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Thermal Conductivity of a Homogeneous Body in Magnetic Field

  • THERMOPHYSICAL PROPERTIES OF MATERIALS
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High Temperature Aims and scope

Abstract

An experimental setup and a technique for measuring the thermal conductivity of permanent-magnet samples with different orientations of magnetic-field lines in space are described. The anisotropy of the thermal conductivity of the magnet is revealed. The obtained measurement results are presented in the form of graphs and generalized by regression equations. The mechanism of heat conduction is refined, and the reason for the anisotropy of the thermal conductivity of a homogeneous body under the influence of a magnetic field is established. An explanation of the causes of the appearance of dark and light spots on the surface of the Sun is given.

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Notes

  1. In [8], in dimension λ, “cal” is erroneously indicated instead of “W.”

  2. License agreement no. 777455-03. Serial no. M71X16236.

  3. The temperature of the photosphere does not exceed 6000–6500 K [14], which is lower than the temperature of complete ionization of hydrogen and helium atoms.

  4. https://i007.fotocdn.net/s111/125321ac9b283f05/publ-ic_pin_m/2488166861.jpg

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Funding

This work was carried out under an agreement on creative cooperation between the Institute of Energy and Advanced Technologies of Federal Research Center “Kazan Scientific Center of the Russian Academy of Sciences,” and Tupolev Kazan National Research Technical University, no. 7 of January 28, 2015.

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Authors and Affiliations

  1. Institute of Power Engineering and Advanced Technologies of FRC Kazan Scientific Center of RAS, 420111, Kazan, Russia

    Yu. A. Kirsanov

  2. Kazan National Research Technical University named after Tupolev—KAI, 420111, Kazan, Russia

    A. Yu. Kirsanov

Authors
  1. Yu. A. Kirsanov
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  2. A. Yu. Kirsanov
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Correspondence to Yu. A. Kirsanov or A. Yu. Kirsanov.

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APPENDIX

APPENDIX

MEASUREMENT TECHNIQUE

The calculation of the thermal conductivity of the test sample in each experiment was carried out in accordance with GOST (State Standard) 23630.2-79 according to formula

$$\lambda = \frac{{{{h}_{2}}}}{{{{R}_{2}}}}\left( {1 - {{\sigma }_{\beta }}} \right),$$

where h2 is the sample height, m; R2 is the thermal resistance of the sample, m K/W; σβ = βΔT is the correction for thermal expansion of the sample; β is the coefficient of linear thermal expansion, 1/K; ΔT = T − T0; T is the sample temperature, K; and T0 is the ambient temperature, K.

The thermal resistance is calculated by the formula

$${{R}_{2}} = \frac{{\pi {{D}^{2}}\Delta {{T}_{2}}}}{{4\Delta {{T}_{1}}{{K}_{T}}}}\left( {1 + {{\sigma }_{c}}} \right),$$

where D is the sample diameter, m; ΔT1 and ΔT2 is the temperature differences on the standard and sample, K; KT is the thermal conductivity of the standard; and σc is the correction for the specific heat of the sample:

$${{\sigma }_{c}} = \frac{{{{c}_{2}}{{M}_{2}}}}{{2\left( {{{c}_{1}}{{M}_{1}} + {{c}_{2}}{{M}_{2}}} \right)}};$$

where c is the specific heat, J/(kg K); M is mass, kg; and indices 1 and 2 refer to the standard and the test sample.

The thermal conductivity of the standard was calculated by the formula

$${{K}_{T}} = {{\lambda }_{1}}\frac{{\pi {{D}^{2}}\Delta {{T}_{2}}}}{{4\Delta {{T}_{1}}{{h}_{1}}}}\left( {1 + {{\sigma }_{c}}} \right)$$

in a series of experiments in which a disk of the same dimensions made of 12Cr18Ni9Ti steel served as the test sample. The average value for a series of experiments was KT = 0.896.

The temperature differences on the surfaces of the standard and the sample were corrected for temperature differences on copper plates 4–6 (Fig. 1):

$$\Delta {{T}_{1}} = \Delta {{T}_{{{\text{1}}{\text{.test}}}}} - \Delta {{T}_{{{\text{pl}}}}},\,\,\,\,\Delta {{T}_{2}} = \Delta {{T}_{{{\text{2}}{\text{.test}}}}} - \Delta {{T}_{{{\text{pl}}}}},$$

where \(\Delta {{T}_{{{\text{1}}{\text{.test}}}}} = {{T}_{{\text{1}}}} - {{T}_{{\text{2}}}}\); \(\Delta {{T}_{{{\text{2}}{\text{.test}}}}} = {{T}_{{\text{2}}}} - {{T}_{{\text{3}}}}\); T1, T2 and T3 are the temperatures of copper plates 4–6 measured in the experiment, K; and ΔTpl is the temperature drop across the plate, K:

$$\Delta {{T}_{{{\text{pl}}}}} = q{{{{h}_{{{\text{pl}}}}}} \mathord{\left/ {\vphantom {{{{h}_{{{\text{pl}}}}}} {{{\lambda }_{{{\text{pl}}}}}}}} \right. \kern-0em} {{{\lambda }_{{{\text{pl}}}}}}},$$

where hpl = 10–3 m is the thickness of the copper plate; λpl is the thermal conductivity of copper, W/(m K); and \(q \approx {{\lambda }_{{\text{1}}}}{{\Delta {{T}_{{{\text{1}}{\text{.test}}}}}} \mathord{\left/ {\vphantom {{\Delta {{T}_{{{\text{1}}{\text{.test}}}}}} {{{h}_{{\text{1}}}}}}} \right. \kern-0em} {{{h}_{{\text{1}}}}}}\) is the heat flux rate, W/m2.

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Kirsanov, Y.A., Kirsanov, A.Y. Thermal Conductivity of a Homogeneous Body in Magnetic Field. High Temp 60, 165–171 (2022). https://doi.org/10.1134/S0018151X22020249

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