Steady and Unsteady Flow in a Side Heated Free Convection Loop Placed in Magnetic Field

In this study consideration is given to the hydrodynamic characteristics of a buoyancy-driven convection loop containing an electrically-conducting fluid in a transverse magnetic field in one-dimensional model. We study three problems. In problem one, we analyze the unsteady flow in closed loop in which the right side is isothermal heated and the left side is isothermal cooled, while the top and bottom regions are insulated. In problems two and three, we analyze the steady and unsteady flow in closed loop in which the bottom region is isothermal heated and the top region is isothermal cooled, while the right and left sides are insulated regions. The Laplace transformation technique is used to solve problems one and three, while in problem two we found an analytical solution