Temperature Distribution Inside the Liquid Inclusion in the Field of the External Temperature Gradient

Abstract

The paper is devoted to the analytical dependence of the temperature gradient inside a liquid inclusion in a single crystal of halite on the gradient of the external temperature field. The corresponding formula was obtained for ellipsoidal inclusions. According to this expression, the temperature gradient inside the inclusion depends on the ratio of the sides (axes) of the inclusion, the thermal conductivity coefficients of the inclusion and the medium, as well as the external temperature gradient. The results obtained by the formula were compared with the previously known results and with the results of numerical calculation of the thermal conductivity equation in a three-dimensional formulation for different values of the ratio of the inclusion axes. The best accordance of the calculation results according to the obtained dependence with the results of the numerical solution of the heat equation is shown. A good coincidence of the results of numerical and analytical calculations allows us to use the obtained analytical expression for the temperature gradient in the inclusion of an ellipsoidal shape in order to further construct the theory of thermomigration of liquid inclusions.