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Flexible Thermoelectric Polymers and Systems. Группа авторовЧитать онлайн книгу.

Flexible Thermoelectric Polymers and Systems - Группа авторов


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upper R Subscript e x Baseline Over upper R Subscript i n Baseline EndFraction comma"/> the equation (1.55) becomes

      When R in = R ex, the external load has the maximum power (P max),

      (1.57)upper P Subscript max Baseline equals StartFraction left-parenthesis 2 StartAbsoluteValue upper S EndAbsoluteValue upper Delta upper T right-parenthesis squared Over 4 upper R Subscript i n Baseline EndFraction period

      The equation for the efficiency (η) can be obtained as it is the ratio of the output power to the incident heat (Q in) into the system,

      (1.58)eta equals StartFraction upper P Over upper Q Subscript i n Baseline EndFraction period

Schematic illustration of variations of the power output of a TEG with the load resistance at ΔT = 10 and 20 K.

      Source: Madan et al. [34]. © American Chemical Society.

      (1.60)minus StartFraction upper Q Subscript o u t Baseline Over upper A EndFraction plus 2 StartFraction upper S upper T Subscript upper C Baseline upper I Over upper A EndFraction minus 2 kappa left-parenthesis StartFraction partial-differential upper T Over partial-differential x EndFraction right-parenthesis Subscript upper L Baseline equals 0 comma a t x equals upper L comma c o l d s i d e period

      By ignoring the Thomson effect, the equation (1.50) for one leg becomes

      (1.61)kappa StartFraction partial-differential squared upper T Over partial-differential x squared EndFraction plus StartFraction upper I squared Over upper A squared sigma EndFraction equals 0 period

      Using the boundary conditions of T(0) = T H and T(L) = T C, the following equations can be obtained,

      (1.62)upper T left-parenthesis x right-parenthesis equals minus StartFraction upper I squared x squared Over 2 kappa upper A squared sigma EndFraction plus left-parenthesis StartFraction upper I squared upper L Over 2 kappa upper A squared sigma EndFraction minus StartFraction upper Delta upper T Over upper L EndFraction right-parenthesis x plus upper T Subscript normal upper H Baseline comma

      (1.63)StartFraction d upper T Over d x EndFraction equals minus StartFraction upper I squared Over 2 kappa upper A squared sigma EndFraction x plus StartFraction upper I squared upper L Over 2 kappa upper A squared sigma EndFraction minus StartFraction upper Delta upper T Over upper L EndFraction period

      At x = 0,

      (1.64)left-parenthesis StartFraction d upper T Over d x EndFraction right-parenthesis Subscript 0 Baseline equals StartFraction upper I squared upper L Over 2 kappa upper A squared sigma EndFraction minus StartFraction upper Delta upper T Over upper L EndFraction period

      where upper R Subscript l e g Baseline equals StartFraction upper L Over sigma upper A EndFraction is the intrinsic resistance of one leg.

      where z is the figure of merit of the thermoelectric module,

      (1.67)z equals StartFraction 2 upper S squared Over kappa upper R Subscript i n Baseline EndFraction StartFraction upper L Over upper A EndFraction period

      The internal resistance (R in) includes the contact resistances and


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