52 lines
2.1 KiB
Markdown
52 lines
2.1 KiB
Markdown
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title = "Thermoelectric cooler"
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author = ["Dehaeze Thomas"]
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draft = false
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: [Temperature Control]({{< relref "temperature_control.md" >}})
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## First principles {#first-principles}
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From (<a href="#citeproc_bib_item_1">Evers et al. 2021</a>):
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<a id="figure--fig:thermoelectric-cooler-schematic"></a>
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{{< figure src="/ox-hugo/thermoelectric_cooler_schematic.svg" caption="<span class=\"figure-number\">Figure 1: </span>Schematic of a Peltier module" >}}
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The thermoelectric dynamics is described by 3 phenomena:
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1. the Fourier effect
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2. Joule heating
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3. the Peltier effect
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### The Fourier effect {#the-fourier-effect}
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The Fourier effect \\(Q\_f\\) describes the energy transfer through **conduction** between the two sides of the Peltier module:
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\\[ Q\_f^{1 \rightarrow 2} = \frac{K\_m \cdot A}{d} (T\_1 - T\_2) \\]
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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\\).
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### Joule heating {#joule-heating}
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Joule heating \\(Q\_j\\) occurs when an electrical current flows through a resistive element:
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\\[ Q\_j = R\_m I^2 \\]
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where \\(R\_m\\) is the electrical resistance in \\(\Omega\\) of the Peltier module and \\(I\\) is the electrical current in \\(A\\).
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### The Peltier effect {#the-peltier-effect}
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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:
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\\[ Q\_p = S\_m T I \\]
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where \\(S\_m\\) is the Seebeck coefficient of the Peltier module, and \\(T\\) is the temperature at the cold/hot side.
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## Bibliography {#bibliography}
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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<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>
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</div>
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