High Marangoni number convection in a square cavity

• DOI: 10.1063/1.865300
• Publication Date: 2002-07-26T13:17:17Z
• Authors: A. Zebib; G. M. Homsy; E. Meiburg
• Keywords: Marangoni number; Free surface

The steady thermocapillary motion in a square cavity with top free surface the absence of gravitational forces is considered. heated from side vertical boundaries isothermal while horizontal are adiabatic. relative change tension very small, i.e., an appropriate capillary number tends to zero, so that assumed remain flat at leading order. A finite-difference method employed compute flow field. Numerically accurate solutions obtained for range Prandtl numbers and Reynolds Re as high 5×104. Surface deflections computed domain perturbation small number. In addition, asymptotic methods used infer boundary layer structure cavity, limit large values Marangoni numbers. For fixed Pr, it shown Nusselt number, liquid circulation, maximum vorticity Re1/3, Re−1/3, Re2/3, respectively. These results agreement solutions. leading-order solution free-surface deformation sensitive value Pr. With Pr>1, depression near hot corner may exceed elevation cold corner, secondary be induced when Pr<1.