Through the aim of this study, the effects of combined buoyancy-driven flows and thermo capillary flows, which are emerged from temperature differences, on fluid flow and heat transfer numerically investigated with differentially heated side walls in a free surface square cavity. The study has been accomplished with three milestones to achieve the right solutions. For every milestone Navier-Stokes, continuity and energy equations are discretized by using finite volume method and grids with 52 x 52 control volumes. Results are presented Pr=1, Pr=7 and Pr=100. The effect of positive and negative Marangoni number on fluid flow and heat transfer at different Rayleigh number are considered and discussed.
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