Thermoelectric Microgenerators. Optimization for energy harvesting. Gennady Gromov

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СКАЧАТЬ is important issue for energy harvesting tasks, where low-power heat sources usually have very small values of heat flow power density.

      Illustrative example – recycling of the human body heat. Heat flow density of such kind of heat “source” is small compared with tabular values for the microgenerators (Table 6.2) – no more than 10^—1…10^-2 W/cm². Clearly, the generator device in such tasks should include heat flow concentrators. Moreover, the area of such a hub should significantly exceed size of the generator micromodule.

      Another example is soil generators which utilize heat flowing in the upper layers of soil in the daily cycle. Here the heat flows have values at the level of 100W/m² (0.01W/cm²). It also requires the concentration of heat for the supply to generator micromodule.

      Another important task is to effectively dissipate heat passed through the generator. If this is not achieved, the useful heat, transported through generator system, limited to a size not more than wasted on a radiator.

      Here it is also important to the specific characteristics of the density of heat flow through the radiator -" flow capacity” of the radiator. It is necessary to calculate the dimensions of the radiator (see Chapter 9). In many practical cases, dimensions of a heat sink should be also noticeably larger than the generator micromodule.

      Chapter 7. Thermoelectric materials

      Summary. In this Chapter properties of the thermoelectric materials applied in microgenerators for energy harvesting are considered. On the working temperature range of these tasks, such generators can be classified as “low-temperature”. Besides in this temperature range the majority of thermoelectric coolers works. Therefore also thermoelectric materials for generator applications are used same, as for thermoelectric cooling – solid-state solutions on the basis of the Bi-Sb-Te.

      Typical parameters

      As shown above (Chapter 6), thermoelectric material properties of the thermoelements play decisive role in the parameters of efficiency of microgenerator modules.

      Therefore, when designing of microgenerator it is necessary to pay great attention to properties of thermoelectric material from which they are should be made.

      Application of energy harvesting means heat recycling from heat sources of low power, small temperature difference relating to the environment. Approximately this temperature range can be defined as ~250 … 450K (-25… +180°C).

      In this regard an analogy arises to other field of applications of thermoelectricity – thermoelectric cooling. Practical temperature range of thermoelectric cooling is approximately similar stated above.

      It explains that for thermoelectric generation in energy harvesting tasks practically the same thermoelectric materials on the basis of solid solutions of Bi-Sb-Te, as successfully can be applied as to thermoelectric cooling. Such thermoelectric semiconductor materials have maximal efficiency in this temperature range.

      Key properties of thermoelectric material are combined in expression for its Figure-of-Merit Z.

      where α – thermoEMF coefficient (Seebeck coefficient) of thermoelectric material; σ – electrical conductivity; k – thermal conductivity.

      Typical parameters of thermoelectric material applied for manufacturing of microgenerators and microcoolers are given in Table 7.1.

      Table 7.1 Typical parameters of thermoelectric materials of p-and n-types at 300K.

      Also temperature dependences of properties in the working temperature ranges are important for detailed calculations and modeling of real devices operation.

      For convenience of calculations and mathematical modeling temperature dependences can be presented in the polynomial form.

      Temperature dependences of properties of the applied thermoelectric materials are described well by a polynomial of the 3rd order of general view as following

      where x=T/100

      Detailed data for typical polynomial temperature dependences of the major properties are provided in Table 7.2. In Fig. 7.1 these typical temperature dependences are graphically presented.

      Table 7.2 Polynomial coefficients of temperature dependences (7.2) of properties of thermoelectric materials.

      a)

      b)

      c)

      d)

      Figure. 7.1 Temperature dependences of thermoelectric materials properties: Seebeck coefficient (a), electric conductivity (b), thermal conductivity (c) and Figure-of-Merit (d).

      In calculated parameters of thermoelectric microgenerators average characteristics of pair of thermoelements of n-and p-types are applied. Therefore temperature dependences of properties of materials of both n-and p-types and these average dependences are given in Fig. 7.1. Average dependences characterize properties of p-n pair of such thermoelements. In mathematical formulas for parameters of thermoelectric generators such average properties on p-n to pair of thermoelements are just used.

      On the presented temperature dependences it is necessary to make several important remarks.

      Voltage

      Voltage U provided by generator linearly depends on thermoEMF E, defined by Seebeck coefficient α.

      According to temperature dependence α=f(T) (Fig. 7.1a) with increasing of temperature the thermoEMF E, although not significantly, but is growing.

      Maximum power

      Maximum power of generator can be written as

      where N×f – the product of the number N of pairs of thermoelements on the geometrical form-factor f is the specified value.

      The factor α²×σ in thermoelectricity is often called as a “power factor”. This factor is significant both for applications in the field of cooling, and in the generator direction. For generators – it shows dependence of the maximum power of P_max of generator on parameters α and σ of thermoelectric material (7.5).

      Since СКАЧАТЬ