Numerical study of three-dimensional combined buoyancy and thermocapillary convection and evaluation of entropy generation

Abstract

Purpose – The main purpose of this paper is to conduct on three-dimensional buoyancy and thermocapillary convection in an enclosure. Entropy generation is obtained from the calculated values of velocities and temperatures. Design/methodology/approach – As numerical method, the vorticity-vector potential formalism allows, in a three-dimensional configuration, the elimination of the pressure, which is a delicate term to treat. The control volume finite difference method is used to discretize equations. The central-difference scheme for treating convective terms and the fully implicit procedure to discretize the temporal derivatives are retained. The grid is uniform in all directions with additional nodes on boundaries. The successive relaxation iterating scheme is used to solve the resulting non-linear algebraic equations. Findings – Results are presented via entropy generation due to heat transfer, entropy generation due to fluid friction and total entropy generation. It is found that Marangoni number becomes more effective parameter on total entropy generation for lower values of Rayleigh numbers. Practical implications – In any thermal system under buoyancy induced and thermocapillary flow. Originality/value – It is believed that this is the first paper on three-dimensional solution of entropy generation in a cubical cavity under thermocapillary buoyancy flow.