RESEARCH OF OPERATION OF ANISOTROPIC OPTICAL THERMOELEMENT WITH LATERAL TEMPERATURE REGULATION

The object of research is a direct mutual conversion of thermal and electrical energy using anisotropic optical thermoelectric elements (AOTE). Receivers of through-type radiant flux, containing optically transparent heat sinks, to which the AOTE attach with the help of an adhesive dielectric layer, lead to a significant distortion of the amplitude-phase characteristics of the transmitted radiant flux. This is limited the energy and timing characteristics of receivers. Therefore, the task of creating such design of the receiver, which would be free of these shortcomings, is necessary. The design of a radiant flux receiver based on an anisotropic optical thermoelement is developed and tested, and the amplitude-phase characteristics of the flux do not change during its passage. The receiver can be used as a filter or a semitransparent mirror of an optical resonator. Such effect is due to the fact that at a thickness of 1 cm AOTE is selected with parameters α=10 -4  V/K, χ=10 -2  W/(cm K), ρ=10 -3  Ω, current I=10 A and temperature of the thermostat 300 K cm gives the minimum temperature of 239 K. A separate anisotropic thermoelement, which is made of a material with the same kinetic parameters under the same conditions, yields 265 K. Thus AOTE leads to an increase in the temperature drop.


Introduction
The wide use of thermoelectric devices as sources of electric energy, coolers and measuring equipment is due to their reliability, high service life, ability to work under extreme conditions and ecological purity.Thermoelectric devices are used in space and defense technology, metrology, electronics, medicine, etc.
The basis of most thermoelectric devices is a semiconductor thermocouple element, which, along with positive qualities, has drawbacks that prevent further progress in the development of thermoelectricity.The principal shortcomings of the thermocouple element include the ineffective participation of its volume in thermoelectric energy conversion, switching problems, and limitations on the Q-factor of the used materials.Therefore, the further development of thermoelectricity by searching for semiconductor materials with a higher quality factor has already almost exhausted itself.
Progress in thermoelectricity is possible with the introduction of new thermoelements (TE), which are dominated by the possibilities of thermocouple elements.Among the new promising TEs there are vortex TEs with unique properties, which are based on the use of the effect of vortex thermoelectric currents (VTC).It is possible to indicate, in particular, spiral vortex thermoelements, in which the problem of commutation and obtaining the necessary stresses is solved [1,2].
However, the elemental base of thermoelectricity needs replenishment due to the creation of new types of thermoelements based on known thermoelectric phenomena and phenomena that have not been sufficiently studied.To known phenomena, the mechanisms of their origin have been studied, but on the basis of which TE is created, for example, the volume effects of Peltier and Bridgman can be attributed.Studies of the feasibility of creating anisotropic optical thermoelements (AOTE) on these effects on the basis of existing and hypothetical materials, as well as studying the depth of their cooling, are of current interest.Such studies could lead to the creation of AOTE for cooling or stabilizing the temperature of various kinds of microsensors and microelectronic devices, and are distinguished by a simpler design than the known ones.To the insufficiently studied phenomena from the point of view of practical application it is possible to attribute umkehr effect, VTC effect, the effect of the anisotropy of thermal conductivity on the transverse thermoelectric power.
An in-depth study of the influence of the anisotropy of thermal conductivity on the temperature field and the transverse thermoelectric power of electrically insulated AOTE and its energy would lead to a refinement of the ТЕХНОЛОГІЧНИЙ АУДИТ ТА РЕЗЕРВИ ВИРОБНИЦТВА -№ 3/1(35), 2017 ISSN 2226-3780 physical processes in it and expansion of the field of its application.

The object of research and its technological audit
The object of research is direct mutual conversion of thermal and electric energy using anisotropic thermoelectric media.
The subject of research is physical processes in AOTE and the possibilities of their practical use.
The present time is characterized by an increase in information needs and, consequently, the development of media means.Hence the promise of using thermoelectricity to solve information problems arises.With thermoelectric means, it is possible to effectively measure temperatures, heat flux densities, radiation powers, etc.Thus, the creation and use of new types of thermoelements should be directed primarily to the creation of information technology devices.
To register the radiant flux, AOTE is used.On their basis, through-type radiant energy receivers have been created, containing optically transparent heat sinks, to which AOTE are attached by means of an adhesive dielectric layer [3,4].Such heat sink, while ensuring a reliable removal of the heat generated in TE, leads nevertheless to a significant distortion of the amplitude-phase characteristics of the transmitted radiant flux, thus limiting the energy and time characteristics of the receivers.Therefore, the problem of creating such receiver design, which would be free of these shortcomings, is promising.One of the variants of the constructive solution of this problem is given in this paper.

The aim and objectives of research
The aim of research is the discovery of new AOTEs, the study of physical processes, the processes in which they occur, the determination of their application areas, and the improvement in the characteristics of standard AOTE by constructive changes.
To achieve this aim, it is necessary to solve the following tasks: 1. To study the effect of heat inflow inside the AOTE through the lateral faces on the temperature distribution in their middle part, depending on the ratio of geometric dimensions.
2. To find the possibility of creating new AOTE, which can be used to cool or stabilize the operating temperature of various kinds of microdevices.

Research of existing solutions of the problem
The first results of experimental studies of the umkehr effect in AOTE are given in [6,7].It is shown that for certain orientations of the magnetic field induction and the temperature gradient relative to the crystallographic axes of the Bi single crystal, the inversion induction of the magnetic field leads to a change in the magnitude and sign of the longitudinal thermoelectric power.The physical nature of this phenomenon was first elucidated in [8,9], in which the dependence of the longitudinal thermoelectric power on the direction of induction of the transverse magnetic field was studied in the direction of the temperature gradient.
AOTE is considered from the standpoint of a onedimensional temperature model, which was used in [10][11][12].A one-dimensional temperature model was also used in [13].The essence of this model is that the AOTE sample, which is in a transverse magnetic field, or has a transverse thermoelectric power, exhibits either the Ettingshausen effect or the transverse Peltier effect, so long that the effects on the end faces can be neglected.That is, the flow of heat inside the AOTE through the ends does not affect the processes occurring in its middle part.In this case it is assumed that in the middle part of the sample the temperature is one-dimensional, and the electric field along the current direction is constant.The creation of new AOTEs was considered in [14].The disadvantage of these studies is that the calculation of the performance characteristics did not take into account the dependence of the thermoelectric power on the inversion of magnetic field induction.This dependence was to some extent taken into account by the author when studying the work of AOTE in the mode of electric energy generation and partly in the cooling mode in [15].However, a number of important issues remained unresolved.

Methods of research
Let's consider AOTE, which is made of optically transparent in a given frequency range and material in the form of a circular cylinder 1 of radius a and height b with a temperature-controlled lateral surface at the temperature T 0 (Fig. 1).The crystallographic axes with the maximum and minimum thermoelectric power are located in the (x, y) plane.In Fig. 1 hatching shows the direction of the crystallographic axis, electrical probes for measuring the thermoelectric power -2.The orientation of the crystallographic axes is selected when the maximum transverse thermoelectric power is obtained [16].
Neglecting the reflection of the incident monochromatic radiant flux q 0 at the AOTE boundaries (y=0 and y=b), let's represent the generalized heat equation taking into account Bouguer's law in the form: where χ, γ -coefficients of heat conductivity and absorption, respectively, which are considered as a constant.
Equations ( 1) are valid for any section (x, y), since χ is isotropic.In this setting, the isothermal lines for each of the planes y=const are concentric circles.The third term in (1) is the internal heat source.This equation must be considered together with the boundary conditions: The conditions (3) follow from the requirements for the continuity of the heat flux at the boundaries (y=0 and y=b).
Let's write the solution of equation ( 1) in the form of a Fourier expansion in cosines: where δ = π , n n b 0 f -zero term of the expansion.Substituting (2) into (1), obtain: where 0 , n C C -coefficients of the Fourier series expansions in the cosines of the function: which have the form: From these equations obtain: where , , , A B G F -constants of integration.Using the boundary conditions (4) and expressions (2), ( 6), (7), write: From the first two equations find: and two other will give: So the temperature distribution will look like:

C ch a ch x T x y T C a x y ch a
The potential difference between the points (a, b/2) and (-a, b/2) (probes 2 in Fig. 1) has the value: Substituting n C and δ n instead of their value for the potential difference ∆ϕ, get: sin .The potential difference ∆ϕ is a thermoelectric power, which is due to the presence of the incident radiant heat flux q 0 , anisotropy of the thermoelectric power factor α 12 , thermal conductivity χ and absorption γ.The potential difference depends on the geometric dimensions of the AOTE a and b.
In the case of applying the considered AOTE as the sensor of the flow-through receiver under conditions > γ << , 1 a b b for the potential difference ∆ϕ with great accuracy, write:

( ) . q a b
The volt-watt sensitivity is represented by the expression: .

S b a
The equivalent noise power P of a given receiver has the form: The time constant: Maximum density of controlled energy max : q ISSN 2226-3780 In the above expressions: 0 k -the Stefan-Boltzmann constant; 0 , a σ, ΔТ -thermal diffusivity, electrical conductivity and permissible temperature of AOTE material overheating, respectively.

Research results
Table 1 shows the parameters of real optically transparent crystals that have anisotropy of the thermoelectric power coefficient at 300 K [17].The use of materials in Table 1 allows to create the construction of various anisotropic thermoelectric elements: -time-stable through-type receivers with a volt-watt sensitivity of S=10 -6 -10 -3 V/W -1 ; -working area 0.1-5.0cm 2 with the maximum value of the energy flux density q max =10 -3 -10 1 W/cm 2 in a wide spectral range, with the possibility of using them as a filter.
Based on AOTE, the design of the laser radiation receiver is developed (Fig. 2).With the help of this receiver, it is possible to determine the energy distribution of the radiant flux over the cross section of the beam in a wide spectral and energy range, which is protected by the patent of Ukraine [18].An anisotropic optical thermoelement is widely used in measuring technology.New anisotropic optical thermoelements are effectively used to register and measure energy flows.They are indispensable in the study, for example, of powerful laser radiation.In the field of nitrogen temperatures and below, the use of galvanothermomagnetic cooling devices for cooling and stabilizing the temperature of various microsensors and microelectronic devices is prospective.

SWOT analysis of research results
Strengths.The strength of the research is the study of the nature of physical processes in thermoelectric media, which are the basis for the invention of the original elements that are important from a practical point of view and the study of phenomena in them.
Weaknesses.The weak side of research is the neglect of the dependence of the thermoelectric power on the inversion of magnetic field induction (umkehr effect), which is significant limits these possibilities.
Opportunities.In the future, it is necessary to investigate the effect of magnetic field induction inversion (umkehr effect) on longitudinal AOTE characteristics and to analyze the possibility of creating on the basis of the obtained AOTE results, whose operation principle is based on the umkehr effect.It is also necessary to propose and investigate physical models of longitudinal AOTE based on the Thomson effect, the volume Peltier effect and the Bridgman effect in terms of maximum temperature reduction.
The introduction of research results in production will allow to determine the economic efficiency from the current costs associated with their use in production.The profit from the introduction of the developed receiver of thermal radiation at the enterprise will be 100 c. u. [18].
Threats.When calculating the temperature distribution and efficiency, it is assumed that the temperature distribution is two-dimensional, the electric current density, which is produced by AOTE, is constant, the kinetic parameters of the AOTE material are also constant.Efficiency depends on the values of heat flow and external electrical resistance.Numerically, for modern thermoelectric homogeneous anisotropic materials it can reach ~0.8 %.Such AOTE can be used as a thermal radiation sensor.
Estimates of all financial costs from the introduction of a thermal radiation receiver based on an anisotropic optical thermoelement in the enterprise will amount to 0.007 % of the cost of this device [18].

Conclusions
1.It is shown that anisotropic thermoelectric elements with a working area of 0.1-5.0cm 2 with a maximum value of the energy flux density of 10 -3 -10 1 in a wide spectral range give optimal cooling of the equipment.
2. Design of a radiant flux receiver based on an anisotropic optical thermoelement is developed and tested, and the amplitude-phase characteristics of the flow do not change during passage.The receiver can be used as a filter or a semitransparent mirror of an optical resonator.Such effect is due to the fact that at a thickness of 1 cm AOTE is selected with parameters α = 10 -4 V/K, χ = 10 -2 W/(cm K), ρ = 10 -3 Ω, current I = 10 A and temperature of the thermostat 300 K cm gives the minimum temperature of 239 K.

Fig. 1 .
Fig. 1.Scheme of an anisotropic optical thermoelement, which is used to calculate the temperature distribution

Table 1
Materials for manufacturing of anisotropic thermoelements