Engineering Physics Annotation << Back LAMINAR THERMAL CONVECTION OF AN INCOMPRESSIBLE FLUID IN A CYLINDER FOR A GIVEN HEAT FLOW THROUGH THE BOUNDARY V.A. SUMIN, A.V. RYAZHSKIKH, YU.YU. GROMOV The article considers a method for solving a spatial problem of finding a non-stationary hydrothermal field in a cylinder under mixed boundary conditions and thermal boundary conditions of the second kind. The assessment of the initial stage of convective mixing of a liquid medium in closed volumes is carried out using the Stokes equations and heat transfer. The problem is divided into two parts, thermal and thermodynamic, each of which is solved analytically using the Laplace transform in dimensionless time, the finite integral cosine Fourier transform in the spatial coordinate, and the Hankel transform. When solving the thermal problem, it is shown that with an increase in the Prandtl coefficient, the temperature decreases, which confirms the reliability of the solution obtained. An analysis of the calculation of hydrothermal fields showed that the mathematical model physically correctly describes the structure of the hydrodynamic field. Keywords: cryogenic liquids, newtonian incompressible fluid, stream function, cylindrical region, free convective flow, heat transfer phenomenon, free convective flow analytical solution. DOI: 10.25791/infizik.8.2023.1350 Pp. 29-37.