DEFORMATION OF CONVECTIVE CELLS IN A FLAT HORIZONTAL LAYER WITH PERMEABLE BOUNDARIES UNDER A DIRECTIONAL FLOW OF A LIQUID
UDC 536.24:66.045
Key words: free convection, exhaust shaft, finned tube, heat transfer, Rayleigh – Benard cell, Rayleigh, Prandtl, Peclet numbers.
For citation: Karlovich T. B., Sukhotskii A. B., Danilchik E. S. Deformation of convective cells in a flat horizontal layer with permeable boundaries under a directional flow of a liquid. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2022, no. 2 (260), pp. 31–35 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2022-260-2-31-35.
Abstract
The problem of deformation of two-dimensional Rayleigh-Benard convective cells, which arise in a flat horizontal layer of liquid heated from below, in the case of its seepage through the boundaries at a constant speed, is considered. Such a phenomenon can be observed in an exhaust shaft installed to intensity heat transfer above a four-row finned tube bundle that serves to remove heat from a hot source. The model of thermogravitational convection is used to describe the air flows in the mine. Unlike previous works, where the average air flow velocity in the shaft was assumed to be zero, in this article it is taken into account as a constant vector directed along z-axis. The nonzero air velocity in the shaft arises as a result of its continuous suction from below through the finned tube bundle.
In the case of low speed of air flows in the shaft, an analytical solution is obtained for perturbations of speed and temperature. It is shown that the own values of the considered thermal and hydrodynamic problem are complex numbers. This indicates the presence of not only the damping of temperature and velocity perturbations (the so-called monotonic instability), but also the appearance of an oscillatory instability in the system, which leads to deformation of the Rayleigh-Benard cells. This fact is also confirmed by numerical calculations of the model equations.
References
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