digital-brain/content/zettels/thermoelectric_cooler.md

+++ title = "Thermoelectric cooler" author = ["Dehaeze Thomas"] draft = false +++

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[Temperature Control]({{< relref "temperature_control.md" >}})

First principles

From (Evers et al. 2021):

{{< figure src="/ox-hugo/thermoelectric_cooler_schematic.svg" caption="<span class="figure-number">Figure 1: Schematic of a Peltier module" >}}

The thermoelectric dynamics is described by 3 phenomena:

1. the Fourier effect
2. Joule heating
3. the Peltier effect

The Fourier effect

The Fourier effect \(Q_f\) describes the energy transfer through conduction between the two sides of the Peltier module: \[ Q_f^{1 \rightarrow 2} = \frac{K_m \cdot A}{d} (T_1 - T_2) \] for conduction from temperature \(T_1\) to \(T_2\) with \(K_m\) the conductivity of the Peltier module in \(W/m \cdot K\), \(A\) the area in \(m^2\) and \(d\) the thickness in \(m\).

Joule heating

Joule heating \(Q_j\) occurs when an electrical current flows through a resistive element: \[ Q_j = R_m I^2 \] where \(R_m\) is the electrical resistance in \(\Omega\) of the Peltier module and \(I\) is the electrical current in \(A\).

The Peltier effect

The Peltier effect describes the occurrence of a heat flow over a semi-conductor in the presence of an electrical potential difference and resulting current: \[ Q_p = S_m T I \] where \(S_m\) is the Seebeck coefficient of the Peltier module, and \(T\) is the temperature at the cold/hot side.

Bibliography

Evers, Enzo, Rens Slenders, Rob van Gils, Bram de Jager, and Tom Oomen. 2021. “Thermoelectric Modules in Mechatronic Systems: Temperature-Dependent Modeling and Control.” Mechatronics 79 (nil): 102647. doi:10.1016/j.mechatronics.2021.102647.