AME 60634 Int. Heat Trans.
Thermoelectric Effect & Thermoelectric Devices
*borrowed heavily from presentation by G. Chen, MIT
D. B. Go Slide 1 AME 60634 Int. Heat Trans. Seebeck Effect
Seebeck Effect: Temperature difference generates a voltage between two different materials
hot
Conductor 1 Conductor 2
cold Thomas Johann Seebeck 1821, Germany
D. B. Go Slide 2 AME 60634 Int. Heat Trans. Seebeck Effect
electrons diffuse from hot to cold
Thot Tcold
electric potential builds up that resists diffusion
ΔV V −V S = − = − hot cold ΔT Thot −Tcold
Seebeck coefficient: S [V/K]
D. B. Go Slide 3 AME 60634 Int. Heat Trans. Peltier Effect
Peltier Effect: Current flow can induce a temperature gradient depending on direction of current flow
hot
Conductor 1 Conductor 2
A
Jean Charles Athanase Peltier 1834, France
D. B. Go Slide 4 AME 60634 Int. Heat Trans. Current and Heat Flow Newton’s 2nd Law m*v dv F = −qE − = m* τ dt
Coulombic force drag due to collisions
The€ steady-state solution gives the average electron “drift” velocity qτ qτ v = − * E µe = * ≡ electron mobility m m
The current density is the rate of charge transport per unit area (like heat flux) n q2τ elec compare to Ohm’s law! j€ele c = −nelecqv = * € E = σ∇Φ m
But the electrons carry heat with them! u Peltier coefficient: Π [J/A] j = n uv = j = Πj heat elec q elec elec
D. B. Go Slide 5 AME 60634 Int. Heat Trans. Peltier Effect
- Induced heating and cooling at the two junctions due to mismatch - Reversible by reversing the direction of current flow - A refrigerator! (current is “work” to drive “heat”)
jelec, jheat 1
q q 2
jelec, jheat
q (Peltier): (Π1-Π2)×j
D. B. Go Slide 6 AME 60634 Int. Heat Trans. Thomson Effect
Thomson Effect: Current flow through a temperature gradient will generate/absorb heat because thermoelectric properties are temperature dependant
heat release/adsorption
Thot Tcold
current
William Thomson, Lord Kelvin 1855, Ireland
D. B. Go Slide 7 AME 60634 Int. Heat Trans. Thomson Effect
heat release/ absorption needed for energy balance electrons diffuse q(x) from hot to cold
Thot Tcold
current i
Thomson coefficient: τ = (1/i)×(dq/dx)/(dT/dx)
Kelvin Relations: dS Π = ST; τ = T dT
D. B. Go Slide 8 AME 60634 Int. Heat Trans. Thermocouples & The Thermoelectric Effect
Thermocouples operate under the principle that a circuit made by connecting two dissimilar metals produces a measurable voltage when a temperature gradient is imposed between one end and the other.
D. B. Go Slide 9 AME 60634 Int. Heat Trans. Thermoelectric Devices
http://www.energybandgap.com
D. B. Go Slide 10 AME 60634 Int. Heat Trans. Peltier Coolers
T , q c c Ideal Device: • No conduction (hot to cold) • No Joule heating
qc = (Π p − Πn )×i
Real Device: • conduction (hot to cold) Th, qh • Joule heating
2 qc = (Π p − Πn )i −i R 2 −σ cond (Th −Tc )
electrical resistance thermal conductance A k A k L L σ = p p + n n R p n cond = + Lp Ln Apσ p Anσ n
D. B. Go Slide 11 AME 60634 Int. Heat Trans. Peltier Coolers: Refrigeration Performance
Voltage Drop: Sp − Sn Real Device: V = iR + • conduction (hot to cold) Th −Tc • Joule heating
Coefficient of Performance: S S iT i2 R 2 T T qc ( p − n ) c − −σ cond ( h − c ) COP = = 2 W (Sp − Sn )i(Th −Tc ) +i R
Optimal Current to Maximize COP:
1 Tc 1+ ZTM −Th Tc COP = Tm = (Th +Tc ) max 2 (Th −Tc ) 1+ ZTM +1
D. B. Go Slide 12 AME 60634 Int. Heat Trans. The Z Parameter
2 2 S − S S − S Z = ( p n ) = ( p n ) R " %" % σ cond Lp Ln Apkp Ankn $ + '$ + ' # Apσ p Anσ n &# Lp Ln &
To Maximize Z:
1 ! $2 ! $ 2 k k Ln Ap σ k Rσ = # p + p & when = # n n & ( cond )min # & L A #σ k & " σ p σ p % p n " p p %
Leading to Z: 2 (Sp − Sn ) Zmax = 2 k k ( p σ p + n σ n ) D. B. Go Slide 13 AME 60634 Int. Heat Trans. Figure of Merit: ZT
For a Single Material:
2 σ S T increase electrical conductivity ZT = k decrease thermal losses (conduction)
D. B. Go http://chemgroups.northwestern.edu/kanatzidis/greatthermo.html Slide 14 AME 60634 Int. Heat Trans. Superlattice
increase electrical conductivity decrease thermal losses (conduction) 2 2 2 σ S T constrained by k π kB ZT = Widemann-Franz = 2 k σT 3q
σ S2T ZT = kelec + kphonon
http://lucidthoughts.com.au/ D. B. Go Slide 15 AME 60634 Int. Heat Trans.
http://www.kickstarter.com/projects/flamestower/flamestower-charge-your-gear-with-fire
http://energyblog.nationalgeographic.com/2013/09/24/google-science-fair-winner-makes-flashlight-powered- by-body-heat/
http://www.customthermoelectric.com/
D. B. Go Slide 16