Influence of the Linearly Distributed Concentration of Carriers on the Operating Regimes of a Thermoelectric Arm

Markov, O. I.

doi:10.1023/b:joep.0000012053.17281.af

Journal of Engineering Physics and Thermophysics

2003

DOI: 10.1023/b:joep.0000012053.17281.af

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Influence of the Linearly Distributed Concentration of Carriers on the Operating Regimes of a Thermoelectric Arm

O. I. Markov

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Cited by 3 publications

(4 citation statements)

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“…In [6,7], this problem was formulated somewhat differently and solved with allowance for the temperature dependence of the kinematic coefficients on the assumption that the carrier-concentration distribution is linear. The regimes of maximum temperature drop and maximum refrigerating capacity were considered.…”

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Influence of the concentration distribution of weakly degenerate carriers on the efficiency of an arm of a thermocouple

Markov

2006

J Eng Phys Thermophys

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The one-dimensional boundary problem on determination of a stationary temperature field in an adiabatically isolated one-dimensional arm of a thermocouple has been numerically solved. Calculations were carried out for two regimes of operation of the thermocouple, one which was characterized by a maximum temperature drop and the other by a maximum refrigerating capacity. The method of quantum statistics of carriers was used in the calculations. Homogeneous and inhomogeneous arms with different carrier-concentration distributions were considered. It is shown that a linear distribution cannot be considered as optimum.The insufficiently high efficiency of thermoelectric coolers limits their use in practice; therefore, upgrading the quality of thermoelectric conductors is one of the most important problems of their physics. At present, there are no reliable methods of optimizing these conductors; this being so, their potentialities are not used completely. The use of thermoelectric conductors in coolers is determined by the operating conditions and temperatures for which they are designed; therefore, it is necessary improve the properties of a thermoelectric conductor in a definite temperature range. This problem can be solved by different methods. In the present work, we propose a method of upgrading the quality of a thermoelectric conductor in the operating-temperature range of a thermocouple.A thermoelectric conductor is usually optimized by its thermoelectric-quality coefficient Z [1], determined asThe dependence of the value of Z on the temperature and the characteristics of the charge carriers in a conductor is usually determined without regard for the lattice component or the electronic component of heat conduction. In the latter case, the kinetic effects proceeding with the participation of nongenerate carriers are defined by comparatively simple analytical expressions and, therefore, the thermoelectric quality of a conductor can be calculated practically completely [1]. However, these calculations give an approximate value of Z because the charge carriers in thermoelectric conductors are somewhat degenerate in the range of their maximum efficiency [2]. Moreover, it is well to bear in mind that the thermoelectric-quality coefficient is introduced to characterize the temperature-independent kinetic effects [1] occurring in a conductor and cannot be considered as a reliable characteristic of variable processes. Therefore, to determine the efficiency of an arm of a thermocouple, we will calculate the temperature drop in it. The temperature field of an adiabatically isolated, homogeneous, one-dimensional arm of a thermocouple operating in a stable regime is defined, with allowance for the Thomson effect, by the stationary heat-conduction equation

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Influence of the concentration distribution of weakly degenerate carriers on the efficiency of an arm of a thermocouple

Markov

2006

J Eng Phys Thermophys

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“…The last-mentioned case was considered earlier in [5]. The temperature field of the adiabatically isolated inhomogeneous one-dimensional arm of an unloaded thermocouple is defined, without regard for the Thomson effect, by the steady-state heat-conduction equation [4] d dx…”

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“…at this point and, consequently, to a partial decrease in the temperature drop. Since the Thomson effect was not taken into account in [5], it is interesting to consider its contribution to the processes studied. Figure 2 shows, for comparison, the temperature distributions obtained with and without regard for the Thomson effect.…”

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Influence of the linear distribution of the charge-carrier density along the arm of a thermocouple on the regime of its operation

Markov

2005

J Eng Phys Thermophys

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The problem on the temperature field in an inhomogeneous one-dimensional arm of a thermocouple has been solved by numerical methods with regard for both the distributed Peltier effect and the Thomson effect. It was assumed that the charge carriers are nondegenerate. The temperature field of the thermocouple was optimized for the regimes of maximum temperature drop and maximum refrigerating capacity. An optimum range of change in the charge-carrier density gradient has been determined.The widespread use of thermoelectric temperature transducers in practice poses the problem of increasing their efficiency. This can be done first of all by increasing the thermoelectric Q of these devices. The values of this parameter attained to date in practice are far from the theoretically predicted limit [1]. As is known, a thermocouple with an arm with properties changing along its length has a higher thermoelectric Q than a thermocouple with a homogeneous arm [2]. An investigation of thermocouples with arms with properties changing along their length, as a limiting case of a complex thermocouple, [3] has shown that the thermoelectric Q of a thermocouple increases with increase in its conductivity and decrease in the thermal e.m.f. from the hot to the cold end of the arm. A distinctly different approach to the solution of this problem has been proposed in [4]. This approach is based on solution of the boundary problem on steady-state heat conduction. In this case, the optimum distribution of an impurity along the length of an arm is determined by solving the variational problem with the use of the Pontryagin maximum principle. However, in the case where this formalism is used, the problem should be substantially simplified. For example, in [4] it was assumed that the thermal e.m.f., the heat conduction, and the electrical conduction depend only slightly on the temperature and the Thomson effect can be disregarded, which significantly diminishes the usefulness of the results obtained. Moreover, only one regime was considered in this work -the regime of maximum temperature drop, while the regime of maximum refrigerating capacity is the most interesting from the practical standpoint. In the present work, we made an effort to solve the boundary problem of [4] with allowance for the temperature dependence of the kinetic coefficients and for the Thomson effect. Since the problem is nonlinear in this case, we numerically solved the boundary problem and numerically optimized the solution obtained. The regimes of maximum temperature drop and maximum refrigerating capacity were considered.To determine the role of the Thomson effect, we solved both problems with and without regard for this effect. The last-mentioned case was considered earlier in [5]. The temperature field of the adiabatically isolated inhomogeneous one-dimensional arm of an unloaded thermocouple is defined, without regard for the Thomson effect, by the steady-state heat-conduction equation [4] d dx

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Temperature Field and Refrigeration Output of Thermoelectric Arm

Zhang

Yang

2011

AMR

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Temperature field in thermoelectric arm and refrigeration output equation of a thermoelectric cooler was investigated by theoretical and experimental methods. Temperature differences between hot side and cold side were measured. Experimental data were used to prove the peak of the temperature parabola is located at hot side. The terms in refrigeration output equation can’t be explained as heat conducted from hot side to cold side and half of Joule heat respectively.

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Influence of the Linearly Distributed Concentration of Carriers on the Operating Regimes of a Thermoelectric Arm

Cited by 3 publications

References 2 publications

Influence of the concentration distribution of weakly degenerate carriers on the efficiency of an arm of a thermocouple

Influence of the concentration distribution of weakly degenerate carriers on the efficiency of an arm of a thermocouple

Influence of the linear distribution of the charge-carrier density along the arm of a thermocouple on the regime of its operation

Temperature Field and Refrigeration Output of Thermoelectric Arm

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