Update Content - 2025-01-13

content/zettels/thermoelectric_cooler.md

@@ -7,10 +7,40 @@ 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>):
 
 {{< figure src="/ox-hugo/thermoelectric_cooler_schematic.svg" >}}
 
+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 \righarrow 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}