Onset of Marangoni convection and multiple solutions in a power-law fluid layer under a zero gravity environment

• Published in: International journal of heat and mass transfer Vol. 58; no. 1-2; pp. 43 - 52
• Main Authors: Alloui, Z., Vasseur, P.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2013
• Subjects: Aspect ratio; Computational fluid dynamics; Critical Marangoni number; Fluid flow; Fluids; Gravitation; Heat transfer; Holes; Mathematical analysis; Mathematical models; Multiple solutions; Onset of motion; Power-law model; Multiple solutions; Onset of motion; Critical Marangoni number; Power-law model; Heat transfer
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2012.11.052

The Marangoni flows in a shallow cavity subject to uniform heat fluxes on all sides are investigated. A power law model is used to characterize the non-Newtonian fluid behavior of the fluid. The system with an underformable free upper surface is assumed to be under a zero gravity environment. The governing parameters for the problem are the thermal Marangoni number Ma, power-law index n, Prandtl number Pr and cavity aspect ratio aspect ratio A. An analytical solution, valid for an infinite layer (A≫1), is derived on the basis of the parallel flow approximation. For the case of a layer heated from the bottom it is demonstrated that, for shear-thinning fluids (n<1), the onset of convection is subcritical. For shear thickening fluids (n>1), convection is found to occur at a supercritical Rayleigh equal to zero. For the case of a layer heated from all sides it is shown that multiple steady state solutions are possible, some of which are unstable. The effects of the non-Newtonian behavior on the fluid flow, temperature field and heat transfer are discussed. A good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations.