the lost power T σ, which is produced by etropy geeratio i the syste ad its surroudigs. cological perforace optiizatio has bee carried out for edoreversible ad irreversible Carot, Brayto, Stirlig ad ricsso heat egies [3-9] ad irreversible Carot refrigerator [, ]. Based o the poit of view of exergy aalysis, Che et al. [2] provided a uified ecological optiizatio objective fuctio for all of the therodyaic cycles, that is = A/ τ T Δ S / τ = A/ τ T σ () where A is the exergy output of the cycle, T is the eviroetal teperature of the cycle, Δ S is the etropy geeratio of the cycle, τ is the cycle period, ad σ is the etropy geeratio rate of the cycle. quatio () represets the best coproise betwee the exergy output rate ad the exergy loss rate (etropy productio rate) of the therodyaic cycles. For heat egie cycles, the exergy output of the cycle is the work output, ad the ecological optiizatio fuctio is = P T σ. For heat pup cycles, the exergy output rate of the cycle is A / τ = Q ( T / T ) Q ( T / T ) (2) TRMOTNICA 2/29 6

2 OPTIMA COOGICA PRFORMANC OF A GNRAIZD IRRVRSIB CARNOT AT PUMP where Q is the rate of heat trasfer supplied by the heat source, Q is the rate of heat trasfer released to the heat sik (heatig load), ad T ad T are teperatures of the heat sik ad heat source, respectively. The coefficiet of perforace (COP) ad the heatig load of the heat pup are Q /( Q Q) ad π =. Therefore, oe has Q T T = T (3) π[( ) ( )( )] σ T φ T It is clear that the optiizatio based o the exergy aalysis is ore reasoable. Bi et al. [3] ivestigated the optial ecological perforace of a edoreversible air heat pup cycle based o the exergy aalysis. The edoreversible heatpup requires o iteral irreversibility. owever, real heat pups are usually devices with both iteral ad exteral irreversibilities. Besides the irreversibility of fiite rate heat trasfer, there are also other sources of irreversibilities, such as heat leakages, dissipatio processes iside the workig fluid, etc. Soe authors have assessed the effect of fiite rate heat trasfer, together with ajor irreversibilities o the perforace of Carot heat pups usig the heat resistace ad heat leakage odel [4], heat resistace ad iteral irreversibility odel [5, 6] ad heat resistace, heat leakage ad iteral irreversibility odel [7-2]. Based o Refs. [7-2], the optial ecological perforace of a Newto s law geeralized irreversible Carot heatpup with the losses of heat-resistace, heat leakage ad iteral irreversibility is derived by takig a ecological optiizatio criterio as the objective by Che et al [2]. Tyagi et al. [22] studied the ecological optiizatio of irreversible Stirlig ad ricsso heat pups. I geeral, heat trasfer is ot ecessarily liear. The fiite tie therodyaic perforace of heat pup is affected by heat trasfer law. Soe authors have assessed the effect of the heat trasfer law o the perforace of edoreversible ad irreversible heat pups [23-29]. Recetly, i et al. [3] obtaied the fudaetal optial relatioship of the edoreversible Carot heat pup by usig a coplex heat trasfer law, icludig geeralized covective heat trasfer law [ Q ( Δ T) ][26, 28, 29] ad geeralized radiative heat trasfer law[ Q ( Δ T )][24, 25, 26], Q ( Δ T ) i the heat trasfer processes betwee the workig fluid ad the heat reservoirs of the pup. Zhu et al. [3, 32] obtaied the optial ecological perforace for irreversible Carot heat pup with geeralized radiative heat trasfer law Q ( Δ T )[3] ad geeralized covective heat trasfer law Q ( Δ T) [32]. Oe of ais of fiite tie therodyaics is to pursue geeralized rules ad results. I this paper, o the basis of [3, 32], the optial ecological perforace of a geeralized irreversible Carot egie with the losses of heat resistace, heat leakage ad iteral irreversibility, i which the heat trasfer betwee the workig fluid ad the heat reservoirs obeys a ew geeralized heat trasfer law Q ( Δ T ), is derived by takig a ecological optiizatio criterio as the objective. The effects of heat trasfer laws ad various loss ters are aalyzed. The results iclude those obtaied i ay literatures. 2. GNRAIZD IRRVRSIB CARNOT AT PUMP MOD The geeralized irreversible Carot heat pup ad its surroudigs to be cosidered i this paper is show i Figure l. Φ > αf βf 2 Fig.. A geeralized irreversible Carot heat pup odel. The followig assuptios are ade for this odel [7-2, 3, 32]: ) the workig fluid flows through the closed syste i a steady -state coditios. 2) the cycle cosists of two isotheral ad two adiabatic processes. All four processes are irreversible. 3) there exist exteral irreversibilities due to heat trasfer i the high- ad low-teperature heat exchagers betwee the heat pup ad its surroudig heat reservoirs. Because of the heat trasfer, the workig fluid teperatures ( T C ad T C ) are differet fro the reservoir teperatures ( T ad T ). The four teperatures are of the followig order: T C > T > T > T C. The heat trasfer surface areas ( F ad F 2 ) of the highad low-teperature side heat exchagers are fiite. The total heat trasfer surface area (F) of the two heat exchagers is assued to be a costat, i.e. F + F = F TRMOTNICA 2/29

3 Ju I, ige CN, Fegrui SUN 4) there exists a costat rate of heat leakage (q) fro the heat sik to the heat source. Thus Q = π = QC q ad Q = QC q, where Q C is the rate of heat flow fro workig fluid to the heat sik due to the drivig force of ( TC T), Q C is the rate of heat flow fro heat source to workig fluid due to the drivig force of ( T TC ), Q is rate of heat trasfer released to the heat sik, i.e. the heatig load ( π ), ad Q is rate of heat trasfer supplied by the heat source. 5) there are irreversibilities i the syste due to (a) heat resistace betwee the workig fluid ad the heat reservoirs; (b) heat leakage betwee the heat reservoirs; ad (c) iscellaeous factors such as frictio, turbulece ad o-equilibriu activities iside the heat pup. Thus, whe copared with a edoreversible Carot heat pup of the sae heatig load, a larger power supply is eeded. I other words, the rate of heat absorbed fro the source ( Q C ) of the geeralized irreversible Carot heat pup is less tha that of a edoreversible oe ( Q C ). A costat coefficiet Φ is itroduced i the followig expressio, to characterize the additioal iteral iscellaeous irreversibility effect: Φ= Q C / QC. The odel described above is a ore geeral oe tha the edoreversible Carot heat pup odel. If q = ad Φ=, the odel is reduced to the edoreversible Carot heat pup[24, 25, 3]. If q > ad Φ=, the odel is reduced to the irreversible Carot heat pup with heat resistace ad heat leak losses [4]. If q = ad Φ >, the odel is reduced to the irreversible Carot heat pup with heat resistace ad iteral irreversibilities [5, 6]. 3. OPTIMA CARACTRISTICS The secod law of therodyaics requires that QC QC =Φ TC TC (4) The first law of therodyaics gives that the heatig load ( π ) ad the coefficiet of perforace (COP φ ) of the heat pup are Q π = (5) φ= Q P = π ( Q Q ) (6) C C where P is the power iput to the heat pup. Cosider that the heat trasfer betwee the heat pup ad its surroudigs follows a ew geeralized law, icludig geeralized covective heat trasfer law ad geeralized radiative heat trasfer law, Q ( Δ T ). The QC = α F ( TC T ) (7) Q = β F ( T T ) (8) C 2 C where α is the overall heat trasfer coefficiet ad F is the heat trasfer surface area of the high-teperatureside heat exchager (codeser); β is the overall heat trasfer coefficiet ad F 2 is the heat trasfer surface area of the low-teperature-side heat exchager (evaporator). Defiig the heat trasfer surface area ratio ( f ) ad workig fluid teperature ratio ( x ) as follows: f = F F2, x = TC TC, where x T T. Fro quatios (4)-(8), oe ca obtai the heatig load ( π ) ad the COP( ε ) αff T Tx π = [ ] q (9) + f x + ( rfx Φ) Φ Φ + + Φ α ff( T Tx ) q ( f )[ x ( rfx ) ] α ff( Φ x)( T Tx ) () where r = αβ. Thus the etropy geeratio rate of the heat pup is as followig x αff T Tx σ = ( ) [ ] + T Φ T + f x + ( rfx Φ) + q( ) T T () Substitutig equatios (9)-() ito equatio (3) yields αff T Tx 2Tx x 2T = [ ] ( + ) + ( + f) x + ( rfx Φ) TΦ Φ T T T + 2 q( ) T T (2) quatios (9)-(2) idicate that the heatig load ( π ), etropy geeratio rate ( σ ) ad ecological fuctio ( ) of the geeralized irreversible Carot heat pup are fuctios of the heat trasfer surface area ratio ( f ) for give T, T, T, α, β,, ad x. Takig the derivatives of π, α ad with respect to f ad settig the equal to zero yields the sae optiu surface area ratio f x r ( + ) ( + ) a = ( Φ ) (3) The correspodig optial heatig load, optial COP, optial etropy geeratio rate ad optial ecological fuctio are as follows x T) π = q (4) ( + ) + [ + ( rx Φ) ] ( + ) + Φ x T) qφ [ + ( rx Φ) ] α F( Φ x)( T x T) (5) x T) x σ = ( ) + ( + ) + [ + ( rx Φ) ] T ΦT + q( ) T T (6) TRMOTNICA 2/29 63

4 OPTIMA COOGICA PRFORMANC OF A GNRAIZD IRRVRSIB CARNOT AT PUMP x T) 2Tx x 2T = ( + ) + ( + ) + [ + ( rx Φ) ] TΦ Φ T T T + 2 q( ) T T (7) quatios (6) ad (7) are the ajor results of this paper. The heatig load ( π ) ad etropy geeratio rate ( α ) versus COP ( φ ) curves are parabolic shaped oes ad the ecological fuctio ( ) versus COP ( φ ) curve is a loop-shaped oe. At the axiu ecological fuctio coditio ( ax ), the correspodig heatig load, COP ad etropy geeratio rate are π, φ ad σ. Because of the coplexity of equatios (4)-(7), it is difficult to obtai the aalytical expressios of φ, π, ax ad σ, they ca be obtaied by uerical calculatios. 4. DISCUSSIONS 4. ffect of various losses o optial characteristics () If there is o bypass heat leakage i the cycle (i.e., q = ), quatios (4)-(7) becoe x T) π = ( ) [ ( rx Φ ) ] (8) ϕ =Φ ( Φ x) (9) x T) x σ = ( ( + ) + [ + ( rx Φ) ] T ΦT ) (2) x T ) 2Tx x 2T = + [ + ( rx Φ) ] T Φ Φ T ( ) ( + ) + (2) The heatig load ( π ) ad etropy geeratio rate ( σ ) versus COP ( φ ) curves are decreasig oes ad the ecological fuctio ( ) versus COP( φ ) curve is parabolic shaped oe. (2) If there are oly heat resistace ad by pass heat leakage i the cycle (i.e., Φ= ), quatios(4)-(7) becoe x T) π = q ( + ) + [ + ( rx ) ] x T ) q[ + ( rx ) ] ϕ = ( + ) + α F( x)( T x T) (22) (23) x T) x σ = ( ) + q( ) (24) ( + ) + [ + ( rx ) ] T T T T x T) 2Tx 2T = ( x + ) + ( + ) + [ + ( rx ) ] T T (25) T T + 2 q( ) T T The heatig load ( π ) ad etropy geeratio rate ( σ ) versus COP( φ ) curves are parabolic shaped oes ad the ecological fuctio ( ) versus COP( φ ) curve is a loop-shaped oe. (3). If the egie is a edoreversible oe (i.e., Φ =, q = ),quatios (4)-(7) becoe x T) π = (26) ( ) [ ( rx ) ] x T) (27) α ( )( ) F x T x T x T) x σ = ( ) (28) ( + ) + [ + ( rx ) ] T T x T) 2Tx 2T = ( x + ) (29) ( + ) + [ + ( rx ) ] T T The heatig load ( π ) ad etropy geeratio rate ( σ ) versus COP ( φ ) curves are decreasig oes ad the ecological fuctio ( ) versus COP ( φ ) curve is a parabolic shaped oe. 4.2 ffects of heat trasfer law o optial characteristics () quatios (4)-(7) ca be writte as follows whe = : x T) π = q 2 2 [ + ( rx Φ) ] Φ x T) qφ [ + ( rx Φ) ] α F( Φ x)( T x T) x T) x σ = ( ) + q( ) 2 2 [ + ( rx Φ) ] T ΦT T T x T) 2Tx x 2T = 2 2 ( + ) + [ + ( rx Φ) ] TΦ Φ T T T + 2 q( ) T T 2 2 (3) (3) (32) (33) They are the sae results as those obtaied i Ref. [3]. If =, they are the results of irreversible Carot heat pup with Newtoia heat trasfer law [2, 3, 32]. If =, they are the results of irreversible Carot heat pup with liear pheoeological heat trasfer law [3]. If = 4, they are the results of 64 TRMOTNICA 2/29

5 Ju I, ige CN, Fegrui SUN irreversible Carot heat pup with radiative heat trasfer law [3]. (2) quatios (8)-(2) ca be writte as follows whe = : ( T) ( + ) + α FTx π = [ + ( rx Φ) ] q (34) ( + ) + Φα FTx ( T) qφ [ + ( rx Φ) ] α F( Φ x)( Tx T) (35) α FTx ( T) x σ = ( ) + ( + ) + [ + ( rx Φ) ] T ΦT + q( ) T T (36) α FTx ( T) = ( + ) + [ + ( rx Φ) ] 2Tx x 2T T T ( + ) + 2 q( ) T Φ Φ T T T (37) They are the sae results as those obtaied i Ref. [32]. If =, they are the results of irreversible Carot heat pup with Newtoia heat trasfer law [2, 3, 32]. If =.25, they are the results of irreversible Carot heat pup [32] with Dulog-Petit heat trasfer law [33]. 5. NUMRICA XAMP To show the ecological fuctio, etropy geeratio rate, exergy output rate ad heatig load versus the COP characteristics of the irreversible Carot heat pup with the coplex heat trasfer law, oe uerical exaple is provided. I the uerical calculatios, T = 3 K, T = 26 K, T = 3 K, αf= 4 W K, Φ =. ad.2, α= β( r = ), q = C ( T T ) ad i C i =. W K ad.2 W K are set, where C i is the heat coductace of the heat leakage. Fig. 2 shows the relatios betwee ecological fuctio, heatig load, etropy geeratio rate, exergy output rate ad COP of the irreversible Carot heat pup with = 4 ad =.25. This case eas the heat trasfer obeys ier radiative ad outer Dulog ad Petit laws. The diesioless ecological fuctio, diesioless heatig load ad diesioless exergy output rate are defied as ratios of the ecological fuctio, heatig load ad exergy output rate of the heat pup to the axiu ecological fuctio, axiu heatig load ad axiu exergy output rate, respectively. The diesioless etropy geeratio rate is defied as a ratio of the etropy geeratio rate of the heat pup to the iiu etropy geeratio rate whe φ is teds to oe. I this uerical exaple, at the axiu ecological fuctio coditio ( ), the ax correspodig COP, diesioless heatig load, exergy output rate ad etropy geeratio rate are , 5 π πax = , ( A τ) ( A τ) ax =.399, σ σ i,φ = of the upper poits ad π π.452 ( A τ) ( A τ) =.8, 5 ax =, ax σ σ i,φ = of the lower poits, respectively. I order to copare desig poit perforace, oe ca select aother arbitrary workig poit, for exaple the poit where the exergy output rate ( A τ) ( A τ) ax =.432. The correspodig COP 5 is 4.643, ad the heatig load is ππ ax = 5.3, 8 etropy geeratio rate is σσ = i, ε.689. The copariso betwee the axiu ecological fuctio poit ad the poit where the exergy output rate ( A τ) ( A τ) ax =.432 shows that the ecological optiizatio akes the COP icrease about.24% ad the exergy output rate decrease about 7.64 %, the heatig load decrease about.44%, the etropy geeratio rate decrease about 3.32% of the upper poit ad the exergy output rate decrease about 72.69%, the heatig load decrease about 72.66%, the etropy geeratio rate decrease about 73.3% of the lower poits. It ca be see that the heat pup should operate at the upper poit ad the optiizatio of the ecological fuctio akes the etropy geeratio rate of the cycle decrease greatly ad the COP icreases with the cost of a little decrease i the exergy output rate. So it represets a coproise betwee the exergy output rate ad the etropy geeratio rate. Fig. 2. cological fuctio, etropy geeratio rate, exergy output rate ad heatig load versus the COP relatioship for =.25 ad = 4. The effects of heat-leakage ad iteral irreversibility o relatios betwee heatig load, ecological fuctio, etropy geeratio rate ad COP are show i Figs.3-5, respectively. I Figs. 3-5, = 4 ad =.25 are set. Oe ca see that the bypass heat-leakage chages the heatig load, ecological fuctio ad etropy geeratio rate versus COP relatioships qualitatively. The characteristic of the ecological fuctio versus COP becoe the loop-shaped curve fro the parabolic TRMOTNICA 2/29 65

6 OPTIMA COOGICA PRFORMANC OF A GNRAIZD IRRVRSIB CARNOT AT PUMP shaped oe if the heat pup suffers a heat leakage loss. The characteristics of the heatig load ad etropy geeratio rate versus COP becoe the parabolic shaped curves fro the decreasig oes if the heat pup suffers a heat leakage loss. The iteral irreversibility chages the coolig load, ecological fuctio ad etropy geeratio rate versus COP relatioships quatitatively. The COPs correspodig to axiu heatig load, axiu ecological fuctio ad iiu etropy geeratio rate with iteral irreversibility are saller tha those without iteral irreversibility. The axiu-heatig load, axiu-ecological fuctio value ad iiuetropy geeratio rate with iteral irreversibility are saller tha those without iteral irreversibility. Fig. 5. The effects of heat-leak ad iteral irreversibility o relatio betwee etropy geeratio rate ad COP. The effects of heat trasfer law o relatios betwee coolig load, ecological fuctio, etropy geeratio rate ad COP are show i Figs. 6-8, respectively. I Figs. 6-8, Φ =.2 ad C i =.2 W K are set. Oe ca see that heat trasfer law chages the heatig load, ecological fuctio ad etropy geeratio rate versus COP relatioships quatitatively. Fig. 6. The effect of heat trasfer law o relatio betwee heatig load ad COP. Fig. 3. The effects of heat-leak ad iteral irreversibility o relatio betwee heatig load ad COP. Fig. 7. The effect of heat trasfer law o relatio betwee ecological fuctio ad COP. Fig. 4. The effects of heat-leak ad iteral irreversibility o relatio betwee ecological fuctio ad COP Fig. 8. The effect of heat trasfer law o relatio betwee etropy geeratio rate ad COP. 6. CONCUSION 66 TRMOTNICA 2/29

7 Ju I, ige CN, Fegrui SUN The optial ecological perforace of a irreversible Carot heat pup with the losses of heat-resistace, heat leak ad iteral irreversibility, i which the trasfer betwee the workig fluid ad the heat reservoirs obeys a coplex heat trasfer law Q Δ ( T ), is derived by takig a ecological optiizatio criterio as the objective, which cosists of axiizig a fuctio represetig the best coproise betwee the exergy output rate ad exergy loss rate (etropy productio rate) of the heat pup. The results obtaied iclude those obtaied i recet literatures, such as the optial ecological perforace of edoreversible Carot heat pup with differet heat trasfer laws (,, q =, Φ= ), the optial ecological perforace of the Carot heat pup with heat resistace ad iteral irreversibilities (,, q =, Φ > ), the optial ecological perforace of the Carot heat pup with heat resistace ad heat leakage (,, q >, Φ = ), ad the optial ecological perforace of the irreversible Carot heat pup ( q >, Φ > ) with geeralized radiative heat trasfer law Q ( Δ T ) ( =, ) or geeralized covective heat trasfer law Q ( Δ T) (, = ). The results ca provide soe theoretical guidelies for the desig of practical heat pups. Ackowledgeets This paper is supported by Progra for New Cetury xcellet Talets i Uiversity of P. R. Chia (Project No. 2436) ad The Foudatio for the Author of Natioal xcellet Doctoral Dissertatio of P. R. Chia (Project No. 236). RFRNCS [] Agulo-Brow F. A ecological optiizatio criterio for fiite-tie heat egies. J. Appl. Phys., 99, 69(): [2] Ya Z. Coet o ecological optiizatio criterio for fiite-tie heat egies. J. Appl. Phys., 993, 73(7): [3] Cheg C, Che C. cological optiizatio of a edoreversible Brayto-cycle. ergy Covers. Maage., 998, 39(/2): [4] Tyagi S, Kaushik S, Salhotra R. cological optiizatio ad perforace study of irreversible Stirlig ad ricsso heat-egies. J. Phys. D: Appl Phys., 22, 35(2): [5] Che, Zhou J, Su F, Wu C. cological optiizatio for geeralized irreversible Carot-egies. Appl. ergy, 24, 77(3): [6] Khaliq A, Kuar R. Fiite-tie heat-trasfer aalysis ad ecological optiizatio of a edoreversible ad regeerative gas-turbie power-cycle. Appl. ergy, 25, 8(): [7] Sogut O, Durayaz A. cological perforace optiisatio of a solar drive heat egie. J. ergy Istitute, 26, 79(4): [8] Che, Zhag W, Su F. Power, efficiecy, etropy geeratio rate ad ecological optiizatio for a class of geeralized irreversible uiversal heat egie cycles. Appl. ergy, 27, 84(5): [9] Arago-Gozalez G, Caales-Pala A, eo-galicia A, Morales-Goez J. R. Maxiu power, ecological fuctio ad efficiecy of a irreversible Carot cycle. A cost ad effectiveess optiizatio. Brazilia J. Physics, 28, 38(4): -8. [] Zhu X, Che, Su F, Wu C. xergy-based ecological optiizatio for a geeralized irreversible Carot refrigerator. J. of ergy Istitute, 26, 79(): [] Che, Zhu X, Su F, Wu C. cological optiizatio of a geeralized irreversible Carot refrigerator for a geeralized heat trasfer law. It. J. Abiet ergy, 27, 28(4): [2] Che, Su F, Che W. O the ecological figures of erit for therodyaic cycles. J. gg. Theral ergy Pow., 994, 9(6): (i Chiese). [3] Bi Y, Che, Su F, Wu C. xergy-based ecological optiizatio for a edoreversible air heat pup cycle. It. J. Abiet ergy, 29, 3(): [4] Che, Wu C, Su F. eat pup perforace with iteral heat leak. It. J. Abiet ergy, 997, 8(3): [5] Su F, Che W, Che. Optial perforace ad rate of etropy productio for forward ad reverse irreversible Carot cycles. Chiese J. gg. Therophys., 99, 2(4): (i Chiese). [6] Ait-Ali M A. The axiu coefficiet of perforace of iterally irreversible refrigerators ad heat pups. J. Phys. D: Appl. Phys., 996, 29(4): [7] Che, Su F. A ew odel of irreversible heat pups ad its perforace optiizatio. J. Naval Acad. gg., 995(4): 49-58(i Chiese). [8] Cheg C, Che C. Perforace optiizatio of a irreversible heat pup. J. Phys. D: Appl. Phys., 995,28(2): [9] Che, Su F. The effect of heat leak, heat resistace ad iteral irreversibility o the optial perforace of Carot heat pups. J. gg. Therophys., 997,8(): 25-27(i Chiese). [2] Kodal A, Sahi B, Yilaz T. ffects of iteral irreversibility ad heat leakage o the fiite-tie theroecooic perforace of refrigerators ad heat-pups. ergy Covers Maage, 2, 4(6): [2] Che, Zhu X, Su F, Wu C. xergy-based ecological optiizatio for a geeralized irreversible Carot heatpup. Appl. ergy, 27, 84(): [22] Tyagi S K, Kaushik S C, Salohtra R. cological optiizatio ad paraetric study of irreversible Stirlig ad ricsso heat pups. J. Phys. D: Appl. Phys., 22,35(6): [23] Zhu X, Che, Su F, Wu C. The optial perforace of a Carot heat pup uder the ixed heat resistace coditio. Ope Syste & Iforatio Dyaics, 22, 9(3): [24] Su F, Che W, Che, Wu C. Optial perforace of a edoreversible Carot heat pup. ergy Covers. Mgt., 997, 38(4): [25] Che W, Su F, Cheg S, Che. Study o optial perforace ad workig teperature of edoreversible forward ad reverse Carot cycles. It. J. ergy Res., 995, 9(9): [26] Feidt M. Therodyaics ad optiizatio of reverse cycle achies. I: Therodyaic Optiizatio of Coplex ergy Systes. (ditors: Beja A, Maut ), Dordrecht: Kluwer Acadeic Press, 999: TRMOTNICA 2/29 67

8 OPTIMA COOGICA PRFORMANC OF A GNRAIZD IRRVRSIB CARNOT AT PUMP [27] Ni N, Che, Su F, Wu C. ffect of heat trasfer law o the perforace of a geeralized irreversible Carot heat pup. J. Istitute ergy, 999, 72(49): [28] Kodal A. eatig rate axiizatio for a irreversible heat pup with a geeral heat trasfer law. I: Recet Advaces i Fiite Tie Therodyaics. (ds. Wu C, Che, Che J). New York: Nova Sciece Publishers, 999: [29] Zhu X, Che, Su F, Wu C. Optial perforace of a geeralized irreversible Carot heat pup with a geeralized heat trasfer law. Physica Scripta, 2, 64(6): [3] i J, Che, Su F. eatig load vs. COP characteristic of a edoreversible Carot heat pup subjected to heat trasfer law Q Δ ( T ). Appl. ergy, 28, 85(2-3): 96-. [3] Zhu X, Che, Su F, Wu C. ffect of heat trasfer law o the ecological optiizatio of a geeralized irreversible Carot heat pup. It. J. xergy, 25, 2(4): [32] Zhu X, Che, Su F, Wu C. The ecological optiizatio of a geeralized irreversible Carot heat pup for a geeralized heat trasfer law. J. of ergy Istitute, 25, 78(): 5-. [33] O Sulliva C T. Newto s law of coolig - A critical assesset. A. J. Phys., 99, 58(2): TRMOTNICA 2/29