Thermoelectric Effect and Thermoelectric Devices

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.

View Full Text

Details

  • File Type
    pdf
  • Upload Time
    -
  • Content Languages
    English
  • Upload User
    Anonymous/Not logged-in
  • File Pages
    33 Page
  • File Size
    -

Download

Channel Download Status
Express Download Enable

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

  • Not to be reproduced or distributed without explicit permission.
  • Not used for commercial purposes outside of approved use cases.
  • Not used to infringe on the rights of the original creators.
  • If you believe any content infringes your copyright, please contact us immediately.

Support

For help with questions, suggestions, or problems, please contact us