The present work is an analytical study of the optimal design of an automotive thermoelectric air conditioner (TEAC) using a new optimal design method with dimensional analysis that has been recently developed by our research group. The optimal design gives not only the optimal current but also the optimal geometry (i.e., the number of thermocouples, the geometric factor, or the hot fluid parameters). The optimal design for the TEAC is carried out with two configurations: air-to-liquid and air-to-air heat exchangers.
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Abbreviations
- A e :
-
Cross-sectional area of thermoelement (mm2)
- A b :
-
Total base area of thermoelectric air conditioner (TEAC) (mm2)
- A c :
-
Total fin surface area of cold-side heat sink (mm2)
- A h :
-
Total fin surface area of hot-side heat sink (mm2)
- A UC :
-
Unit cell base area (mm2)
- COP:
-
Coefficient of performance
- c p :
-
Specific heat (J/kg/K)
- H :
-
Total height of TEAC (mm)
- h :
-
Heat transfer coefficient of fluid (W/m2/K)
- \( I \) :
-
Electric current (A)
- L :
-
Total length of TEAC (mm)
- L c :
-
Unit cell cold-side length (mm)
- L e :
-
Length of thermoelement (mm)
- L h :
-
Unit cell hot-side length (mm)
- k :
-
Thermoelement thermal conductivity (W/m/K), \( k = k_{p} + k_{n} \)
- n :
-
Number of thermocouples
- \( n_{\rm{c}} \) :
-
Number of fins for the cold-side heat sink
- \( n_{\rm{h}} \) :
-
Number of fins for the hot-side heat sink
- \( N_{\rm{k}} \) :
-
Dimensionless thermal conductance, N k = n(A e k/L e)/η h h h A h
- \( N_{\rm{h}} \) :
-
Dimensionless convection, N h = η c h c A c/η h h h A h
- \( N_{\rm{I}} \) :
-
Dimensionless current, N I = αI/(A e k/L e)
- Q c :
-
Total cooling power from TEAC (W)
- P in :
-
Total input power of TEAC (W)
- \( {\hbox{PD}} \) :
-
Power density (W/cm2)
- R :
-
Electrical resistance of a thermocouple (Ω)
- Re :
-
Fluid Reynolds number
- T c :
-
Cold-junction temperature (°C)
- T h :
-
Hot-junction temperature (°C)
- T ∞c :
-
Fluid temperature (°C)
- T ∞h :
-
Hot fluid temperature (°C)
- \( \Delta T \) :
-
Thermoelectric temperature difference (°C)
- \( \Delta T_{\rm{cooling}} \) :
-
Cold air temperature inlet–outlet (°C)
- t c :
-
Cold-side air fin thickness
- t h :
-
Hot-side air fin thickness
- V c :
-
Cold fluid volume flow rate (CFM)
- V h :
-
Hot fluid volume flow rate (L/min for liquid) or (CFM for air)
- W :
-
Total width of TEAC (mm)
- Z :
-
Figure of merit (1/K) = α 2/ρk
- z c :
-
Fin spacing for the cold-side air (mm)
- z h :
-
Fin spacing for the hot-side air (mm)
- α :
-
Seebeck coefficient (V/K), α = α p − α n
- ρ :
-
Electrical resistivity (Ω/cm), ρ = ρ p + ρ n
- η c :
-
Fin efficiency of cold-side heat sink
- η h :
-
Fin efficiency of hot-side heat sink
- c:
-
Cold
- e:
-
Thermoelement
- h:
-
Hot
- p :
-
p-Type element
- n :
-
n-Type element
- opt.:
-
Optimal quantity
- UC:
-
Unit cell
- *:
-
Dimensionless
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Attar, A., Lee, H. & Weera, S. Optimal Design of Automotive Thermoelectric Air Conditioner (TEAC). J. Electron. Mater. 43, 2179–2187 (2014). https://doi.org/10.1007/s11664-014-3001-0
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DOI: https://doi.org/10.1007/s11664-014-3001-0