+++ title = "Thermoelectric cooler" author = ["Dehaeze Thomas"] draft = false +++ Tags : [Temperature Control]({{< relref "temperature_control.md" >}}) ## First principles {#first-principles} From (<a href="#citeproc_bib_item_1">Evers et al. 2021</a>): <a id="figure--fig:thermoelectric-cooler-schematic"></a> {{< figure src="/ox-hugo/thermoelectric_cooler_schematic.svg" caption="<span class=\"figure-number\">Figure 1: </span>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} 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} 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} 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 {#bibliography} <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body"> <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Evers, Enzo, Rens Slenders, Rob van Gils, Bram de Jager, and Tom Oomen. 2021. “Thermoelectric Modules in Mechatronic Systems: Temperature-Dependent Modeling and Control.” <i>Mechatronics</i> 79 (nil): 102647. doi:<a href="https://doi.org/10.1016/j.mechatronics.2021.102647">10.1016/j.mechatronics.2021.102647</a>.</div> </div>