A Study of the Nonlinear Thomson Effect Produced by Changing the Current in a Thermoelectric Cooler

Luis G. Lafaurie-Ponce; Farid Chejne; Luis M. Ramirez-Aristeguieta; Carlos A. Gomez

doi:10.1515/jnet-2022-0037

Article

A Study of the Nonlinear Thomson Effect Produced by Changing the Current in a Thermoelectric Cooler

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Published/Copyright: September 16, 2022

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From the journal Journal of Non-Equilibrium Thermodynamics Volume 47 Issue 4

Abstract

This work describes the nonlinear Thomson effect produced by a transient current source powering a thermoelectric cooler. The electric effect of the capacitive impedance in the semiconductors was considered in the equations as a novelty term that naturally appears by solving the Boltzmann equation to find the mathematical form of the current density. Thus, considering the new term and heath energy balances, a one-dimensional mathematical model for a thermoelectric cooler (TEC) powered by a time-dependent current was developed, finding a new nonlinear Thomson effect in the heath transfer equations. To evaluate the impact of the nonlinear effect on the thermodynamic behavior of the thermoelectric cooler, a continuous, sinusoidal and square-pulse current conditions were simulated. The temperature profile, temporal evolution, and the effective coefficient of performance (COP) were calculated. The results revealed a new thermoelectric heat transfer in addition to the Thomson flow created by virtual junctions throughout the semiconductors caused by the instantaneous change of current. This fact was evidenced by three results: the shifting of the temperature mean value due to the peak current change 0.45 A is 1.68 K and 2.56 K to sinusoidal and square current supplies, respectively; it was determined that a TEC powered by a square-pulse current signal had greater effective efficacy, having more pronounced cold side supercooling temperature peaks compared to those powered by a constant sinusoidal current signal.

Keywords: thermoelectric phenomena; local Peltier effect; coefficient of performance; time-dependent current; mathematical model

Funding source: Universidad de Antioquia

Award Identifier / Grant number: 20830002

Funding source: Universidad Nacional de Colombia

Award Identifier / Grant number: 53024

Funding statement: This work was funded by a grant from the Universidad de Antioquia (code: 20830002 Fondo de apoyo a proyectos de desarrollo experimental e innovación_PGT Vicerrectoria de Extensión). The authors Farid Chejne and Carlos Gómez wish to thank to the project “Strategy of transformation of the Colombian energy sector in the horizon 2030” funded by the call 788 of Minciencias Scientific Ecosystem (contract number FP44842-210-2018) and to thank the Alliance for Biomass and Sustainability Research–ABISURE-Universidad Nacional de Colombia, Hermes code 53024, for its support in the realization of this study.

Acknowledgment

We would like to thank the members of the “Basic and Applied Biotechnology” research group for their support during this work with their initiative. This work was carried out jointly with the “Universidad Nacional de Colombia” TAYEA research group in collaboration with “Universidad de Antioquia” facilities.

Nomenclature

A: Area ( m 2 )
a E: Acceleration due extern force ( m s − 2 )
C p: Heat capacity ( J kg − 1 K − 1 )
E: Electrical field ( V m − 1 )
e: Electron charge (C)
f: Frequency ( Hz)
g: Probability density function ( s m − 4 )
h: Convective heat transfer coefficient ( J m − 2 s − 1 K − 1 )
I: Current (A)
I mean: Mean current (A)
I peak: Peak current (A)
J e: Current density ( A m − 2 )
k: Thermal conductance ( J m − 1 s − 1 K − 1 )
k e: Electrical conductance ( Ω − 1 m − 1 )
k B: Boltzmann constant ( J K − 1 )
L: Length (m)
m: Mass ( kg)
n: Amount semiconductors pairs
n ˜: Carriers’ density ( m − 3 )
P: Power (W)
P r: Prandtl number (1)
Q ˙: Heat flow
R: Juncture resistance (Ω)
Re: Reynolds number (1)
T: Temperature (K)
T mean: Mean temperature (K)
T peak: Peak temperature (K)
t: Time (s)
U ( t ): Step signal (1)
V: Volume ( m 3 )
v: Velocity ( m s − 1 )
w: Collision frequency ( s − 1 )
x: Position (m)

Greek symbols

α: Seebeck coefficient ( V K − 1 )
ρ: Bulk density ( kg m − 3 )
τ: Thomson coefficient ( V K − 1 )
φ: Electric potential (V)
ϕ: Phase (1)

Subscript

air: Air
coll: Collision
cs: Cold side
hs: Hot side
P: P type
N: N type
∞: Environment

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Received: 2022-05-25

Accepted: 2022-08-26

Published Online: 2022-09-16

Published in Print: 2022-10-31

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Articles in the same Issue

https://doi.org/10.1515/jnet-2022-0037

Keywords for this article

thermoelectric phenomena; local Peltier effect; coefficient of performance; time-dependent current; mathematical model