Model of the executive body of a thermoelectric system providing thermal regimes

Abstract

The conditions for creating a mathematical model of a thermoelectric cooling device of a reliability-oriented type are considered. The design feature of thermoelectric coolers, which consists in the serial electrical connection of identical thermoelements with uniform physical characteristics, is used as the basis of the model. This made it possible to use the mathematical apparatus of the reliability theory, which significantly simplifies the description of the process, assuming the homogeneity of the components. The introduction of coefficients of connection of the product failure intensity with the failure of one thermoelement made it possible to connect this indicator with the influence of energy indicators, which reflect the modulation of the thermophysical indicators of thermoelements. The representation of energy indicators in relative units made it possible to move from a qualitative model of the connection of the failure intensity with constructive and energy indicators to a quantitative one. The relevance of the development of a reliability-oriented model in the direction of identifying extreme dependencies of the connection of the indicators of a thermoelectric cooler is obvious. A mathematical model of the relationship between the heat dissipation capacity of the heat sink and such energy indicators as heat output, relative operating current, and temperature difference has been developed. A preliminary analysis of the model has shown the presence of extrema of dependencies, which potentially allows minimizing the massdimensional characteristics of the heat sink, which is one of the most important parameters of aircraft onboard systems. It is shown that when designing a system for providing thermal regimes “object - thermoelectric cooler - heat sink device”, there are a number of unified series of industrially produced devices. In this case, it is necessary to minimize the mass-dimensional characteristics of the system, consisting of a limited range of manufactured products. To solve this problem, an optimization model has been developed that allows obtaining a quasi-optimal value with a limited number of nomenclatures. Expressions have been obtained that allow analyzing the behavior of the thermoelectric cooler under different operating modes. It is shown that for the maximum cooling capacity mode, an optimized value of the heat dissipation capacity from the relative temperature difference is achieved. Mathematical models of a thermoelectric cooling device have been obtained, which link the structural, energy, mass-dimensional and reliability characteristics. Analysis of these dependencies allows us to make many useful theoretical and practical conclusions regarding extreme values, range of change, comparison of values at different current operating modes, influence of temperature differences, and appropriate areas of application.