Abstract
The problem of stability of a plane horizontal layer of liquid heated from below is considered with surface tension at the upper surface taken into account. The problem is stated in section 1, proof of the existence of stability threshold is given in section 2, while section 3 concerns the construction of neutral curves by numerical methods and with the stabilizing effect of surface tension on the state of equilibrium.
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A. Pellew and R. V. Southwell, “On maintained convective motion in a fluid heated from below,” Proc, Roy. Soc., Ser. A, vol. 176, pp. 312–342, 1940.
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, 1961.
L. D. Landau and E. M. Lifshitz, Mechanics of Continuous Media [in Russian], 2-nd ed., Gostekhizdat, Moscow, 1954.
V. Kh Izakson and V. I. Yudovich, “On the onset of convection in a liquid layer with a free surface,” Izd, AN SSSR, MZhG [Fluid Dynamics], no. 4, 1968.
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 89–92, May–June, 1969.
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Izakson, V.K. Effect of surface tension on the onset of convection in a layer of liquid with a free surface. J Appl Mech Tech Phys 10, 412–415 (1969). https://doi.org/10.1007/BF00916171
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DOI: https://doi.org/10.1007/BF00916171