Gennady Gromov - Thermoelectric Microgenerators. Optimization for energy harvesting

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 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 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 α 2×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 both parameters α and σ have temperature dependencies, with multidirectional (Fig. 7.1a and 7.1b, respectively), to understand the temperature dependence of maximum power P max you must be aware of the temperature dependence of α 2×σ that is presented in Fig.7.2.

Figure. 7.2 Dependence of α 2×σ on temperature.

Follows from this temperature dependence that useful power decreases with growth of temperature.

In the first approximation energy conversion efficiency (4.1) can be expressed as the following

Apparently from a formula (7.6) at the given temperature difference (for example, single Δ T =1℃) efficiency η approximately linearly depends on Figure-of-Merit Z . But this dependence becomes complicated existence of a factor – fractions with Figure-of-Merit parameter.

We will consider the modes of the maximum efficiency m≈ 1.4 and maximum power mode m= 1. Simplified formulas for the efficiency for such modes are the following, respectively.

Fractional factors in both formulas (7.7) and (7.8) – Figure-of Merit factors, have temperature dependences, as shown in Fig. 7.3.

Figure. 7.3 Dependence of Figure-of-Merit on temperature.

The key parameter of material (its Figure-of Merit Z ) influencing efficiency has obviously expressed maximum near room temperatures (Fig. 7.1g) – in the range of 280—290K.

Текст предоставлен ООО «ЛитРес».

Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.

Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.