Performance Characteristics and Thermodynamic Investigations on Single-Stage Thermoelectric Generator and Heat Pump Systems

Transcription

1 ertanika J. Sci. & Tecnol. 6 (): (18) SCIECE & TECHOLOGY Journal omepage: ttp:// erformance Caracteristics and Termodynamic Investigations on Single-Stage Termoelectric Generator and Heat ump Systems Rajes Arora 1 * and Ranjana Arora 1 Department of Mecanical Engineering, Amity University Haryana, Gurgaon-113, India Renewable Energy Department, Amity University Haryana, Gurgaon-113, India ABSTRACT Te termodynamic analysis of termoelectric devices (TEs) discards te impact caused by eat leak between source and sink. It could lead towards te partial/incomplete modelling of TEs along wit some analytical gaps in teir performance evaluation. Conversely, appropriate agreement among different design constraints of TEs is a must to upgrade teir operating caracteristics. In view of tis, te modelling of multi-element single-stage termoelectric generator (TEG) and termoelectric eat pump (TEH) is carried out in matrix laboratory (MATLAB 9.). Te irreversibilities caused by eat leak between te source/sink along wit Fourier/Joule effects are considered for te modelling and analysis. Te power output/termal efficiency and eating capacity/coefficient of performance (CO) of TEs are analytically derived and optimized on te basis of finite time termodynamic principles. Te predetermined termoelectric couples are cosen to maximize te eating capacity/co in proposed configurations. Moreover, te influence of design variables viz electrical current, termoelectric couples on system trougput is analyzed and presented. Te effects of geometrical parameters viz lengt and area of individual modules on te performance of TEG and TEH are also discussed. Keywords: Finite time termodynamic, termoelectric generators, termoelectric eat pumps, (FTT), termodynamic optimization ITRODUCTIO ARTICLE IFO Article istory: Received: 7 February 18 Accepted: 8 May 18 ublised: October 18 addresses: rajesarora119@rediffmail.com (Rajes Arora) ranjana119@rediffmail.com (Ranjana Arora) * Corresponding autor In today s era, te rapid rise in energy demand as led researcers/scientists to searc for new resources of energy. As te conventional energy resources are coming to an end, innovative/smart energy conversion tecnologies are gaining wide ISS: e-iss: Universiti utra Malaysia ress

2 Rajes Arora and Ranjana Arora attraction globally. Due to non-moving parts, low maintenance requirements, low/zero noise operation, compact configuration and small volume occupancy, tese are getting very popular amongst various commercial applications. Te termoelectric devices viz. termoelectric generators and eat pumps are direct termal to electricity conversion devices requiring low maintenance, capable to operate in modular form and ave possibility to utilize eat from sources over a wide range of temperature (Angrist, 199; Disalvo, 1999; Goldsmit, 196; Rowe, ). Tese devices consist of a semiconductor termocouple aving two junctions. Wen tese two junctions, named as ot junction and cold junction are maintained at different temperatures, te voltage is generated in te order of microvolts/kelvin. Tis is known as Seebeck effect. Te reverse effect in wic a junction can be eated or cooled wit te passage of current troug it, is known as eltier effect. Several termocouples are joined in electrically series configuration to ave desired voltage output (Cen & Wu, ; Min et al., 3; Riffat & Ma, 3; Xuan et al., ). Termoelectric devices are coupled wit te source/sink and according to classical termodynamics, it takes infinite time for eat transfer between system and coupled termal reservoirs. Tis is not desirable from practical point of view. Te finite time eat transfers are te need of practical termoelectric devices to obtain finite output power/termal efficiency, eating capacity/ coefficient of performance (Andresen, 1983). It is observed tat classical termodynamic does not provide te compreensive picture of equilibrium states/reversible processes. On te oter and, finite time termodynamic (FTT) provides an extension to conventional termodynamic teory as it accounts for finite time consumption of eat transfer between system and coupled termal reservoirs. Finite time termodynamic approac takes into account bot external and internal irreversibilities of te system. In termoelectric devices, internal irreversibility is because of Joule/conduction eat loss wile external irreversibility is because of finite rate eat transfers between eat reservoirs/system (Cen et al., 199). In te present literature, several investigations are carried out on termodynamic optimization and analysis of termoelectric generators/eat pumps wit conventional/non-equilibrium termodynamics. Cen et al. (a) enunciated optimization of series mode operated multi-stage TEG wit respect to different designing operators. Afterwards, tey investigated te caracteristics of termoelectric refrigerator (Cen et al., b). Later, Cen et al. (8) optimized te trougput of -stage eat pumps in electrically series mode wit internal/external irreversibilities employing finite time termodynamic (FTT) principles. David et al. (1) investigated termodynamic studies and optimizations of TEH in view of different design/operating variables and designed a eat excanger for a system. Afterwards, an experimental model of TEGs ad been tested in order to caracterize te different performance parameters (Cen et al., 1; Zu et al., 11). A compreensive comparison of single/two-stage series connected TEGs operating wit an automobile exaust was demonstrated by Sun et al. (1). Tey observed tat two-stage system can 1976 ertanika J. Sci. & Tecnol. 6 (): (18)

3 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems yield better output in case of ig source-side temperature. Riffat et al. () developed te strategy to optimize termoelectric modules for space conditioning applications were as te optimum design of te modules for space eating applications in te buildings was presented by Kim et al. (1). Kausik et al. (1) analyzed single-stage termoelectric eat pumps (TEH) in view of energy/exergy concepts. Tey noticed tat te effects of internal irreversibility were more in comparison wit external irreversibility. Hans et al. (1) enunciated an optimization study for series/ parallel modes operated TEGs, wit respect to various design variables for obtaining maximum output power and first law efficiency. Later, tey carried out te comparative performance optimization of -stage termoelectric eat pumps in tree different modes (Hans et al., 16). Furter, Kumar and andey (17) calculated te efficiency of a TEG in order to study te impacts of different termoelectric materials. In te present literature, a few termodynamic investigations and optimization studies are available on multi-element single-stage termoelectric generators and eat pumps (Hans et al. 1; ami et al. 17; Tan et al. 17). Moreover, te influence of eat leak between te source and sink as not been considered wic leads to incomplete modelling of te system. Additionally, tere is a need of analyzing te effects of geometric variables and temperature dependent pysical properties on performance parameters and optimal designing of termoelectric devices. In tis context, te termodynamic models of multielement irreversible TEG and TEH systems taking into account bot internal and external effects, wit and witout eat leak between source and sink are developed in MATLAB. Te performance analysis of above mentioned devices is done on te basis of ewton s law of eat transfer and finite time termodynamic principles. A comparative study of multielement irreversible TEG and TEH based on finite time termodynamic modeling is carried out considering internal/ external effects. A formulation of performance parameters of termoelectric devices wit respect to electric current, termoelectric couples, temperature of ot/cold side and termal conductances of ot/cold side is presented. Te internal irreversibilities are caused by Joule/conduction eat losses wile, external irreversibilities are because of finite eat transfers between reservoir and devices. Te impacts of design factors on output power/termal efficiency and eating capacity/ coefficient of performance (CO) are analyzed and outcomes are presented grapically. Te effects of geometric parameters viz. lengt and area of termoelectric elements ave been investigated on performance aspects of above mentioned systems. Te geometry of te termoelectric element is directly linked to termoelectric material and cost of manufacturing. Te major outcomes of tis study are te comparative investigations along wit novel analytical and parametric analysis of multi-element termoelectric systems wit and witout eat leak considerations. ertanika J. Sci. & Tecnol. 6 (): (18) 1977

4 Rajes Arora and Ranjana Arora Finite-Time Termodynamic Modeling of Termoelectric Devices Termodynamic modeling of multi-element single-stage termoelectric generator (TEG) and termoelectric eat pumps (TEH) wit bot external/internal irreversibilities is done troug finite-time termodynamic principles. Te termodynamic modeling of te proposed TEs as been carried out based on te following assumptions. Steady-state one-dimensional eat flow as been considered. Te exoreversible configurations wit negligible contact/interconnection resistances are considered. Te Tomson effect in termoelectric elements is not taken into account. Convection and radiation losses in termoelectric elements are not considered. Te material used for TECs is assumed to be Bismut Telluride (Bi Te 3 ). Te following temperature reliant properties of te termoelectric materials, as given by Xuan et al. () are used in te present study. 9 α = αp ( αn) = ( Tav.99 Tav ) 1 V / K ρ 1 n = ρp = ( av av ) 1 Ω/ T T m k k T T W mk n = p = ( av +.13 av ) 1 / 9 τ = τ p ( τn) = (93.6Tav Tav ) 1 V / K () T av T + Tc = ρ L ρ L R = + A p An p p n n (1) () (3) () (6) kpap ka n n K = + L p L n (7) Termodynamic Modeling of Single-Stage Termoelectric Generator (TEG) Te TEG model wit / type semiconductor legs is illustrated in Figure 1(a). Te termoelectric couples are arranged in electrical series and termally parallel configurations in pursuance of generating a considerable voltage output from te system. Te generalized TEG model revealing te eat flow and generating te electrical output is presented in Figure 1(b). In corresponding figures, and T signifies te input source/ot junction 1978 ertanika J. Sci. & Tecnol. 6 (): (18)

5 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems temperatures wereas te and T c are te eat sink and cold junction ones. Larger te differential temperature amongst te two junctions, more is te potential difference generated at external resistance R L. (a) Figure 1. (a) Single-stage TEG; and (b) Generalized FTT model of TEG (b) Te energy equations for -type semiconductor legs can be written as Q Kin -Q Kout +Q J = (8) were, Q Kin and Q Kout are te eat input/output of te termoelectric elements by conduction and Q J is te Joule eat generated in te element. Equation 8 can be rewritten as d dt ALdx ( T + dt ) k A k A + ( J ) = (9) dx dx σ L Similarly, te equation for -type semiconductor leg can be stated as d dt ALdx ( T + dt ) k A k A + ( J ) = (1) dx dx σ L Boundary conditions for / types semiconductor leg can be given as T () = T () = T (11) c T ( L ) = T ( L ) = T (1) Te temperature dependent termoelectric properties k, σ are te functions of T and k, σ are te functions of T. utting te boundary conditions to Equations (9) and (1) and substituting k, σ by teir mean values k and σ, differential equations can be given as dt I k A + = (13) dx A σ ertanika J. Sci. & Tecnol. 6 (): (18) 1979

6 Rajes Arora and Ranjana Arora dt I k A + = (1) dx A σ Te total eat flows via te ot-side/cold-side junctions are dt Q = ( α α ) TI+ k A + k A x= L x= L dx x= L dx x= L dt (1) dt Q = ( α α ) TI+ k A + k A x= x= c c c c dx x= dx x= Te rate of eat flows from eat source/sink are given as dt (16) Q = K ( T T ) (17) H H H QC = KL( Tc TL) (18) Te eat flows from ot/cold junctions are given as Q = IT + k T T I R (19) [ α ( c). ] Q = IT + k T T + I R () c [ αc c ( c). ] Were, α = αp αn andα c = α c α cp According to eat flow balance, one can ave following condition as Q Q H C = Q (1) c = Q () Te output is given by = Q Q (3) c By putting te values of Q and Q c in Eq. (3) from Equations (19) and () = I( α T α T IR) () c c Te efficiency is given by I[ α T α T IR] η = = Q IT k T T I R c c [ α + ( c). ] utting, α = αc = α From above Equations, one can get T and T c as () 198 ertanika J. Sci. & Tecnol. 6 (): (18)

7 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems T = 3. αri + ( Rk. RKL) I + αkhthi K( KHTH + KLTL) KLKHTH α I + αi( KH KL) K( KH + KL) KLKH (6) T c = 3. αri + ( Rk +. RKH) I + αkltli + K( KHTH + KLTL) + KLKHTL α I + αi( KL KH) + K( KH + KL) + KLKH (7) TEG Model wit Heat Leak between Source and Sink Te eat flows from ot/cold junctions due to small eat leak is given as Q = [ α IT + k( T T ) +. I R + K ( T T )] (8) ' c c c c c L Q = [ α IT + k( T T ) +. I R + K ( T T )] (9) ' c c c c c L Te output is given as Q ' Q ' c = (3) Te efficiency in tis case can be given as I[ α T α T IR] η = = Q [ IT + k( T T ). I R + K ( T T )] (31) c c ' α c H Te values of various parameters used in FTT modeling of multi-element TEG is given in Table 1. Table 1 Value (s) of various parameters arameters R K α 17 Source: (Cen et al., ) Values Ω.77 W/K 1-6 V/K K 3 K 1W/K ertanika J. Sci. & Tecnol. 6 (): (18) 1981

8 Rajes Arora and Ranjana Arora Termodynamic Modeling of Single-Stage Termoelectric Heat ump (TEH) Te TEH model wit / type semiconductor legs is illustrated in Figure (a). Te termoelectric couples are arranged in electrical series and termally parallel configurations. Te generalized TEH model revealing te eat flow and wit te electrical input is presented in Figure (b). In corresponding figures, and T signifies te input source/ ot junction temperatures wereas te and T c are te eat sink and cold junction ones. Wen electrical current, I flows troug TEH, eat flows α ITc and α IT are captivated from te surroundings and rejected to te space to be eated. Te eat source is maintained at low temperature wereas te sink i.e., eated space is maintained at ig temperature. Figure. (a) Single stage TEH; and (b) Generalized FTT model of TEH Te energy equations of -type semiconductors are given as Q Kin -Q Kout +Q J = (3) were, Q Kin and Q Kout are te eat input/output of te termoelectric element by conduction and Q J is te Joule eat generated in te element. Eq. 3 can be rewritten as d dt ALdx ( T + dt ) k A k A + ( J ) = (33) dx dx σ L Similarly, te equation for -type semiconductor leg can be written as d dt ALdx ( T + dt ) k A k A + ( J ) = (3) dx dx σ L Boundary conditions for and type semiconductor legs can be given as T () = T () = T (3) c 198 ertanika J. Sci. & Tecnol. 6 (): (18)

9 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems T ( L ) = T ( L ) = T (36) Te temperature dependent termoelectric properties k, σ are te functions of T and k, σ are te functions of T. utting te boundary conditions to Equations (33) and (3) and substituting k, σ by teir mean values k and σ, differential equations can be given as dt I k A + = (37) dx A σ dt I k A + = (38) dx A σ Te total eat flows via te ot-side/cold-side junctions are dt Q = ( α α ) TI k A k A x= L x= L dx x= L dx x= L dt Q = ( α α ) TI k A k A = = c c c c x x dx x= dx x= dt dt (39) () Te rate of eat flows from eat source/sink are given as Q = K ( T T ) (1) H H H Q = K ( T T ) () C L L c Te rate of eat flows from ot/cold junctions are given as Q = IT k T T + I R (3) [ α ( c). ] Q = IT k T T I R () c [ αc c ( c). ] utting, α = α = α c According to eat flow balance, one can ave following condition as Q Q H C = Q () c = Q (6) Te eating power is given by = Q Q (7) c ertanika J. Sci. & Tecnol. 6 (): (18) 1983

10 Rajes Arora and Ranjana Arora Te CO of TEH can be calculated as CO = Q Q c Q (8) From Eqs. () and (6), one can get T and T c as T = 3. αri + ( Rk +. RKL) I + αkhthi + K( KHTH + KLTL) + KLKHTH α I + αi( KH KL) + K( KH + KL) + KLKH (9) T c = 3. αri + ( Rk. RKL) I + αkhthi K( KHTH + KLTL) KLKHTH α I + αi( KL KH) K( KH + KL) KLKH () TEH Model wit Heat Leak between Source and Sink Te eat flows from ot/cold junctions due to small eat leak is given as Q = [ α IT + k( T T ). I R K ( T T )] (1) ' c H Q = [ α IT + k( T T ) +. I R K ( T T )] () ' c c c c c L Te eating power is given as Q ' Q ' c = (3) Te CO of TEH wit eat leak Q ' CO = Q ' ' Q c () Te values of various parameter used in FTT modeling of multi-element TEH system is given in Table. 198 ertanika J. Sci. & Tecnol. 6 (): (18)

11 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems Table Value (s) of various parameters arameters R K α 17 Source: (Cen et al., 8) Values Ω.77 W/K 1-6 V/K 3 K K 1 W/K DISCUSSIO Figure 3 sows te variations of output power () wit electric current (I) for various values of sink temperature ( ), assuming a fixed source temperatures ( ) of multi-element TEG. Te output power is a parabolic function of I and its peak value decreases as increases. For a fixed value of source temperature, as increases te temperature differences (DTG) between te eat source/sink decreases and power output eventually falls down. Likewise, te variation of output power () wit electric current (I) for various values of source temperatures ( ), assuming a fixed sink temperature ( ) of TEG is demonstrated in Figure 3. Te output power is a parabolic function of I and its maximum value increases wit increase in te value of. For a fixed value of sink temperature, as increases te temperature differences (DTG) between eat source and sink increases and power output ultimately goes up. Figure and Figure 6 sows te parabolic variations of first law efficiency (η) wit I for different values of and respectively. Te termal efficiency increases as increases (for fixed value of ) and drops wit increase in (for fixed value of ). Te reason beind tis is, as te value of DTG increases in TEG system te first law efficiency goes up and vice versa. Te variation of wit I for different number of termoelectric elements () is illustrated in Figure 7. Te output power attains its peak at an optimum value of, nearly 1. umber of termoelectric elements affects power output of TEG system for optimal values. Te variations in and η wit I for different values of termal conductance at ot and cold junction ( and K L ) are illustrated in Figure 8 and Figure 9. As te value of and K L increases, maximum values attained by and η also go up. Te power output and termal efficiency first increases wit current but afterwards it decreases due to dominating effect ertanika J. Sci. & Tecnol. 6 (): (18) 198

12 Rajes Arora and Ranjana Arora of Joule internal irreversibility (I R). Terefore, one as to obtain te optimum current wit respect to desirable power output and termal efficiency of te system for given set of design variables. ower Output, (Watts) = K =3 K =3 K = K ower Output, (Watts) =3 K = K = K = K = K Figure 3. ower output vs I wit different values of and fixed value of for TEG 1 1 Figure. ower output vs I wit various values of and fixed value of for TEG Efficiency, η =3 K = K = K = K = K Efficiency, η = K =3 K =3 K = K Figure. Termal efficiency vs I wit various values of and fixed value of for TEG Figure 6. Termal efficiency vs I wit different values of and fixed value of for TEG ower Output, (Watts) =3 =6 =9 =1 =1 Efficiency, η = WK -1 =1 WK -1 =1 WK -1 = WK -1 = WK Figure 7. ower output vs I wit different values of number of termoelectric elements for TEG Figure 8. Termal Efficiency vs I wit different values of and K L for TEG 1986 ertanika J. Sci. & Tecnol. 6 (): (18)

13 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems ower Output, (Watts) = WK -1 =1 WK -1 =1 WK -1 = WK -1 = WK -1 Efficiency, η = 3 K = K = K = K = K Figure 9. ower Output vs I wit different values of and K L for TEG Current,I (A) Figure 1. Termal efficiency vs I wit different values of and fixed for TEG wit eat leak between source and sink Figure 1 to Figure 1 sow te relationsip of termal efficiency wit current for different values of, and termal conductance ( and K L ) wit addition of an external irreversibility K in te system. Tis external irreversibility K is because of eat leak between source/sink, due to wic tere is considerable drop in te value of maximum termal efficiency attained by te device. Figure 13 sows te variations of CO wit electric current (I) for various values of sink temperature ( ), assuming a fixed source temperatures ( ) of multi-element TEH. Te CO initially increases up to a maximum limit and declines afterwards wit working electrical current for all cosen values of. Te TEH yields better CO as te value of sink temperature goes up because for fixed eat source temperature, as te temperature difference between source and sink (DTH) decreases CO rises ultimately. Similarly, te variation of CO wit electric current (I) for different values of source temperatures ( ), assuming a fixed sink temperature ( ) of TEH is demonstrated in Figure 1 Te TEH yields reduced CO as te value of eat source temperature goes up because for fixed eat sink temperature, as DTH increases CO drops considerably. Figure 1 sows te variations of eating capacity (Q ) wit I for various values of assuming a fixed eat sink temperature. Te system attains a maximum eating capacity of nearly 11 Watts at =3K and minimum eating capacity of nearly 18Watts at =37K. Hence, increase in source temperature inversely affects eating capacity of te system. Te variation of CO and Q wit I for different number of termoelectric elements () is illustrated in Figure 16 and Figure 17. Te eating capacity Q significantly goes up wit number of termoelectric elements. Te maximum CO accomplised by multi-element TEH system is iger for iger values of. ertanika J. Sci. & Tecnol. 6 (): (18) 1987

14 Rajes Arora and Ranjana Arora Te grapical relationsips of CO and Q wit I for different values of termal conductance at ot and cold junction ( and K L ) are demonstrated in Figure 18 and Figure 19. As te value of and K L increases, maximum value attained by CO decreases and Q increases ultimately. Figure and Figure 1 sow te relationsip of Q wit current for different values of and termal conductance ( and K L ) wit addition of an external irreversibility K in te system. Tis external irreversibility K is because of tis additional eat leak between source/sink, due to wic tere is considerable drop in te value of maximum eating capacity attained by te system, as we compare tese values from Figure 17 and Figure 19. Correspondingly, by comparing Figures to 3 and Figures 16 to18, one can make out te fall in CO of TEH due to eat leak between source and sink = K = K =3 K =3 K..3.3 = WK -1 =1 WK -1 =1 WK -1 = WK -1 Efficiency, η...1 = K Efficiency, η...1 = WK Figure 11. Termal efficiency vs I wit different values of and fixed for TEG wit eat leak between source and sink 1 1 Figure 1. Termal efficiency vs I wit different values of and K L for TEG wit eat leak between source and sink. 3. = K =6 K =7 K =8 K. 3. =3 K =3 K =3 K =37 K CO 3 CO Figure 13. CO vs I wit different values of and fixed value of for TEH Figure 1. CO vs I wit different values of and fixed value of for TEH 1988 ertanika J. Sci. & Tecnol. 6 (): (18)

15 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems Heating Capacity, Q (Watts) =3 K =3 K =3 K =37 K CO =3 =6 =9 =1 = Figure 1. Heating capacity vs I wit different values of and fixed value of for TEH Figure 16. CO vs I wit different values of number of termoelectric elements for TEH Heating Capacity, Q (Watts) =3 =6 =9 =1 =1 CO =1 WK -1 = WK -1 = WK -1 =3 WK Figure 17. Heating capacity vs I wit different values of number of termoelectric elements for TEH Figure 18. CO vs I wit different values of and K L for TEH Heating Capacity, Q (Watts) =1 WK -1 = WK -1 = WK -1 =3 WK -1 Heating Capacity, Q (Watts) =3 =6 =9 =1 = Figure 19. Heating capacity vs I wit different values of and K L for TEH Figure. Heating capacity vs I wit different values of for TEH wit eat leak between source and sink ertanika J. Sci. & Tecnol. 6 (): (18) 1989

16 Rajes Arora and Ranjana Arora Heating Capacity, Q (Watts) =1 WK -1 = WK -1 = WK -1 =3 WK -1 CO =1 =1 =9 = Figure 1. Heating capacity vs I wit different values of and K L for TEH wit eat leak between source and sink Figure. CO vs I wit different values of for TEH wit eat leak between source and sink 3. 3 =1 WK -1 = WK -1 = WK -1 =3 WK -1 CO Figure 3. CO vs I wit different values of and K L for TEH wit eat leak between source and sink Effect of Geometric arameters on te Single-Stage TEG and te Systems Te power output/first law efficiency of TEG depends on te working electric current, I and for given design parameters, tere exists optimal electric current related to wic peak power and termal efficiency can be obtained. Similarly, maximum CO and eating capacity can be obtained for optimal values of working electrical current. From te previous literature, it can be observed tat geometry of termoelectric elements can significantly affect te performance parameters viz. output power, first law efficiency, CO and eating capacity of termoelectric devices. Te geometric parameters comprises lengt and area of termoelectric elements. 199 ertanika J. Sci. & Tecnol. 6 (): (18)

17 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems 6 3 I (A) L (mm) 3 1 Lengt, L (mm) Area, A (mm - ) Figure. Variations of current and lengt wit area of te termoelectric element Figure sows te variations of electric current and lengt wit area of termoelectric couples. It is observed tat lengt possess a linear relationsip wit te corresponding area of termoelectric elements wereas te working electrical current initially increases wit increase in area and stabilizes afterwards. It is clearly sown tat te working electrical current is influenced by te geometric parameters of termoelectric elements. Terefore, variations in lengt and area can considerably vary te required performance caracteristics of termoelectric devices. Tese geometric parameters are associated wit te economical aspects of designing and ence, teir optimum value sould be cosen by appropriate numerical computations. Figure demonstrates te variations of power output wit area for different values source side temperature for an irreversible single stage TEG system. For numerical computation te values of oter parameters are cosen as =3K, =1W/K, L=.mm, I=A and =17.For a fixed value of sink side temperature, as goes up te value of T( - ) increases and as a result te corresponding power output enances. Initially te power output sarply rises wit area A but subsequently attains almost steady values. As te area of termoelectric element increases more termoelectric material is required wic directly affects te cost of te system. Te parallel variations are observed for te termal efficiency of an irreversible single stage TEG system wit area, for different values of in Figure 6. For numerical computation te values of oter parameters are cosen as =3K, =1W/K, L=.mm, I=A and =17.For a fixed value of as enances, iger values of termal efficiency are attained for iger T ( - ). Te termal efficiency increases wit te area of termoelectric elements initially wereas, attains almost steady values afterwards. It is recommended to coose te optimum values of area of termoelectric elements from economical point of view. ertanika J. Sci. & Tecnol. 6 (): (18) 1991

18 Rajes Arora and Ranjana Arora Figure 7 and Figure 8 demonstrate te effects of area of termoelectric couples on output power and termal efficiency for a predetermined value of and various values of. For numerical computation te values of oter parameters are cosen as =K, =1W/K, L=.mm, I=A and =17.As te value of T ( - ) rises, bot power output and termal efficiency consequently goes up. Hence, te temperature difference source and sink side plays an important in obtaining iger values of performance caracteristics of termoelectric devices. In te beginning, tere exists a linear relationsip of area of termoelectric elements and performance parameters, but afterwards power output and efficiency get stabilize. Figure 9 and Figure 3 exibit te effects of area of termoelectric couples on output power and termal efficiency for different values of external termal conductance. For numerical computation te values of oter parameters are cosen as =K, =3K, L=.mm, I=A and =17. Te output power increases gradually as external termal conductance increases. Figure 31 and Figure 3 demonstrate te effects of area of termoelectric couples on coefficient of performance (CO) and eating capacity for some predetermined values of and various values. For numerical computation te values of oter parameters are cosen as =K, =1W/K, L=.mm, I=9A and =17.As te value of T ( - ) rises, CO of an irreversible single stage TEH system consequently goes down. Wit te increase in area, CO initially increases and attains a stable value afterwards. Hence, to design a practical space conditioning system one sould judiciously cose te area of termoelectric elements as area effect te economic aspects of te system. Figure 3 illustrates te relationsip of area and eating capacity for an irreversible single stage TEH system for a predetermined value of and different values of. Te eating capacity possesses inverse relationsip wit area and T ( - ). Figure 33 and Figure 3 exibit te effects of area of termoelectric couples on coefficient of performance (CO) and eating capacity for a predetermined value and different values. For numerical computation te values of oter parameters are cosen as =3K, =1W/K, L=.mm, I=9A and =17.As te value of T ( - ) rises, CO of an irreversible single stage TEH system subsequently declines. Figure 3 illustrates te relationsip of area and eating capacity for an irreversible single stage TEH system for a predetermined value of and different values of. Te eating capacity possesses inverse relationsip wit area and T ( - ). Figure 3 and Figure 36 exibit te effects of area of termoelectric couples on CO and eating capacity for different values of external termal conductance. For numerical computation te values of oter parameters are cosen as =3K, =K, L=.mm, I=9A and =17. Te CO of an irreversible single stage TEH system declines wit rise in external termal conductances. Te eating capacity of te system declines wit te rise 199 ertanika J. Sci. & Tecnol. 6 (): (18)

19 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems in area of termoelectric couples as sown in Figure 36. Hence, CO and eating capacity attain teir maximum values for different values of area of termoelectric elements and for practical design one as to optimize bot simultaneously. Te similar effect as been observed for te lengt of termoelectric couples on output power /termal efficiency for TEG system and CO/eating capacity for TEH system. Te direct relationsip of area and lengt as been sown in Figure. It is concluded from above studies tat for geometric parameters put considerable effect on te performance parameters as well as economic aspects of designing of termoelectric devices. Cost of termoelectric material is concerned wit te geometry of termoelectric elements. For real designing, performance and cost sould be optimized simultaneously in order to acieve most effective operation of termoelectric devices in minimum possible cost ower output, (Watts) = K = K = K Efficiency, η = K = K = K = K. =K Area, A (mm ) Figure. ower output vs area wit different values of and fixed value of for TEG Area, A (mm ) Figure 6. Efficiency vs area wit different values of and fixed value of for TEG ower output, (Watts) = K =3 K = 3 K = K Efficiency, η = K =3 K =3 K = K Area, A (mm ) Figure 7. ower output vs area wit different values of and fixed value of for TEG Area, A (mm ) Figure 8. Termal efficiency vs area wit different values of and fixed value of for TEG ertanika J. Sci. & Tecnol. 6 (): (18) 1993

20 Rajes Arora and Ranjana Arora 3..3 ower output, (Watts) 1 1 = WK -1 =1 WK -1 =1 WK -1 Efficiency, η = WK -1 =1 WK -1 =1 WK -1 = WK -1 = WK Area, A (mm ) Area, A (mm ) Figure 9. ower output vs area wit different values of and K L for TEG Figure 3. Termal efficiency vs area wit different values of and K L for TEG 7 8 CO 6 3 T =3 T =3 T =3 T =37 Heating capacity, Q (Watts) =3 K =3 K =3 K =37 K Area, A (mm ) Figure 31. CO vs area wit different values of and fixed value of for TEH Area, A (mm ) Figure 3. Heating capacity vs area wit different values of and fixed value of for TEH 7 8 CO 6 3 =8 K =7 K =6 K = K Area, A (mm ) Figure 33. CO vs area wit different values of and fixed value of for TEH Heating capacity, Q (Watts) =8 K =7 K =6 K = K Area, A (mm ) Figure 3. Heating capacity vs area wit different values of and fixed value of for TEH 199 ertanika J. Sci. & Tecnol. 6 (): (18)

21 Termodynamic Analysis of Termoelectric Generator & Heat ump Systems 7 8 =3 WK = WK -1 CO 3 =1 WK -1 = WK -1 = WK -1 =3 WK -1 Heating capacity, Q (Watts) = WK -1 =1 WK Area, A (mm ) Figure 3. CO vs area wit different values of and K L for TEH Area, A (mm ) Figure 36. Heating capacity vs area wit different values of and K L for TEH Validation of te Study In order to verify/validate te termodynamic modeling of TEG and TEH systems, te data stated in te previous studies are utilized and te comparison is done as illustrated in Table 3. For TEG, te obtained outcomes sow an agreement wit tat of stated in Hogblom and Andersson (1). Conversely, CO of TEH obtained in te present work matces wit tat of stated in ami et al. (17) wereas eating capacity matces wit tat of reported in Kuasik et al. (1), on te basis of same operating conditions and input parameters. Table 3 Comparison of designing and performance parameters wit previous literature Comparative Investigations I (A) T (K) Designing arameters erformance arameters TEG TEH TEG TEH T c (K) I (A) T (K) T c (K) (W) η Q H (W) resent Study Hogblom and Andersson (1) Kausik et al. (1) ami et al. (17) CO ertanika J. Sci. & Tecnol. 6 (): (18) 199

22 Rajes Arora and Ranjana Arora COCLUSIO Finite time termodynamic analysis carried out on multi-element irreversible TEG and TEH devices directs te major concluding points as follows: Te generalized finite time termodynamic models of TEG and TEH systems are establised considering inner geometrical dimensions, eat transfer in external mode and temperature dependent pysical properties. Formulation of performance parameters of termoelectric devices in context wit electric current, termoelectric couples, temperature of ot/cold side and termal conductances of ot/cold side is presented. Te analytical formulation of ot/cold sides temperature based on energy balanced equation is acieved for TEG and TEH devices. Te proposed system configurations are investigated wit and witout eat leak between eat source and sink. Te effects of design factors on power output/first law efficiency and eating capacity/ coefficient of performance are analyzed. Te effect of area and lengt on power output/termal efficiency, CO and eating capacity is investigated wit variations in,, /K L for single stage TEG and TEH systems. It is concluded from above studies tat for geometrical parameters put considerable effect on te performance parameters as well as economic aspects of designing of termoelectric devices. Cost of termoelectric material is concerned wit te geometry of termoelectric elements. For real designing, performance and cost sould be optimized simultaneously in order to acieve most effective operation of termoelectric devices. It is also observed tat various parameters impact te design variables in different ways and performance parameters of termoelectric devices. Te termodynamic optimization is mandatory and operative for practical operations at variable conditions. Te varying features of various input and geometric/design variables obtained in tis study is utilized as te bencmark for assessing te effects of external/internal irreversibility on optimum performances of TEG and TEH systems. Moreover, a practical setup of te proposed termoelectric systems could be fabricated based on te obtained optimal values of design parameters. REFERECES Andresen, B. (1983). Finite-time Termodynamics. ysics Laboratory II, University of Copenagen. Angrist, S. W. (199). Direct Energy Conversion. Boston: Allyn and Bacon Inc. Cen, J., & Wu, C. (). Analysis of te performance of a termoelectric generator. Journal of Energy Resource-ASME, 1(), ertanika J. Sci. & Tecnol. 6 (): (18)

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24 Rajes Arora and Ranjana Arora Sun, X., Liang, X., Su, G., Tian, H., Wei, H., & Wang, X. (1). Comparison of te two-stage and traditional single-stage termoelectric generator in recovering te waste eat of te ig temperature exaust gas of internal combustion engine. Energy, 77, Tan, H., Fu, H., & Yu, J. (17). Evaluating optimal cooling temperature of single-stage termoelectric cooler using termodynamic second law. Applied Termal Engineering, 13, Xuan, X. C., g, K. C., Yap, C., & Cua, H. T. (). Te maximum temperature differences and polar caracteristics of two-stage termoelectric coolers. Cryogenics, (), Zu, J., Gao, J., Cen, M., Zang, J., Du, Q., Rosendal, L. A., & Suzuki, R. O. (11). Experimental study of a termoelectric generation system. Journal of Electronic Materials, (), ertanika J. Sci. & Tecnol. 6 (): (18)