A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

Abstract

The properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x≪x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nux∝x3/4. In the second regime, at x≫ x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is \(Nu_x \propto {{\sqrt x } \mathord{\left/ {\vphantom {{\sqrt x } B}} \right. \kern-\nulldelimiterspace} B}\). The location of the boundary between these regimes strongly depends on the magnetic field, x*∝ B−4.