J. Electrical Systems 12-3 (2016): Regular paper. Parametric analysis of temperature gradient across thermoelectric power generators

Transcription

1 Kaled Caine, *, Moamad Ramadan, Zaer Meri, Hadi Jaber, Mamoud Kaled, 3 J. Electrical Systems -3 (6): Regular paper Parametric analysis of temperature gradient across termoelectric power generators JES Journal of Electrical Systems is paper presents a parametric analysis of power generation from termoelectric generators (EGs). e aim of te parametric analysis is to provide recommendations wit respect to te applications of EGs. o proceed, te one-dimensional steady-state solution of te eat diffusion equation is considered wit various boundary conditions representing real encountered cases. Four configurations are tested. e first configuration corresponds to te EG eated wit constant temperature at its lower surface and cooled wit a fluid at its upper surface. e second configuration corresponds to te EG eated wit constant eat flu at its lower surface and cooled wit a fluid at its upper surface. e tird configuration corresponds to te EG eated wit constant eat flu at its lower surface and cooled by a constant temperature at its upper surface. e fourt configuration corresponds to te EG eated by a fluid at its lower surface and cooled by a fluid at its upper surface. It was sown tat te most promising configuration is te fourt one and temperature differences up to 7 C can be acieved at 5 C eat source. Finally, a new concept is implemented based on configuration four and tested eperimentally. Keywords: Energy arvesting; termoelectric generation; Seebec effect; waste eat recovery. Article istory: Received 8 Marc 6, Accepted 6 August 6. Introduction e adverse climate canges being witnessed across te planet togeter wit te everdecreasing reserves of primary resources, resulting from rapid growt in energy demand due to population growt and industrialization, ave raised public awareness to te dire consequences of pollution and inefficient energy usage. Indeed, promoting energy efficiency [], energy-saving beaviors and renewable energy systems [-5] as become an essential part of te energy policies and strategies in developed countries. In 7, te European Council set te following ambitious targets to be acieved by : reducing emissions of greenouse gases by % wit respect to te 99 levels, improving energy efficiency wit te aim of saving % of te European Union energy consumption, and raising te renewable energy sources sare to % [6]. It is ence of strategic importance to optimize energy usage and eplore new green energy sources. An abundant source of energy tat remains largely unarvested is waste energy [7], and especially waste eat [8-]. Almost one-tird of te energy consumed by industry is released as termal losses directly to te atmospere or to cooling systems []. ese discarges result from te losses tat occur in engineering systems. is waste eat can be recovered into a useful source of energy. * Corresponding autor: K. Caine, Electrical and Electronics Engineering Department, ebanese International University, PO Bo 4644 Beirut, ebanon, aled.caine@liu.edu.lb Energy and ermo-s Group EF, Scool of Engineering, ebanese International University, PO Bo 4644 Beirut, ebanon aboratoire de Génie Industriel, CentraleSupélec, 99 Câtenay-Malabry, France 3 Univ Paris Diderot, Sorbonne Paris Cité, Institut des Energies de Demain, Paris-France Copyrigt JES 6 on-line : journal/esrgroups.org/jes

2 K. Caine et al: Parametric analysis of temperature gradient across EGs ermoelectric materials allow converting a temperature gradient into electricity. Altoug tey are not yet efficient enoug to be applied industrially on large scale, EGs present te advantages of being silent, scalable and reliable [, 3]. erefore, a deeper understanding of te parameters tat affect te termoelectric performance of EGs is required for reacing adequate conversion levels. e present wor concerns eat transfer modeling and parametric analysis of te termal beaviors of EG subjected to different boundary conditions. e ultimate aim is to suggest new applications and/or strategies towards maimizing te temperature gradient across a EG and ence its power output. Upon te investigation of four different configurations, eac aving different modes and boundary conditions, promising results were obtained regarding one configuration in wic te temperature gradient is formed between two convection boundaries. A new concept is ten implemented based on te promising configuration and tested eperimentally. e remaining of te paper is organized as follows: section presents te parametric analysis for te different configurations, section 3 sows te eperimental results, and finally section 4 draws te conclusions.. Parametric analysis and recommendations is section concerns a parametric analysis of te EG termal beavior subjected to several conditions. e aim is to find recommendations as to obtaining significant temperature gradient troug te EG module. Altoug a temperature gradient is te trigger for a EG to generate power, practically tis gradient is not eactly nor necessarily obtained by fiing te temperatures at te two EG surfaces. Moreover, fiing te temperatures at te two surfaces of te EG requires eternal means requiring power. e most common boundary conditions tat are encountered in practice will be eposed and treated below. For eac case, te temperature gradient between te ot and cold surfaces of te EG will be evaluated at steady state and parametrically analyzed. Figure sows scematics of te different configurations tat will be tested. EG, (a) EG, q (b) EG, q (a) EG, (d) Fig.. Scematics of (a) configuration, (b) configuration, (c) configuration 3, and (d) configuration 4. 64

3 J. Electrical Systems -34 (6): In configuration one (Figure -a), te EG of ticness and termal conductivity is subjected to a constant temperature at its ot side and simultaneously cooled by air aving a convective coefficient and temperature. In configuration two (Figure -b), te EG is subjected to a constant eat flu q at its ot side and simultaneously cooled by air aving a convective coefficient and temperature. In configuration tree (Figure -c), te EG is eated at its ot side wit a constant eat flu q and simultaneously subjected to a constant temperature at its cold side. In configuration four (Figure -d), te EG is eated at one side wit air aving a temperature and convective eat transfer coefficient wile being simultaneously cooled wit air aving a temperature and convective eat transfer coefficient at te oter side. For te different conditions, te EG is considered as a plane wall and te conduction troug it as one-dimensional and steady. en, te eat diffusion equation is reduced to: d d = () e temperature distribution and te temperature gradient in all configurations can bot be obtained by solving te differential equation of te eat diffusion equation above, but will vary according to te boundary conditions. In all of te above configurations, integrating te reduced form of te eat diffusion equation wit respect to yields te below linear variation dependent on two constants A and B function of te boundary conditions: ( ) A B + = () Below, te boundary conditions, temperature distributions and temperature differences corresponding to te four configurations are eposed. Configuration (, t) = (3-a) d d ( ) = = = ( ) [ ( t) ] + K +, (3-b) (3-c) 65

4 K. Caine et al: Parametric analysis of temperature gradient across EGs = ( ) + (3-d) Configuration d d d d = = q = q = [ ( t) ] ( ) + + q (4-a), (4-b) + = (4-c) q = (4-d) Configuration 3 d d = (, t) = q (5-a) = (5-b) q q ( ) = + + (5-c) q = (5-d) Configuration 4 d d d d ( ) = + = = = = = ( ( ) ) ( ( ) ) ( ) ( + ) + ( ) ( + ) + ( ) ( + ) + + (6-a) (6-b) (6-c) (6-d) Results for configuration 66

5 J. Electrical Systems -34 (6): From equation 3-d, it is obvious tat te iger te temperature prescribed at one surface of te EG, te lower te fluid temperature, and te lower te termal conductivity of te EG, te iger will be te temperature gradient. On te oter and, no direct conclusions can be made wit respect to te ticness and convective coefficient. o proceed and ave clear magnitude orders and recommendations, a parametric analysis wit respect to te mentioned parameters is carried out. Figure sows te variation of te temperature gradient troug te EG in function of te convective coefficient for different ticness of te EG. For te set of calculations corresponding to Figure, te temperature at te ot surface is fied at 5 C, te fluid temperature at C, and te termal conductivity of te EG at W/m.K. From Figure, one can conclude tat increasing te convective coefficient and ticness will increase te temperature gradient. As illustration and magnitude orders for a ticness of mm, wen te convective eat transfer coefficient increases from 5 to 5 W/m.K, te temperature difference troug te EG increases from 3. to 55.7 C. For a ticness of mm, te temperature difference increases from 6 to 4.7 C wen te convective eat transfer coefficient increases from 5 to 5 W/m.K.. emp. Diff. (C) =. m =. m =.4 m =.6 m =.8 m =. m. 5 5 Convective coefficient (W/m.K) Fig.. Variation of te temperature gradient in function of te convective coefficient for different EG ticnesses. Despite aving a relatively ig temperature gradient in correspondence wit te eat convective coefficient, tis configuration only eists wen te convective eat coefficient reaces very ig values (values iger tan W/m.K). Results for configurations and 3 ooing at equations 4-d and 5-d of configurations and 3, it is obvious tat te iger te eat flu q at one of te surfaces of te EG, te larger te ticness of te EG, and te lower te EG termal conductivity, te iger will be te temperature gradient troug te EG module. erefore, configurations two and tree are dependent on tree parameters. e first is te eat flu, wic in most applications is obtained from te solar radiation and can be 67

6 K. Caine et al: Parametric analysis of temperature gradient across EGs approimated by a constant value, tus noting can be improved regarding it wen eistent as boundary condition. e two oter remaining parameters wic bot can be improved are te termal conductivity and te ticness of te EG. is improvement is lined to te design of te EG. So te optimization of te temperature gradient in configurations two and tree depends on te dimensions and pysical properties of te termoelectric generator and sligtly on te boundary condition (application). On te oter and, it is recommended to use EG in configurations two and tree wen ig eat flues are present. Indeed for typical values of of W/m.K and of 5 mm, temperature gradients iger tan C will be obtained for eat flues starting from W/m. Results for configuration 4 From equation 6-d, it is obvious tat te temperature gradient troug te EG increases wen te temperature difference between te ot and cold fluids increases and wen te termal conductivity of te EG decreases. On te oter and, no direct conclusions can be made wit respect to te convective coefficients and. o proceed and ave clear magnitude orders and recommendations, a parametric analysis wit respect to te mentioned parameters is carried out. Figure 3 sows te variation of te temperature gradient troug te EG in function of te convective coefficient for different values of te convective coefficient. For te set of calculations corresponding to Figure 3, te temperature at te ot fluid is fied at 5 C, te temperature of te cold fluid at C, te ticness of te EG module at 3 mm, and te termal conductivity of te EG at W/m.K. emp. Difference (C) = 5 W/m.K = W/m.K = 8 W/m.K = W/m.K = W/m.K = 4 W/m.K = W/m.K = 5 W/m.K. 5 5 (W/m.K) Fig. 3. Variation of te temperature gradient in function of te convective coefficients of te ot and cold fluids. From Figure 3, one can conclude tat increasing te convective coefficients of te ot and cold fluids increases te temperature difference across te EG. As illustration, for a convective coefficient of 5 W/m.K and wen te convective eat transfer coefficient increases from to 5 W/m.K, te temperature difference troug te EG 68

7 J. Electrical Systems -34 (6): increases from.7 to 8.8 C. For a convective coefficient of 5 W/m.K, te temperature difference increases from 3.7 to 68.8 C wen te convective eat transfer coefficient increases from to 5 W/m.K. A remarable feature in te curves of Figure 3 is tat for many values of te convective coefficient, te temperature difference becomes almost constant or sligtly varies wen te convective coefficient increases. is means tat te coice of te two fluid flow configurations in practice sould be selected taing into consideration te couple of values of and tat do not correspond to te constant or sligtly varying regions of te curves. Suc configuration can be promising since up to relatively ig values of convective eat coefficients, te temperature gradient obtained is of significant value and can be used in generating power for different applications. able finally summarizes te different recommendations given wit eac of te four configurations. able. Summary of recommendations. Config. Details Recommendations EG, EG, q - e ticness of te EG, te temperature prescribed at te ot surface of te EG, and te convective coefficient sould be ig; - e fluid temperature at te cold side and te termal conductivity of te EG sould be low. - e ticness of te EG and te eat flu prescribed at te ot surface of te EG sould be ig; - e termal conductivity of te EG sould be low. 3 EG, q - e ticness of te EG and te eat flu prescribed at te ot surface of te EG sould be ig; - e termal conductivity of te EG sould be low. 69

8 K. Caine et al: Parametric analysis of temperature gradient across EGs 4 EG, - e ticness of te EG, te temperature of te ot fluid, te convective coefficients of te ot and cold sides sould be ig; - e termal conductivity of te EG and te temperature of te cold fluid sould be low. As conclusion, te most promising configuration is configuration 4 provided tat te designer selects te appropriate couple of convective eat transfer coefficients since it as te most promising magnitude orders and corresponds at te same time to real configurations tat can be encountered in engineering practice. All te configurations can be more promising if te termal conductivity of te EG can be lowered and its ticness increased wic is related to te enancement of te design of te EG itself. Configurations and 3 can be also promising if te applications involve ig and etreme eat flues. Configuration can also be more promising for applications were ig temperatures are present. e following section will be devoted to te implementation of configuration 4 in a real case and corresponding tests and termal beaviors. 3. Eperimental results e study presented in te previous section as sown tat configuration 4 presents te iger gradient of temperature for te same conditions. As an application, a system tat is eated by solar energy can be suggested, were te ot fluid is eated by solar rays, wereas cold fluid is water (or oter fluid) at ambient temperature. In te frame of tis paper tis system will be simulated eperimentally by a prototype (see Figure 4). Fig. 4. Prototype simulating EG undergoing eating and cooling by convection It is constructed of two boes tat are separated by a layer of epoy representing te EG and aving te same pysical caracteristics, tat is to say te same ticness and almost te same conductivity. e boes contain te ot and cold fluids, wic are respectively oil and water. o measure te temperature difference termo-couples are installed on te upper and lower surfaces of te epoy layer. e tans are insulated to decrease te eat loss wit te surroundings. For simplicity, te oil is eated by an electrical eater. 63

9 J. Electrical Systems -34 (6): Fig. 5. Variation of temperature difference in function of time Figure 5 presents te variations of temperature at te upper and lower surfaces of te epoy layer wit time as well as te variation of te temperature gradient. e eperiment is carried out over 5 minutes. e ot temperature varies from 5 C to C. e cold temperature is almost constant and increases from 5 C to 3 C. e temperature difference in its turn increases wit time to reac a maimum of 8 C. e electrical power tat may be obtained wen te EG undergoes a temperature difference depends on te caracteristics of te EG. If a maimum power voltage of.5 V per C of temperature difference is considered, te obtained variation of te voltage for te above-mentioned time duration is between and V as sown in Figure Conclusions Fig. 6. Variation of voltage in function of time A parametric analysis concerning EG is presented. A matematical model is proposed to simulate te termal beavior of EG. Several configurations were considered. It was sown tat te configuration wit ot and cold fluid on te top and bottom of EG offers te igest temperature difference. An eperimental study is carried out as a proof of concept. e results sowed tat a temperature difference of 8 C could be obtained wen te ot fluid reaces C and te cold fluid is initially at 5 C. e obtained voltage depends on te caracteristics of utilized EG. For suc a temperature difference, an average voltage of V can be obtained. 63

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