The hysteresis phenomenon in the problem of cold water natural convection in a cylinderEvgueny V. Kalabin AbstractThe influence of inclination angle on heat transfer and convection movement of water near the density maximum temperature (about 4°C) in a cylindrical enclosure has been investigated numerically. Vertical walls of the studied cylinder are adiabatic and horizontal walls are isothermal. The cavity height is equal to its diameter. The structure of water flow is defined by description of temperature isosurfaces and velocity vectors in some cylinder sections. Nusselt number (Nu) estimates the heat transfer through the enclosure. The dependencies of Nu on inclination angle (α) have been examined for the three values of Grasshof number (Gr = 10^{5}, 1.5·10^{5}, 2·10^{5}). The method of investigations has been the following: at first, the solution in a vertical cylinder (α = 0) has been obtained. Then the inclination angle has been gradually changed from 0° to 90° and after that it has been decreased to 0°. The resulted Nu(α) dependence is nonlinear and it demonstrates the hysteresis phenomenon at α = 86.787.3°. Selfsustained oscillatory solutions are realized with Gr = 1.5·10^{5}, 2·10^{5}. Steady solutions are obtained at α > 0.8° (for Gr = 1.5·10^{5}) and at α > 7° (for Gr = 2·10^{5}). The behavior of Nu(α) dependencies qualitatively similar to the case of Gr = 10^{5}, but the hysteresis phenomena are not realized. All the obtained solutions with α ≠ 0° are symmetrical relatively the inclination plane. The solution with α = 90° is the same for Gr = 10^{5}, 1.5·10^{5}, 2·10^{5} and it consists of two main vortexes that are symmetrical relatively two planes (one of which is parallel to the cylinder base). 

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