Laminar natural convection flow in magneto-hydrodynamics

Abstract

This paper deals with the two-dimensional laminar natural convection flow of an electrically conducting viscous fluid, such as mercury or liquid sodium, in the presence of electric or magnetic fields. Two different flow régimes are discussed. The first example considered is the steady fully developed natural convection flow, with and without heat sources, between two long parallel plane surfaces with uniform magnetic field applied normal to the surfaces. The plane vertical surfaces are open at both ends to the ambient fluid and are maintained at constant temperatures different from that of the ambient fluid. Tables are given from which the fully developed temperature, velocity and induced magnetic fields may be found. Flow characteristics such as the net mass flow and wall Nusselt numbers are also evaluated. The second example considered is the steady two-dimensional natural convection flow set up by Joule heating when a direct current flows in the axial direction through a horizontal circular tube filled with an electrically conducting viscous fluid. The outside surface of the tube is maintained at constant temperature by a coolant which is assumed to be a non-conductor and non-magnetic. The influence of the non-uniform convection flow on the temperature distribution and wall Nusselt number is calculated.