Buoyant Couette–Bingham flow between vertical parallel plates

The present paper is closely related to a recent work of Bayazitoglu et al. [Y. Bayazitoglu, P.R. Paslay, P. Cernocky, Laminar Bingham fluid flow between vertical parallel plates, Int. J. Thermal Sci. 46 (2007) 349–357], in which the free convection of a Bingham material in a vertical parallel plane channel with a constant temperature differential across the walls has been investigated. Our interest is directed on the additional effect of an external shear, applied on the wall–fluid interface. This forcing shear is induced (in our mathematical model) by a uniform vertical motion of the hot wall of the channel in its own plane. The physically most interesting five-domain configuration of the velocity field of the resulting buoyant Couette–Bingham flow is examined in detail. For the initiation temperature of the flow, whose existence has been predicted in [Y. Bayazitoglu, P.R. Paslay, P. Cernocky, Laminar Bingham fluid flow between vertical parallel plates, Int. J. Thermal Sci. 46 (2007) 349–357], a generally valid formula is reported. Subsequently, it is shown that the core velocities with rigid body motion depend on the wall velocity sensitively. The hot and cold cores possess the same width which, however, decreases with increasing wall velocity rapidly. There always exists a critical downward pointing wall velocity for which the upward motion of the hot core is dropped.