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Flexible Thermoelectric Polymers and Systems. Группа авторовЧитать онлайн книгу.

Flexible Thermoelectric Polymers and Systems - Группа авторов


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target="_blank" rel="nofollow" href="#ulink_ce9bf853-63cf-5d4e-aa70-42c752e7a288">(1.46)StartFraction partial-differential upper J Subscript upper Q Baseline Over partial-differential x EndFraction equals minus StartFraction partial-differential Over partial-differential x EndFraction left-parenthesis kappa StartFraction partial-differential upper T Over partial-differential x EndFraction right-parenthesis plus upper T StartFraction d upper S Over d upper T EndFraction upper J StartFraction partial-differential upper S Over partial-differential x EndFraction minus StartFraction upper J squared Over sigma EndFraction plus upper J upper E plus upper S upper T StartFraction partial-differential upper J Over partial-differential x EndFraction period

      Heat flux can change the temperature of a material. Consider in the volume of Adx with A as the cross‐section area,

      (1.47)d upper C Subscript normal p Baseline StartFraction d upper T Over d t EndFraction equals minus StartFraction partial-differential upper J Subscript upper Q Baseline Over partial-differential x EndFraction comma

      where d is the mass density and C p is the specific heat.

      When a material is initially at thermal equilibrium with homogeneous temperature, its temperature can be varied only when an electrical work or heat transfer is applied to it. If an external electric field is applied to a system, the electrical work will affect the temperature of the system,

      The input heat flux or the temperature difference between the hot and cold sides is usually constant when a thermoelectric system is evaluated. Consider that the material properties are independent of the temperature and they are identical for the p‐type and n‐type legs, the power delivered to the external load is given by

      (1.51)upper P equals upper I upper Delta upper V Subscript e x Baseline comma

      where I is the current through the external load and ΔV ex = IR ex is the voltage drop on the external load.

      The values of I, ΔV ex, and P depend on the resistance of the external load. The resistance of the external load is usually varied from the open‐circuit voltage condition (R ex → ∞) to the short‐circuit voltage (R ex → 0) to find the optimal power on the external load.

      (1.52)upper V Subscript upper O upper C Baseline equals 2 left-parenthesis upper S right-parenthesis upper Delta upper T comma

Schematic illustration of (a) A thermoelectric generator with n- and p-type legs. Heat transfer (Qin) into the thermoelectric legs from the hot side and heat transfer (Qout) out from the cold side. (b) Temperature and voltage profiles at open-circuit condition.

      (1.53)2 StartAbsoluteValue upper S EndAbsoluteValue upper Delta upper T equals upper I upper R Subscript e x Baseline plus upper I upper R Subscript i n

      The current through the circuit can be obtained as

      Thus, the equation for the power is given by

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