[Paper Review] Efficiency calculation of thermoelectric generator by extracting waste heat, for practical applications

Kumar Gaurav, Sudhir K. Pandey|arXiv (Cornell University)|Mar 5, 2016

Advanced Thermoelectric Materials and Devices3 citations

TL;DR

This paper proposes a segmented temperature-range method to accurately calculate thermoelectric generator (TEG) efficiency across large temperature differentials by treating temperature-dependent material parameters as constant within small intervals. By applying thermodynamic formulations to these segments and validating with experimental data, the method achieves a practical and accurate efficiency estimation, successfully bridging theoretical models with real-world automotive applications.

ABSTRACT

Accurate measurement of efficiency for thermoelectric generator (TEG) is of great importance for materials research and development. Approximately all the parameters of a material are temperature dependent, so we can't directly apply the $\eta_ ext{{max}}$ formula for efficiency calculation for large temperature range. To overcome that problem, we tried to calculate the efficiency of TEG by dividing large working temperature range into a number of small temperature difference. The aim is to make temperature dependent parameter to be constant for that temperature range thereafter by using some thermodynamic formulation we found out overall efficiency. This method gives us approximately close to the actual efficiency of TEG. We took values of $z\bar{T}$ for different materials suitable for different temperature range and after validating with experimental results, we directly applied the same concept in real life application, i.e. automobile sector. The efficiency calculation method adopted by us is a prominent method to calculate the efficiency of a TEG. Finally, we came with a bridge between theoretical calculation done by scientific community with real life application.

Motivation & Objective

• To address the inaccuracy of standard maximum efficiency formulas ($\eta_{\text{max}}$) when applied over large temperature ranges due to temperature-dependent material parameters.
• To develop a practical and accurate method for calculating thermoelectric generator (TEG) efficiency in real-world systems where temperature gradients are significant.
• To bridge the gap between theoretical thermoelectric efficiency calculations and actual engineering applications, particularly in the automotive sector.
• To validate the proposed method using experimental results and extend its application to materials with varying $z\bar{T}$ values across different temperature ranges.

Proposed method

• Divide the total temperature range of the TEG into multiple small intervals to minimize variation in temperature-dependent material parameters within each segment.
• Assume each material's thermoelectric figure of merit ($z\bar{T}$) is constant within each small temperature interval to simplify efficiency calculations.
• Apply thermodynamic formulations to compute the efficiency contribution of each segment based on its local temperature difference and material properties.
• Sum the efficiency contributions of all segments to obtain the overall TEG efficiency, ensuring a more accurate approximation than global $\eta_{\text{max}}$ formulas.
• Validate the segmented method using experimental data from TEG systems to confirm its accuracy and practicality.
• Extend the validated method to real-life applications, such as automotive waste heat recovery, by applying it to materials with $z\bar{T}$ values suitable for specific temperature ranges.

Experimental results

Research questions

• RQ1 How can thermoelectric generator efficiency be accurately calculated over a large temperature range when material parameters are strongly temperature-dependent?
• RQ2 To what extent does segmenting the temperature range improve the accuracy of TEG efficiency estimation compared to using the standard $\eta_{\text{max}}$ formula?
• RQ3 Can the segmented efficiency calculation method be successfully validated against experimental results in real-world TEG systems?
• RQ4 How can theoretical thermoelectric efficiency models be effectively translated into practical engineering applications, particularly in the automotive industry?
• RQ5 What role does the temperature-dependent figure of merit ($z\bar{T}$) play in determining the overall efficiency of a TEG, and how can it be handled in multi-range systems?

Key findings

• The segmented temperature-range method provides a more accurate estimation of TEG efficiency across large temperature differentials than the standard $\eta_{\text{max}}$ formula.
• By treating $z\bar{T}$ as constant within small temperature intervals, the method effectively reduces error introduced by temperature-dependent material properties.
• The method was validated using experimental results, confirming its reliability for practical TEG applications.
• The approach successfully enables the application of theoretical thermoelectric models to real-world systems, such as automotive waste heat recovery.
• The segmented method allows for the use of materials with different $z\bar{T}$ values in different temperature ranges, enhancing overall system efficiency.
• The study establishes a practical and accurate framework that bridges theoretical thermoelectric efficiency calculations with real-life engineering implementations.