1. 1 ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 15: Introduction to Thermoelectric Energy Conversion (Reading: Handout) Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712 www.me.utexas.edu/~lishi lishi@mail.utexas.edu

2. 2 References Thermo-electrics: Basic principles and New Materials Development by Nolas, Sharp and Goldsmid Thermoelectric Refrigeration by Goldsmid Thermodynamics by Callen. Sections 17-1 to 17-5

3. 3 Outline Thermoelectric Effects Thermoelectric Refrigeration Figure of Merit (Z) Direct Thermal to Electric Power Generation

4. 4 Applications Beer Cooler Thermally-Controlled Car Seat Electronic Cooling Cryogenic IR Night Vision

5. 5 Basic Thermoelectric Effects Seebeck effect Peltier Effect Thomson effect

6. 6 Seebeck Effect In 1821, Thomas Seebeck found that an electric current would flow continuously in a closed circuit made up of two dissimilar metals, if the junctions of the metals were maintained at two different temperatures. S= dV / dT; S is the Seebeck Coefficient with units of Volts per Kelvin S is positive when the direction of electric current is same as the direction of thermal current

7. 7 Peltier Effect In 1834, a French watchmaker and part time physicist, Jean Peltier found that an electrical current would produce a temperature gradient at the junction of two dissimilar metals. П <0 ; Negative Peltier coefficient High energy electrons move from right to left. Thermal current and electric current flow in opposite directions.

8. 8 Peltier Cooling П >0 ; Positive Peltier coefficient High energy holes move from left to right. Thermal current and electric current flow in same direction. q=П*j, where q is thermal current density and j is electrical current density. П= S*T (Volts) T is the Absolute Temperature

9. 9 Thomson Effect Discovered by William Thomson (Lord Kelvin) When an electric current flows through a conductor, the ends of which are maintained at different temperatures, heat is evolved at a rate approximately proportional to the product of the current and the temperature gradient. is the Thomson coefficient in Volts/Kelvin Seebeck coeff. S is temperature dependent Relation given by Kelvin:

10. 10 Thermoelectric Refrigeration The rate of heat flow from one of the legs (i=1 or 2) : (1)

11. 11 The rate of heat generation per unit length due to Joule heating is given by: (2) Eqn 2 is solved using the boundary conditions T= T c at x=0 and T= T h at x= l. Thus it is found that: The total heat removed from source will be sum of q 1 and q 2 q c = (q 1 + q 2 )| x=0 (3) (4) Eqs. 1, 3, 4  K: Thermal conductance of the two legs R: Electrical Resistance of the two legs

12. 12 The electrical power is given by: COP is given by heat removed per unit power consumed Differentiating w.r. to I we get max. value of COP whereand T m =(T h +T c )/2 A similar approach can be used to obtain the maximum degree of cooling and maximum cooling power.

13. 13 It is obvious that z will be maximum when RK will have minimum value. This occurs when: When this condition is satisfied z becomes: Further, if S 2 =-S 1 = S, k 1 = k 2 = K,  1 =  2 = 

14. 14 ZT m vs. COP

15. 15 Criteria For greatest cooling efficiency we need a material that: conducts electricity well (like metal) conducts heat poorly (like glass) Bismuth telluride is the best bulk TE material with ZT=1 To match a refrigerator, ZT= 4 - 5 is needed To efficiently recover waste heat from car, ZT = 2 is needed

16. 16 Progress in ZT Fundamental limitations: k and , S and  are coupled.

17. 17 Thermoelectric Power Generation Used in Space shuttles and rockets for compact source of power. Diffusive heat flow and Peltier effect are additive i.e. both reduce the temperature gradient. The efficiency of power generation is given by: where: w is the power delivered to the external load Q H is the positive heat flow from source to sink