Thermocapillary and Natural Convection in Double Layer Systems of Herschel-Bulkley and Newtonian Fluids, Exact Solutions
O.M. Lavrenteva, Yu. Holenberg and A. Nir;

doi:10.3970/fdmp.2010.006.041
Source FDMP: Fluid Dynamics & Materials Processing, Vol. 6, No. 1, pp. 41-74, 2010
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Keywords Viscoplastic fluid, liquid layer, convection, Marangoni flow
Abstract A variety of exact analytical solutions describing natural and thermocapillary convection in a horizontal double layer system consisting of Newtonian and Herschel-Bulkley fluids subjected to longitudinal temperature and concentration gradients is constructed. The lower boundary of the system is a solid wall with no-slip, while the upper ones if either a solid wall or a free surface. It was demonstrated that, depending on the governing parameters of the system, viscoplastic layer is entirely yielded or unyielded, or it can be yielded partially, exhibiting up to 5 flowing and quasi-solid layers. The dependence of the flow patterns (appearance and position of unyielded regions), velocity and temperature profiles, on the governing parameters have been studied.
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