From 113065d23bb3751ca2d8c30e749ac9088ca30699 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 13 Jan 2025 15:40:25 +0100 Subject: [PATCH] Update Content - 2025-01-13 --- content/zettels/thermoelectric_cooler.md | 30 ++++++++++++++++++++++++ 1 file changed, 30 insertions(+) diff --git a/content/zettels/thermoelectric_cooler.md b/content/zettels/thermoelectric_cooler.md index fc55b2b..7485e0d 100644 --- a/content/zettels/thermoelectric_cooler.md +++ b/content/zettels/thermoelectric_cooler.md @@ -7,10 +7,40 @@ draft = false Tags : [Temperature Control]({{< relref "temperature_control.md" >}}) + +## First principles {#first-principles} + From (Evers et al. 2021): {{< 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}