Thermocapillary-buoyancy convection of a power-law fluid layer heated from below

Abstract

Buoyant Marangoni convection of a power-law fluid confined in a shallow cavity heated from below is investigated. The free upper surface of the system is assumed to be flat and underformable. A simplified analytical model, valid for an infinite layer, is derived on the basis of the parallel flow approximation. The criteria, for the onset of convection, are predicted for both shear-thinning and shear thickening fluids. For finite amplitude convection, the effects of the power law model on the fluid flow, temperature field and heat transfer are discussed. A good agreement is found between the simplified model and the numerical results obtained by solving the full governing equations, provided that the strength of convection is small enough for the flow pattern to remain parallel.