Numerical study of the laminar thermocapillary flow in a square cavity

The hydrodynamic and heat-transfer processes in the problem of a laminar thermocapillary flow of a viscous incompressible fluid in a square cavity with isothermal vertical and isentropic horizontal surfaces are investigated numerically under the assumption that the gravity is absent, the free surface is flat, and the surface tension depends linearly on the temperature. Calculations were performed by a compact-difference method on irregular grids with a fifth-order accuracy for four Prandtl numbers (Pr=1, 16, 200, and 3000) as the Marangoni (Ma) number varies from 10² to 10⁴. The maximum local heat transfer versus theMa number is obtained. It is shown that, for thePr values considered, the maxima of the distribution of the horizontal velocity component on the surface is displaced to the cold boundary according to a law inversely proportional to theMa number. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 81–89, July–August, 1999.