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Thermoelectric Effect and Thermoelectric Devices

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Thermoelectric Effect and Thermoelectric Devices Thermal Radiaton: Planck’s Law IT Perfectly Basic Relations , M Reflecting Wall Frequency ν n at T he to Inside the Cavity Angular FrequencyC ω=2πν al EM Wave In Wavelength λg m Equilibrium at Wavevectoran magnitudee k=2r π/λ Temperature T k WavevectorG k=(kx,khy,kz) n /T io 2 2 2 ©c =νλ r ωs= ck = c kx + k y + kz ht la er ig So v ω(k): Dispersion relation (linear) yr t on p cHow muchC energy in the cavity? o ire y C g ∞ ∞ ∞ D Ur = 2 ω f (ω ,T ) = λ λ7 λ 7 e ∑∑∑h x x x n x =1 n y =1 nz =1 L x = ,29 ,...,nx 9,... .29 2 .92 En ∞ ∞ ∞ l dk x dk y dk z 2 2π 2 a 2 hω f (ω ,T ) k = n r ∫ (2π / 2L )∫ (2π / 2L )∫ (2π / 2L ) x x o ic 0 x 0 y 0 z 2 Lx tr F c ∞ ∞ dk ∞ dk x y dk z le = 2 hω f (ω ,T ) ∫ (2 / L ) ∫ (2 / L ) ∫ (2 / L ) TwoE polarization −∞ π x −∞ π y −∞ π z –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Thermal Radiaton: Planck’s Law ∞ ∞ ∞ IT 2V • Energy density per interval U = ω f (ω ,T )dk x dk ydkz Mω 8π 3 ∫∫∫ h , − ∞− ∞− ∞ n ∞ u (ω ) = hω f (ω ,e T )D(ω) 2V 2 to = ω f (ω ,T )4 πk dk 3 h 3 ∫ h hω C 1 l 8π 0 = a Planck’s law π 2 c 3 ⎛ ⎞ ∞ 2 g hω m 2V ω ω n exp⎜ r ⎟ −1 ⎛ ⎞ ⎛ ⎞ a e⎜ k T ⎟ = 3 hω f (ω ,T )4 π ⎜ ⎟ d ⎜ ⎟ ⎝ B ⎠ 8π ∫ ⎝ c ⎠ ⎝ c ⎠ G h n 0 • Intensity:/T energyio flux per unit ∞ 2 © r s U ω t lsolida angler = hω f (ω , T ) 2 3 dω V ∫ c h o e 0 π g v i S 3 ∞ r dAnp cu(ω) ω 1 y t o I ()ω = = h = ωf (ω , T )D(ω)d ω p c C 3 2 ∫ h o re 4π 4π c ⎛ hω ⎞ 0 i y exp⎜ ⎟ −1 C k T ∞ D g ⎝ B ⎠ 7 7 er = ∫ u ()ω d9ω 9 Solid Angle Per unit wavelength interval 0 .9 .9 En l dAp I(ω)d ω 4π c 1 2 2 a dΩ = I ()λ = = h r ic R2 d λ λ5 ⎛ 2π c ⎞ D(ω)-densityo of statestr per exp⎜ h ⎟ −1 unit volumeF per cunit whole space ⎜ k Tλ ⎟ e ⎝ B ⎠ angular frequencyEl interval 4π Planck’s law –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Thermal Radiaton: Planck’s Law IT Q& Wien’s displacement la,w M en o λ T = 2898 Kμmh t max C al 4 g m 10 an er G h n Emissive Power m) T o μ 3 / i 2 r t10© la rs h/cm o e g W v Q& ()λ = AπI()λ i S n r 2 y R ( 10t o 5600 K ω 3 1 p E c W C = A h o e 2 2 ir O y 2800 K 4π c ⎛C ω ⎞ P h D 1 g exp⎜ ⎟ −1 E 10r ⎜ ⎟ V 7 ⎝ k B T ⎠ 7 I e 9 9 S S 9 9 EnI 1500 K . M l 0 2 2 E Total r a 10 ∞ ic o r4 Q& = ∫F Q&()λ dλ =cAσtT 800 K 0 e 10-1 l 0 2 4 6 8 10 E WAVELENGTH (μm) –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Introduction to Thermoelectricity Mecha Massachusetts InstituteGang of ChenTechnology n 2.997 Copyrighicalt Engineering© Ga Departmentng C hen, MIT For 2.99URL:7 http://web.mit.edu/nanoengineeringDirect Solar/T hermal to Electrical Energy Conversion –WARREN M. ROHS ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Seebeck Effect IT Hot M n, he to C al g m an er ConducG tor T1 h n Conductor 2 © r/ sio ht la er ig So v yr t on p ec C o ir y Cold C D rg 97 97 e .9 .9 En Voltage 2 2 al r ic Seebeck effect: Discovered in 1821 Thomaso Johanntr Seebeck 1770-1831F c Temperature difference generates voltage le E http://www.sil.si.edu/silpublications/dibner-library-lectures/scientific-discoveries/text-lecture.htm –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Peltier Effect Heating or Cooling Jean Charles Athanase 1785-18452.9 97 Copyright © Gang Chen, MIT Conduc For 2.997 Direct Solatorr 1/ Thermal to Pelt Electrical ierEn ergy Conversion Conduc Peltier An electrical current creates a cooling or tor 2 E A –WARREN M. ROHSheating effectffect: at the Discovered junction dependingin 1834 on the direction of current flow. ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Thomson Effect IT M heat release/absorptionn, q(x) he to C al T g m T coald n er hot h currentn G /T io © ar rs ht ol e rig S nv y ct Thomsono effect predicted, 1855 op re C C Di gy William 7Thomson 7 er (Lord9 9Kelvin)9 9 En 18242. – 19072 . l r ica Fo tr echttp://www.sil.si.edu/silpublications/dibner-library-lectures/scientific-discoveries/text-lecture.htm El –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT An Intuitive Picture of Thermoelectric Effects IT • Current Flow in an Isothermal ConductorM n, • • e• o • • • • • • h t • • • • l • • C • • • • • • • • • • a • • •• • • •• •• • • • • •• g• • m • • • n • • r • • a• • e • • • • • • • • • • • • G• • h• n © • r/T io Electrical t la rs Field [V/m] gh o ve i S n Electrical Current Density Jy r= envt= enμε o= σε =ε / ρ p e c C Resistivity [Ωm] o ire y CElectron g Electron D rDrift Mobility Electrical Charge7 [C] Density7 [1/m3] e 9 9 Velocity [m/s] [m2/s.V] Conductivity [1/Ωm] .9 .9 l En 2 r 2 a q Heat Fluxo ricJ = qn v = J = ΠJ F ct q e e le e E Heat Per Charge [J] Peltier Coefficient [J/A] –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Peltier Q Effect 1 J e , J q1 2.997 Copyright © G2 ang Chen, MIT • Heating andQ (Peltier)cooling = (at junctions For• 2.997 Direct Solar/Thermal to J Q Reversible with current directione , J Electrical Energy Converq2s ion Π 1 −Π 2 )J –WARREN M. ROHS ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Seebeck Effect IT Built-In Potential , M en o h l t • • • • • • • C • a Vcold •• • • • • Vhot •••• •• • • • •• • g m Tcold • • n• r• Thot • • • • • • a• •h•e n G /T io © ar rs hTemp.t Gradientl e ig So v yr t on p ec C • ChargeCo diffusionir undery a temperature gradient • Built-in potentialD resistingrg diffusion 97 97 e .9 .9 l En 2 2S = -ΔaV/ΔT = -(V -V )/(T -T ) r ic hot cold hot cold Fo tr ec El S --- Seebeck Coefficient –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Thomson Effect IT M heat release/absorption q(x)n, he to C al • • • • g• m• T •• • • • •n r Thot cold •••• •• •• • a • e • • •• •• G • h • n • • • • • • • r/T• • io t © la rs gh ocurrent ve ri t S n py c Co o ire y 1dq dT ThomsonC CoefficientD r g τ= 7 7 e Idx dx 99 99 En 2. 2. l r ica Fo tr • Kelveinc Relations: Π = ST; τ=TdS/dT El –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Properties are Temperature Dependent Images removed due to copyright restrictions. Please see Fig. 2a,b in Poudel, Bed, et al. "High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys." Science 2.997 Copyri g320 (Mayh t2, 2008):© 634-638. G ang Chen, MIT For 2.997 Direct Solar/Thermal to Electrical Energy Conversion –WARREN M. ROHS ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Thermoelectric Devices COLD SIDE HOT SIDE COLD SIDE 2.9 97 Copyright © Gang C-hen, MIT I + For 2.997 Direct Solar/ThNe rmal to P Elec trical Energy ConveHOTrs SIDEio n –WARREN M. ROHS ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Performance of Thermoelectric Devices 2.997 Copyright © Gang Chen, MIT For 2.997 Direct Solar/Thermal to Electrical Energy Conversion –WARREN M. ROHS ENOW HE AT AND MASS TRANSF E ER LABORATORY , MIT Other Basic Relations: T h • Fourier Law for heat conduction L Heat Conduction Area A Heat Flux [W/m q • = 2.9 97 CopyrOight © Gang−Chen, MIT ne-dimensional2] heat kconduction∇ For 2.997 Direct Thermal ConductivityT [W/m.K] T Solar/Thermal to c Q Electrical En e= rgy Conversion Ak T Thermal h −T L c –WARREN M. ROHS = Conductanc K ΔT ENOW HE AT AND e : MASS TRANSF K = kA E ER LABORATORYL , MIT Device Analysis: Cooling IT • Ideal Devices M T Q , c c n No Joule Heating,he to No Heat ConductionC a l ng rm Qc = (aΠp- Πn)•Ιe p h n n G /T io • ©Real Devices:ar rs ht ol e rig JouleS Heatingnv & Heat Conduction y ct o op e Q = (CΠ -Π )•Ι−I2R/2 - K (T -T ) T Q ir cy p n h c h Ch D g 7 7 er 9 9 Electrical Resistance Thermal Conductance .9 .9 l En 2 2 a L p ρ p L ρ k A k A or ic R = + n n K = p p + n n F tr A A L L ec p n p n El –WARREN M.
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