A method for calculating the transient time of a multi-stage thermoelectric cooler

The transient time tau of a cascade thermoelectric cooler is calculated. The method applied does not involve the solution of the heat equations with partial derivatives for semiconductor elements. The transient time tau of a two-stage thermopile was obtained in analytical form as a solution of the quadratic equation whose coefficients depend on semiconductor thermoelectric parameters, the specific heat of the thermopile materials, and the sizes of different parts of the cooler. For a thermopile with an arbitrary number of stages N, the calculation was reduced to the standard problem of finding the eigenvalues of two symmetrical matrices of order N. The calculated values of tau for specific two-stage thermopiles are in satisfactory agreement with the experimental data.