# Thermoelectric Energy Equations Considering Convective Heat Transfer Between Thermoelectric Materials and the Environment

## TL;DR

This paper revises thermoelectric energy equations to include heat loss from materials to the environment, improving accuracy for engineering applications.

## Contribution

The novel contribution is deriving revised thermoelectric equations that account for convective heat transfer from material surfaces.

## Key findings

- The revised equations are simple and suitable for engineering calculations.
- Simulated and calculated results differ by less than 1%, validating the linear temperature assumption.

## Abstract

Thermoelectric power generation is increasingly becoming a research field with practical application value and broad application prospects. Many researchers and engineers have used the classic thermoelectric energy equations in the analysis of thermoelectric systems. However, it is assumed that the thermoelectric material is thermally insulated from its surroundings except at the junctions of the hot and cold ends where heat enters and leaves. Based on a detailed study of the classic thermoelectric effects and heat transfer theory, the revised thermoelectric energy equations are derived, which take into account the convective heat dissipation from the surface of thermoelectric materials to the ambient. The revised equations have a very simple form, which is very convenient for engineering calculation and analysis. A comparison of the results of formula calculation and numerical simulation was conducted to verify the reasonableness of the linear temperature distribution assumption in the derivation process. Within the computational range of this study, the differences between the simulated values and the calculated values are controlled to be a little more than 1%, which is sufficient to meet the needs of engineering calculation and analysis.