Open Access

ARTICLE

Thermocapillary and Natural Convection in Double Layer Systems of Herschel-Bulkley and Newtonian Fluids, Exact Solutions

O.M.Lavrenteva, Yu. Holenbergand A.Nir¹

1 Chemical Engineering Dept, Technion, Israel

Fluid Dynamics & Materials Processing 2010, 6(1), 41-74. https://doi.org/10.3970/fdmp.2010.006.041

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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