CN102437280B - Optimization method of structure of minitype thermoelectric cell - Google Patents

Abstract

The invention discloses an optimization method of a structure of a minitype thermoelectric cell. According to the method, real details of a thermoelectric cell are better considered; a hot point conversion efficiency of the thermoelectric cell as well as correlated property parameters of various materials in the thermoelectric cell are linked; and further optimization is carried out, so that a corresponded numerical value of a structural parameter of the thermoelectric cell is obtained on the condition that the hot point conversion efficiency of the thermoelectric cell is optimal. According to the invention, the method has good accuracy; and a great reference value and guiding significance are provided for the design of a structure of a thermoelectric cell.

Description

A kind of optimization method of structure of minitype thermoelectric cell

Technical field

The present invention relates to the thermoelectric cell field, more particularly, relate to a kind of optimization method of structure of minitype thermoelectric cell.

Background technology

Thermoelectric cell is a kind of solid-state energy conversion, utilizes the Seebeck effect of thermoelectric material thermal power transfer can be become electric energy.Thermoelectric cell has the advantages such as the high stability, life-span length, Maintenance free of high degree of adaptability to operational environment, performance, pollution-free, shockproof and noiselessness, its range of application mainly is the recycling to used heat at present, and as the aspects such as independent current source of some equipment, but low conversion efficiency of thermoelectric has become a bottleneck that limits its application.

The conversion efficiency of thermoelectric of thermoelectric cell mainly is subjected to two aspect factor affecting, is the thermoelectricity capability of thermoelectric material on the one hand, is the design of thermoelectric cell structure on the other hand.All the time, more to the research of thermoelectric material, and reached certain level, the performance of material unlikely has a distinct increment in a short time, and design is just receiving increasing concern to the thermoelectric cell structural optimization.Traditional one-dimensional model optimization method has been ignored more actual conditions, optimum results and actual effect differ larger, and the finite element method of bibliographical information is a kind of preferably technology of optimizing the thermoelectric cell structure at present, but the foundation of the method model and the equal more complicated of follow-up analysis use time and effort consuming.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of optimization method of structure of minitype thermoelectric cell is provided.The method is set up the One dimensional Mathematical Model of expressing the minitype thermoelectric cell performance, by calculating under the battery performance optimal situation dependency structure parameter of thermoelectric cell more in conjunction with the actual detail of minitype thermoelectric cell.The method simply is easy to grasp, and accuracy is better, and the structural design of thermoelectric cell is had larger reference value.

Optimization method of the present invention carries out for the thermoelectric cell with Fig. 1 construction unit.This thermoelectric cell is made of outer package layer 1, conduction articulamentum 2, packing material 3, p-type thermoelectric leg 4 and N-shaped thermoelectric leg 5.P-type thermoelectric leg 4 and N-shaped thermoelectric leg 5 in the thermoelectric cell are arranged in parallel, and conduction articulamentum 2 is used for the electricity series connection between realization p-type thermoelectric leg 4 and the N-shaped thermoelectric leg 5, and outer package layer 1 and packing material 3 are for the protection of the internal structure of thermoelectric cell.

Purpose of the present invention is achieved by following technical proposals:

The first step, determine character and the residing operational environment of thermoelectric cell material therefor:

(1) the Seebeck coefficient α of N-shaped thermoelectric material _n, the electricalresistivityρ _n, thermal conductivity λ _n, N-shaped thermoelectric material and the contact resistivity ρ of conduction between articulamentum _N-contact

(2) the Seebeck coefficient α of p-type thermoelectric material _p, the electricalresistivityρ _p, thermal conductivity λ _p, p-type thermoelectric material and the contact resistivity ρ of conduction between articulamentum _P-contact

(3) the thermal conductivity λ ' of packing material

(4) the thermal conductivity λ of outer package layer material on the cold and hot end face of thermoelectric cell ₀And thickness h ₀

(5) the temperature difference T between between the cold junction of thermoelectric cell hot junction

(6) temperature T in thermoelectric cell hot junction _Hot

(7) resistance value of thermoelectric cell external load is R _L0With rated power be P ₀

Second step, the structural parameters of setting thermoelectric cell:

Set span and the stepping amount of the height h of the section radius b of section radius a, p-type thermoelectric leg of N-shaped thermoelectric leg and thermoelectric leg, and carry out progressively iterative computation according to following formula, until obtain the maximum η of the conversion efficiency of thermoelectric of thermoelectric cell _Max, this moment, corresponding a, b, h was the final optimization pass structural parameters

${\mathrm{\ΔT}}_0=\frac{2\sqrt{P_0/R_{L0}}(\frac{{\mathrm{h\ρ}}_n-{2\mathrm{\ρ}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\ρ}}_p-{2\mathrm{\ρ}}_{p-\mathrm{contact}}}{b^2})}{{\mathrm{\π\α}}_{p,n}}$

$A_T/N=\frac{\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;}){\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}{\frac{{\mathrm{\&lambda;}}_{0}h(\mathrm{\&Delta;T}-{\mathrm{\&Delta;T}}_0)}{2h_0{\mathrm{\&Delta;T}}_0}-{\mathrm{\&lambda;}}^{\&prime;}}$

$Q=\frac{\mathrm{\&pi;}{R}_{L0}{\mathrm{\&alpha;}}_{p,n}{T}_{\mathrm{hot}}\sqrt{P_0/R_{L0}}}{\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{<figure-callout\; id="2"\; label="contact\; b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">contact</figure-callout>}}}{b^{}}}$

$+\frac{2\sqrt{P_0{R}_{L0}}(\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;}){\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">b</figure-callout>}}^2+{\mathrm{\&lambda;}}^{\&prime;}{A}_T/N)}{{\mathrm{\&alpha;}}_{p,n}h}-\frac{P_0}{2}$

$\mathrm{\&eta;}=\frac{P}{Q}$

The thermoelectric cell structural optimization method that the present invention proposes, relevant nature parameter with conversion efficiency of thermoelectric and the various materials in the thermoelectric cell of thermoelectric cell, the hot junction of thermoelectric cell and cold junction temperature, the structural parameters of thermoelectric cell, and the relevant parameter of the load that is connected with thermoelectric cell connects.Above-mentioned relevant nature parameter comprises N-shaped thermoelectric material that thermoelectric cell adopts and Seebeck coefficient, thermal conductivity, resistivity and the contact resistivity data of p-type thermoelectric material, the thermal conductivity data of the packing material in the thermoelectric cell between each thermoelectric leg, and the thermal conductivity data of employed outer package layer on thermoelectric cell cold junction and the hot junction, the present invention optimizes the structural parameters of thermoelectric cell with above-mentioned parameter, i.e. the sectional area (being radius) of N-shaped thermoelectric leg and p-type thermoelectric leg and height.This optimization method that the present invention proposes has more been considered the actual conditions of thermoelectric cell, comprising:

(1) sectional area of N-shaped thermoelectric leg 5 and p-type thermoelectric leg 4 is identical or different;

(2) all there is contact resistance between N-shaped thermoelectric leg 5 and p-type thermoelectric leg 4 and the conduction articulamentum 2;

(3) heat (comprise p-type thermoelectric leg 4, N-shaped thermoelectric leg 5) from the hot junction along the thermoelectric leg and the thermoelectric leg between 3 two kinds of channels of packing material be delivered to cold junction;

(4) temperature difference between the upper and lower end face of thermoelectric leg, the temperature difference that equals between thermoelectric cell hot junction and the cold junction deducts the temperature difference that consumes on upper and lower outer package layer;

This optimization method that the present invention proposes connects the structural parameters of conversion efficiency of thermoelectric and thermoelectric cell, take conversion efficiency of thermoelectric as optimization object, obtains the structural parameters of thermoelectric cell corresponding when most effective.The method is scientific and reasonable, and the result of calculation accuracy is better, and this is for the structure of optimizing thermoelectric cell, and the performance that promotes thermoelectric cell has larger directive significance.

Description of drawings

The cross-sectional view of the thermoelectric unit that is consisted of by a N-shaped thermoelectric leg and p-type thermoelectric leg in Fig. 1 thermoelectric cell.The numbering explanation: 1 is outer package layer, and 2 are the conduction articulamentum, and 3 is packing material, and 4 is p-type thermoelectric leg, and 5 is N-shaped thermoelectric leg.

Fig. 2 optimization method schematic diagram of the present invention.

Embodiment

Further specify technical scheme of the present invention below in conjunction with specific embodiment.

The temperature difference structural optimization method that the present invention adopts, considered following actual conditions: the sectional area of (1) N-shaped thermoelectric leg 5 and p-type thermoelectric leg 4 is identical or different; (2) all there is contact resistance between N-shaped thermoelectric leg 5 and p-type thermoelectric leg 4 and the conduction articulamentum 2; (3) heat (comprise p-type thermoelectric leg 4, N-shaped thermoelectric leg 5) from the hot junction along the thermoelectric leg and the thermoelectric leg between 3 two kinds of channels of packing material be delivered to cold junction; (4) temperature difference between the upper and lower end face of thermoelectric leg equals the temperature difference between the cold junction of thermoelectric cell hot junction and deducts the temperature difference that consumes on upper and lower outer package layer.

Concrete optimization method is as follows: the first step, the gross area of supposing thermoelectric cell is A _T, wherein contain N to the thermoelectric unit, and thermoelectric leg 4 or 5 is cylinder (the thermoelectric leg is similar for the situation of other shape), with reference to accompanying drawing 1, take a pair of thermoelectric unit area as research object, then its resistance can be expressed as follows with [1] formula:

$R=R_n+R_p+R_{\mathrm{contact}}={\mathrm{\&rho;}}_n\frac{h}{\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}+{\mathrm{\&rho;}}_p\frac{h}{\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}+\frac{{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{{\mathrm{\&pi;<figure-callout\; id="2"\; label="a"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}+\frac{{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{\mathrm{\&pi;}{b}^2}---\left[1\right]$

Wherein: R, R _n, R _p, R _ContactRepresent respectively the all-in resistance of a pair of thermoelectric leg, the resistance of N-shaped thermoelectric leg 5, the resistance of p-type thermoelectric leg 4, and the contact resistance between N-shaped thermoelectric leg and p-type thermoelectric leg and the conduction articulamentum 2, ρ _n, ρ _p, ρ _N-contact, ρ _P-contactThe resistivity of the p-type thermoelectric material of the resistivity of the N-shaped thermoelectric material of respectively expression formation N-shaped thermoelectric leg 5, formation p-type thermoelectric leg 4, and the contact resistivity of 2 of N-shaped thermoelectric leg 5 and p-type thermoelectric leg 4 and conduction articulamentums, a, b, h represent respectively the section radius of N-shaped thermoelectric leg 5, the section radius of p-type thermoelectric leg 4 and the height of thermoelectric leg.

The overall thermal conductance K of a pair of thermoelectric unit can be expressed as follows with [2] formula:

$K=K_n+K_p+K^{\&prime;}={\mathrm{\&lambda;}}_n\frac{{\mathrm{\&pi;a}}^2}{h}+{\mathrm{\&lambda;}}_p\frac{{\mathrm{\&pi;b}}^2}{h}+{\mathrm{\&lambda;}}^{\&prime;}\frac{A_T/N-{\mathrm{\&pi;a}}^2-{\mathrm{\&pi;b}}^2}{h}---\left[2\right]$

Wherein: K _n, K _p, K ' represents respectively the thermal conductance of packing material 3 between the thermal conductance of thermal conductance, p-type thermoelectric leg 4 of N-shaped thermoelectric leg 5 and the thermoelectric leg, λ _n, λ _p, λ ' represent respectively to consist of the N-shaped thermoelectric material of N-shaped thermoelectric leg 5 thermal conductivity, consist of the thermal conductivity of the p-type thermoelectric material of p-type thermoelectric leg 4 and the thermal conductivity of packing material 3.

The temperature difference between the upper and lower end face of thermoelectric leg can be expressed as follows with [3] formula:

${\mathrm{\&Delta;T}}_0=\frac{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">T</figure-callout>}}{1+2K/K_0};$ $K_0={\mathrm{\&lambda;}}_0\frac{A_T/N}{h_0}$

${\mathrm{\&Delta;T}}_0=\mathrm{\&Delta;T}/\{1+\frac{{2h}_0}{h}[\frac{\mathrm{\&pi;}{\mathrm{Na}}^2({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})}{{\mathrm{\&lambda;}}_0{A}_T}+\frac{\mathrm{\&pi;}{\mathrm{Nb}}^2({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;})}{{\mathrm{\&lambda;}}_0{A}_T}+\frac{{\mathrm{\&lambda;}}^{\&prime;}}{{\mathrm{\&lambda;}}_0}\left]\right\}---\left[3\right]$

Wherein: Δ T, Δ T ₀Represent respectively the temperature difference between the cold junction of thermoelectric cell hot junction and the temperature difference between the thermoelectric leg upper and lower end face, K ₀, λ ₀, h ₀The thermal conductance that represents respectively outer package layer 1 on the cold and hot end face, thermal conductivity and thickness thereof.(as then can think Δ T without outer package layer ₀=Δ T)

Simultaneously, because

$I=\frac{{\mathrm{N\&alpha;}}_{p,n}{\mathrm{\&Delta;T}}_0}{\mathrm{NR}+R_L}---\left[4\right]$

$P=I^2{R}_L=\frac{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">N</figure-callout>}}^2{\mathrm{\&alpha;}}_{p,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&Delta;T}}_0^2{R}_L}{{(\mathrm{NR}+R_L)}^2}---\left[5\right]$

Q＝N (Iα _p，nT _hot+KΔT ₀-I ²R/2) [6]

$\mathrm{\&eta;}=\frac{P}{Q}---\left[7\right]$

Wherein: I, P, Q, η represent that respectively the output current of thermoelectric cell, power output (are the rated power P of load ₀), import the hot-fluid of thermoelectric cell and the conversion efficiency of thermoelectric of thermoelectric cell, α into from the thermoelectric cell hot junction _{P, n}Represent the relative Seebeck coefficient (α of p-type and N-shaped thermoelectric material _{P, n}=α _p-α _n, α wherein _p, α _nBe respectively the Seebeck coefficient of p-type thermoelectric material, the Seebeck coefficient of N-shaped thermoelectric material), R _LRepresent the resistance value of load, T _HotRepresent the temperature in thermoelectric cell hot junction.

Second step supposes that the resistance value of the electrical appliance (load) that is connected with thermoelectric cell is R _L0, rated power is P ₀, and think that thermoelectric cell just in time satisfies the plant capacity requirement in Maximum Power Output, namely work as NR=R _L0The time, the battery power output is P ₀

Then can get following expression through series of iterations:

$N=R_{L0}/R=\mathrm{\&pi;}{R}_{L0}/(\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{b^2})---\left[8\right]$

${\mathrm{\&Delta;T}}_0=\frac{2\sqrt{P_0/R_{L0}}(\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p-{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{b^2})}{\mathrm{\&pi;}{\mathrm{\&alpha;}}_{p,n}}---\left[9\right]$

$A_T/N=\frac{\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;}){\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}{\frac{{\mathrm{\&lambda;}}_{0}h(\mathrm{\&Delta;T}-{\mathrm{\&Delta;T}}_0)}{2h_0{\mathrm{\&Delta;T}}_0}-{\mathrm{\&lambda;}}^{\&prime;}}---\left[10\right]$

$Q=\frac{\mathrm{\&pi;}{R}_{L0}{\mathrm{\&alpha;}}_{p,n}{T}_{\mathrm{hot}}\sqrt{P_0/R_{L0}}}{\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{<figure-callout\; id="2"\; label="contact\; b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">contact</figure-callout>}}}{b^{}}}$

$+\frac{2\sqrt{P_0{R}_{L0}}(\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;}){\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000121873160000011.png"\; state="\{\{state\}\}">b</figure-callout>}}^2+{\mathrm{\&lambda;}}^{\&prime;}{A}_T/N)}{{\mathrm{\&alpha;}}_{p,n}h}-\frac{P_0}{2}---\left[11\right]$

So, formula [9] is updated in the formula [10], formula [10] being updated to is in [11] again, with in formula [11] the substitution formula [7], can obtain the expression formula of conversion efficiency of thermoelectric: η=η (a, b at last, h), remove a, b in the formula, other outer parameter of h all can record concrete numerical value or artificially set numerical value by pertinent instruments, as long as set so independent variable a, b, the span of h, just can obtain η corresponding a, b, h when maximum, and with their substitution formulas [8] and formula [10], obtain N and A _TValue, namely reached the purpose of optimizing battery structure by said method like this.

According to above-mentioned optimization method, at first measure and determined that the character of thermoelectric cell material therefor and residing operational environment are as follows:

1.α _p＝1.2×10 ^-4V/K，ρ _p＝2×10 ^-5Ω·m，λ _p＝1.22W/(m·K)，ρ _p-contact＝3×10 ^-9Ω·m ²

2.α _n＝-1.4×10 ^-4V/K，ρ _n＝1.1×10 ^-5Ω·m，λ _n＝1.85W/(m·K)，

ρ _n-contact＝1×10 ^-9Ω·m ²

3.λ′＝0.306W/(m·K)，λ ₀＝100W/(m·K)，h ₀＝5×10 ^-5m

4.ΔT＝20K，T _hot＝318.15K

5.R _L0＝100Ω，P ₀＝1×10 ^-3W

Then set respectively span and the stepping amount of the height h of the section radius b of section radius a, p-type thermoelectric leg of the structural parameters N-shaped thermoelectric leg of thermoelectric cell and thermoelectric leg, as follows:

1.a ∈ (5 μ m, 1mm), the stepping amount is 10 μ m

2.b ∈ (5 μ m, 1mm), the stepping amount is 10 μ m

3.h ∈ (5 μ m, 2mm), the stepping amount is 10 μ m

When above-mentioned parameter substitution formula is carried out calculation optimization, at first calculate Δ T according to formula [9] ₀, then bring formula [10] into and calculate A _T/ N can obtain Q with operation result substitution formula [11] again, will can obtain the conversion efficiency of thermoelectric η of thermoelectric cell in the as a result substitution formula [7] at last.So carry out iterative computation according to the stepping amount, to obtain maximum efficiency eta as the iteration terminal point, the structure of thermoelectric cell after corresponding a, b, h was and optimized this moment.Final calculation result shows below: η _Max=0.00269, this moment h=875 μ m, a=95 μ m, b=135 μ m, N=121.8, A _T=10.59mm ²

Result according to above-mentioned optimization calculating, according to actual conditions N is chosen as 122, h is chosen as 875 μ m, a is chosen as 95 μ m, b is chosen as 135 μ m, produced a thermoelectric cell, and utilize thermoelectric cell the conversion efficiency of thermoelectric test system and test conversion efficiency of thermoelectric of this battery when above-mentioned operational environment be 0.00267.

The optimization method of structure of minitype thermoelectric cell of the present invention has been considered actual conditions more, with respect to traditional optimization method, optimizing structure closer to actual result of the thermoelectric cell that the method obtains has larger using value for the conversion efficiency of thermoelectric that improves thermoelectric cell by Optimal Structure Designing.During practical operation, the N round numbers, the scope of a, b, h can give the different assignment of above-mentioned parameter or scope according to actual conditions, to obtain the optimization structure of corresponding thermoelectric cell.

More than the present invention has been done exemplary description; should be noted that; in the situation that does not break away from core of the present invention, the replacement that is equal to that any simple distortion, modification or other those skilled in the art can not spend creative work all falls into protection scope of the present invention.

Claims (1)

1. the optimization method of a structure of minitype thermoelectric cell is characterized in that,

At first, determine character and the residing operational environment of thermoelectric cell material therefor:

(1) the Seebeck coefficient α of N-shaped thermoelectric material _n, the electricalresistivityρ _n, thermal conductivity λ _n, N-shaped thermoelectric material and the contact resistivity ρ of conduction between articulamentum _N-contact

(2) the Seebeck coefficient α of p-type thermoelectric material _p, the electricalresistivityρ _p, thermal conductivity λ _P, p-type thermoelectric material and the contact resistivity ρ of conduction between articulamentum _P-contact

(3) the thermal conductivity λ ' of packing material;

(4) the thermal conductivity λ of outer package layer on the cold and hot end face of thermoelectric cell ₀And thickness h ₀

(5) the temperature difference T between the cold junction of thermoelectric cell hot junction;

(6) temperature T in thermoelectric cell hot junction _Hot

(7) resistance of thermoelectric cell external load is R _L0With rated power be P ₀

Then set respectively the structural parameters of thermoelectric cell, the span and the stepping amount that comprise the height h of the section radius b of section radius a, p-type thermoelectric leg of N-shaped thermoelectric leg and thermoelectric leg, and carry out progressively iterative computation according to following formula, until obtain the maximum η of the conversion efficiency of thermoelectric of thermoelectric cell _Max, this moment, corresponding a, b, h was the final optimization pass structural parameters;

${\mathrm{\&Delta;T}}_0=\frac{2\sqrt{P_0/R_{L0}}(\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{b^2})}{{\mathrm{\&pi;\&alpha;}}_{p,n}};$

$A_T/N=\frac{\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;})b^2}{\frac{{\mathrm{\&lambda;}}_{0}h(\mathrm{\&Delta;T}-{\mathrm{\&Delta;T}}_0)}{{2h}_0{\mathrm{\&Delta;T}}_0}-{\mathrm{\&lambda;}}^{\&prime;}};$

$Q=\frac{{\mathrm{\&pi;R}}_{L0}{\mathrm{\&alpha;}}_{p,n}{T}_{\mathrm{hot}}\sqrt{P_0/R_{L0}}}{\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{b^2}}$

$+\frac{2\sqrt{P_0{R}_{L0}}[\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;})b^2+{\mathrm{\&lambda;}}^{\&prime;}{A}_T/N]}{{\mathrm{\&alpha;}}_{p,n}h}-\frac{P_0}{2};$

$\mathrm{\&eta;}=\frac{P}{Q};$

To optimize structure parameter a, b, h obtain the gross area A of final optimization pass structural parameters thermoelectric cell again in the substitution following formula _T, and the thermoelectric element number N that contains in the thermoelectric cell;

$N=R_{L0}/R={\mathrm{\&pi;R}}_{L0}/(\frac{{\mathrm{h\&rho;}}_n+{2\mathrm{\&rho;}}_{n-\mathrm{contact}}}{a^2}+\frac{{\mathrm{h\&rho;}}_p+{2\mathrm{\&rho;}}_{p-\mathrm{contact}}}{b^2});$

$A_T/N=\frac{\mathrm{\&pi;}({\mathrm{\&lambda;}}_n-{\mathrm{\&lambda;}}^{\&prime;})a^2+\mathrm{\&pi;}({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}^{\&prime;})b^2}{\frac{{\mathrm{\&lambda;}}_{0}h(\mathrm{\&Delta;T}-{\mathrm{\&Delta;T}}_0)}{{2h}_0{\mathrm{\&Delta;T}}_0}-{\mathrm{\&lambda;}}^{\&prime;}};$

Wherein parameters unit is as follows:

The Seebeck coefficient α of N-shaped thermoelectric material _nUnit be V/K, the electricalresistivityρ _nUnit be Ω m, thermal conductivity λ _nUnit be W/ (mK), N-shaped thermoelectric material and the contact resistivity ρ of conduction between articulamentum _N-contactUnit be Ω m ²

The Seebeck coefficient α of p-type thermoelectric material _pUnit be V/K, the electricalresistivityρ _pUnit be Ω m, thermal conductivity λ _pUnit be W/ (mK), p-type thermoelectric material and the contact resistivity ρ of conduction between articulamentum _N-contactUnit be Ω m ²

The unit of the thermal conductivity λ ' of packing material is W/ (mK); The thermal conductivity λ of outer package layer on the cold and hot end face of thermoelectric cell ₀Unit be W/ (mK) and thickness h ₀Unit be m; The unit of temperature difference T between the cold junction of thermoelectric cell hot junction is K; The temperature T in thermoelectric cell hot junction _HotUnit be K; The resistance R of thermoelectric cell external load resistance _L0Unit be Ω and rated power P ₀Unit be W;

The unit of the section radius a of N-shaped thermoelectric leg is μ m; The unit of the section radius b of p-type thermoelectric leg is μ m; The unit of the height h of thermoelectric leg is μ m; The gross area A of final optimization pass structural parameters thermoelectric cell _TUnit be mm ²

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