Crate te1d

te1d

te1d is a Rust library for simulation of thermoelectric effect using one-spatial-dimensional mathematical models.

• te1d uses the external ndarray crate for matrix manipulation.

Features

• Simulate Thermoelectric Power Generation for
  • Single-material, single-leg,
  • Maximum energy conversion efficiency.
• Support Temperature-Dependent Material Properties.
• Take account of Thermal diffusion, Joule heating, Thomson heating.

Task Lists

• Steady-State Power Generation
  • Simulation of Single Leg with Single Material: SingleLeg
    • Fixed Electrical Current: SingleLeg::simulate_fixed_elec_cur()
    • Fixed Load Resistance: SingleLeg::simulate_fixed_load_resistance()
    • Fixed Load Resistance Ratio: SingleLeg::simulate_fixed_load_ratio()
    • Power Maximization: SingleLeg::maximize_power_auto_range()
    • Efficiency Maximization: SingleLeg::maximize_efficiency_auto_range()
    • Approximate Max. Power
    • Approximate Max. Efficiency
  • Segmented Leg with Several Materials and Contact Resistance
  • Module with p- and n-type legs
  • Boundary Conditions
    • Fixed Temperature: FixedTempBc
    • Fixed Heat Flux: FixedHeatFluxBc
    • Convection: ConvectionBc
  • Lateral Heat Loss
    • Convection Loss
    • Radiation Loss
  • Bifurcation Analysis
• Steady-State Cooling
• Transient Power Generation
• Transient Cooling

Examples

• We use the material property of AgSbTe2 with 2% GeTe, reported in Figure 5 of Y. Chen et al. (2012).

// Goal: Find the maximum efficiency of a single leg using a AgSbTe2 material
// Import libraries
use ndarray::prelude::*;
use te1d::teg::prelude::*;
 
// Set the material properties
let seebeck_array: Array2<f64> = array![
    [317.358, 1.96E-04], [340.4, 2.12E-04], [366.747, 2.23E-04], [390.492, 2.20E-04],
    [412.868, 2.38E-04], [435.936, 2.42E-04], [458.998, 2.48E-04], [480.75, 2.51E-04],
    [506.455, 2.55E-04], [528.907, 2.40E-04], [552.646, 2.39E-04], [576.396, 2.33E-04],
    [600.135, 2.32E-04]];
let elec_cond_array: Array2<f64> = array![
    [315.737, 10147.0], [341.864, 9861.0], [365.309, 9683.0], [389.428, 9396.0],
    [413.553, 8966.0], [436.995, 8860.0], [460.443, 8610.0], [481.873, 8576.0],
    [504.642, 8543.0], [528.739, 8799.0], [552.82, 9416.0], [574.887, 10178.0],
    [599.653, 10434.0]];
let thrm_cond_array: Array2<f64> = array![
    [304.113, 0.66], [373.047, 0.67], [475.351, 0.65], [526.115, 0.64],
    [572.9, 0.75], [625.049, 0.83]];
let tep: Tep = Tep::from_raw_data_elec_cond(
    &seebeck_array, &elec_cond_array, &thrm_cond_array);
 
// Set the leg spec
let length: f64 = 1e-3;  // (m)
let area: f64 = 1e-6;  // (mm^2)
 
// Set the boundary condition (Dirichlet boundary conditions)
let hot_temp: f64 = 500.0;
let cold_temp: f64 = 300.0;
let left_bc = FixedTempBc::new(hot_temp);
let right_bc = FixedTempBc::new(cold_temp);
 
// Set simulation parameters
let minimizer_kind = MinimizerKind::Bfgs;
let minimizer_param = MinimizerParam {
    grad_tol: 1e-5,
    max_iter: 300,
    ..MinimizerParam::default(minimizer_kind)
};
let simul_param = SimulationParam {
    dx: length/10.0,
    dtemp: (hot_temp - cold_temp)/10.0,
    minimizer_kind,
    minimizer_param,
    ..SimulationParam::default()
};
 
// Create a leg
let leg = SingleLeg::new(&tep, length, area, simul_param);
 
// Find the maximum efficiency: takes about 4.0s
let result = leg.maximize_power_auto_range(&left_bc, &right_bc, hot_temp, cold_temp);
assert!(result.success);
 
// Compare with an approximation: 2% relative error
let approx_max_efficiency = leg.estimate_max_efficiency(hot_temp, cold_temp);
assert!(is_close(approx_max_efficiency, result.efficiency, 2e-2, 0.0));

Modules

bc

Provides boundary conditions for simulation.

calc

Performs calculus of real-valued functions.

func

Describes real-valued functions defined on the real line.

interp

Interpolates real-valued functions defined on the real line.

linalg

Solves linear systems and handles matrices.

ode

Solves ODEs(ordinary differential equations).

opt

Minimizes single cost functions.

prelude

Provides an easy import of the most used types, type aliases, traits and functions as a group.

simul

Provides common features for simulation of thermoelectric effects.

teg

Simulates steady-state thermoelectric power generation.

tep

Handles thermoelectric properties