Application of the perturbation method to construct a refined compact model of a thermoelectric element with temperature-dependent parameters

The paper presents an asymptotically substantiated compact model of the Peltier element. The problem of stationary temperature distribution in a one-dimensional thermoelectric medium with temperature-dependent physical parameters is considered. A direct asymptotic approximation is constructed under the assumption that the ratio of the temperature difference at the boundaries of the Peltier element to the mean absolute temperature of the module is a small value. Expressions for heat fluxes on the absorbing and radiating sides with a nonlinear dependence on the applied current and boundary temperatures are obtained. A method of synthesis based on the obtained solution of a compact system model of a thermoelectric module is proposed. A numerical example is used to compare the obtained model with the classical model with averaged material parameters. It is shown that the heat fluxes of the two models take different values at sufficiently large electric currents. Promising areas of using the proposed new analytical model of the Peltier element in industrial problems are discussed.