MATHEMATICAL MODEL OF CONDUCTION MODE FREE CONVECTION IN A RECTANGULAR CAVITY
The problem of the nonstationary distribution of the temperature field in a rectangular cavity under the inhomogeneous boundary conditions of the second kind is presented in the paper. The problem is solved analytically with the help of a finite integral Fourier cosine transform with its preliminary modification to the equivalent form with the help of Heaviside functions and transformation into a problem with homogeneous boundary conditions.The results of the obtained analytical solution are illustrated by the graphs of the distributions of thecharacteristic temperature fields.The obtained analytical solution can be applied to the analysis of the hydrodynamic structure in the problems of free convection in the conductive regimen. The obtained results can be used, for example, in a cryogenic technique for evaluating the effectiveness of the thermal insulation of tanks, in determining the hydrothermal structure of a freely convective flow, and a number of other problems.