Thermoelectricity (T + φ)

Overview

Thermo-electric (Seebeck/Peltier) coupling. Thermoelectricity() couples the temperature :T and the electric potential :φ through the Seebeck coefficient S, using the material’s conductivity k and electrical conductivity σ.

using Rasmah

# 1. geometry, 2. exact BRep + face selection, 3. mesh
part = box(1.0, 1.0, 1.0)
b = brep(part)
left  = faces_in_box(b, [-0.6, -1.0, -1.0], [-0.4, 1.0, 1.0])   # hot end
right = faces_in_box(b, [ 0.4, -1.0, -1.0], [ 0.6, 1.0, 1.0])   # cold end
mesh = tetrahedralize(b, 8)

res = solve(Thermoelectricity(), mesh, bismuth_telluride;
            fixed_T = [left => 400.0, right => 300.0],
            fixed_φ = [left => 0.0, right => 0.0])
println("T range = ", round(minimum(res.T); digits = 2), " … ",
        round(maximum(res.T); digits = 2))
println("Seebeck voltage φ range = ", round(minimum(res.φ); digits = 4), " … ",
        round(maximum(res.φ); digits = 4))

T range = 300.0 K … 400.0 K
Seebeck voltage φ range = 0.0 m^2·kg/(s^3·A) … 0.0 m^2·kg/(s^3·A)

Visualize the geometry and the temperature field:

vtk(b)

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vtk(mesh; field = res.T, fieldname = "temperature")

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Notes

A temperature gradient across a thermoelectric material produces a thermoelectric (Seebeck) potential — here visible as a nonzero φ despite the grounded electrodes.
Fields are (T, φ); the coupling is one-way (thermal → electric).