Numerical simulation of the maximum temperature difference in a thermoelectric branch made of a variband bismuth-antimony alloy in the temperature range of 70–120 K

Abstract

Inhomogeneous bismuth-antimony alloys are the most efficient thermoelectrics at 100 K. This article describes a numerical simulation by means of COMSOL Multiphysics of the temperature field as a function of the current in a thermoelectric branch made of a gradient-inhomogeneous Bi100-x-Sbx alloy within the semiconductor region of the interval 11 at. %< x<19 at. %. The model takes into account that the parameters of the substance affecting the thermoelectric figure of merit, namely thermal conductivity, thermoelectric power, and electrical conductivity, are variable along the branch. In this case, the alloy inhomogeneity and temperature gradients lie in the cleavage plane of the sample. To simulate this problem, the authors numerically solved a system of heat conduction equations and the generalized Ohm's law equations, taking into account continuously distributed heat sources, for which the Joule heat, the Thomson effect, and the Peltier effect are responsible. It can be seen from numerical calculations that in the region of 70–120 K, there is an increase in the maximum temperature difference in the presence of opposite gradients of the antimony concentration and temperature in the sample, compared to unidirectional gradients or a homogeneous alloy. The results obtained were compared with experimental data for a thermal branch with the same inhomogeneity composition (11 at. %<x<19 at. % Sb).