Exact solutions in MHD natural convection of a Bingham fuid: fully developed fow in a vertical channel

In nature, many fuid-like materials exhibit a yield stress below which they behave like a solid. The Bingham model aims to describe such materials. This paper draws some mathematical considerations on the fow of a Bingham fuid in a vertical channel. The situation due to the presence of an external magnetic feld and natural convection is analyzed: the external mag- netic feld, which is orthogonal to the walls of the channel, generates the Lorentz forces that infuence the motion through the Hartmann number. The behavior of the velocity, the induced magnetic feld and the thickness of the plug regions are discussed and presented graphically. We fnd that the velocity is a decreasing function of the Bingham and Hartmann numbers. In particular, the presence of the external magnetic feld increases the thickness of the plug region. The modulus of the induced magnetic feld is not monotone when the Hartmann number changes, but it is a decreasing function of the Bingham number.