Pattern selection in the thermal convection of non-Newtonian fluids

The thermogravitational instability in a fluid layer of a non-Newtonian medium heated from below is investigated. Linear and weakly nonlinear analyses are successively presented. The fluid is assumed to obey the Carreau-Bird model. Although the critical threshold is the same as for a Newtonian fluid, it is found that non-Newtonian fluids can convect in the form of rolls, squares or hexagons, depending on the shear-thinning level. Similar to Newtonian fluids, shear-thickening fluids convect only in the form of rolls. The stability of the convective steady branches is carried out to determine under which specific conditions a pattern is preferred. The influence of the rheological and physical parameters is examined and discussed in detail.