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

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.