Abstract
This work examines the validity of formulating the effective thermoelectric material properties as a way to predict thermoelectric module performance. The three maximum parameters (temperature difference, current, and cooling power) of a thermoelectric cooler were formulated on the basis of the hot junction temperature. Then, the effective material properties (Seebeck coefficient, electrical resistance, and thermal conductivity) were defined in terms of the three maximum parameters that were taken from either a commercial thermoelectric cooler module or the measurements. It is demonstrated that the simple standard equation with the effective material properties predicts well the performance curves of the four selected commercial products. Normalized parameters over the maximum parameters were also formulated to present the characteristics of the thermoelectric coolers along with the normalized charts. The normalized charts would be universal for a given thermoelectric material.
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Abbreviations
- \(A\) :
-
Cross-sectional area of thermoelement (m2)
- \({\rm COP}\) :
-
Coefficient of performance (dimensionless)
- \( I \) :
-
Electric current (A)
- \( I_{\rm{max} } \) :
-
Maximum current (A)
- \( \vec{j} \) :
-
Electric current density vector (A/m2)
- \( K \) :
-
Thermal conductance (W/K)
- \( L \) :
-
Length of thermoelement (m)
- \( k \) :
-
Thermal conductivity (W/m-K)
- \( n \) :
-
Number of thermocouples
- \( \vec{q} \) :
-
Heat flux vector (W/m2)
- \( \dot{Q}_{\rm{c}} \) :
-
Cooling power, heat absorbed at cold junction (W)
- \( \dot{Q}_{\rm{h}} \) :
-
Heat liberated at hot junction (W)
- \( \dot{Q}_{\rm{c\;max} } \) :
-
Maximum cooling power (W)
- \( R \) :
-
Electrical resistance (Ω)
- \( T \) :
-
Temperature (°C)
- \( T_{\rm{c}} \) :
-
Low junction temperature (°C)
- \( T_{\rm{h}} \) :
-
High junction temperature (°C)
- \( \bar{T} \) :
-
Average temperature \( {{\left( {T_{\rm{h}} + T_{\rm{c}} } \right)} \mathord{\left/ {\vphantom {{\left( {T_{\rm{h}} + T_{\rm{c} }} \right)} 2}} \right. \kern-0pt} 2} \) (°C)
- \( V \) :
-
Voltage of a module (V)
- \( V_{\rm{max} } \) :
-
Maximum voltage (V)
- \( \dot{W} \) :
-
Work per unit time \( \dot{W} = \alpha I\Delta T + I^{2} R \) (W)
- \( x \) :
-
Distance of thermoelement leg (m)
- \( Z \) :
-
Figure of merit (K−1), \( Z = {{\alpha^{2} } \mathord{\left/ {\vphantom {{\alpha^{2} } {\rho k}}} \right. \kern-0pt} {\rho k}} \)
- \( \Delta T \) :
-
Temperature difference \( T_{\rm{h}} - T_{\rm{c}} \) (°C),
- \( \Delta T_{\rm{max} } \) :
-
Maximum temperature difference (°C)
- α :
-
Seebeck coefficient (V/K)
- ρ :
-
Electrical resistivity (Ω cm)
- \( \vec{\nabla } \) :
-
Gradient operator vector
- p :
-
p-Type element
- n :
-
n-Type element
- * :
-
Effective quantity
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Lee, H., Attar, A.M. & Weera, S.L. Performance Prediction of Commercial Thermoelectric Cooler Modules using the Effective Material Properties. J. Electron. Mater. 44, 2157–2165 (2015). https://doi.org/10.1007/s11664-015-3723-7
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DOI: https://doi.org/10.1007/s11664-015-3723-7