Finite Difference Solutions of MFM Square Duct Flow with Heat Transfer Using MatLab Program

Abstract

Many researchers are interested in magneto-hydro-dynamics MHD since the last century due to its important applications. For example, MHD steam plants and MHD generators are used in the modern power plants. The basic concept of the MHD generator is to generate electrical energy from the motion of conductive liquid that is crossing a perpendicular magnetic field. Carnot efficiency is improved by the presence of MHD unit. Another example is the MHD pumps and flow meters. In this type of pumps, the electrical energy is converted directly to a force which is applied on the working fluid. MHD separation in metal casting with superconducting coils is another important application. A very useful proposed application which involves MHD is the lithium cooling blanket in a nuclear fusion reactor. The high-temperature plasma is maintained in the reactor by means of a toroidal magnetic field. The liquid-lithium circulation loops, which will be located between the plasma and magnetic windings, are called lithium blankets. The lithium performs two functions: it absorbs the thermal energy released by the reaction (and subsequently used for power generation) and it participates in nuclear reactions in which tritium is produced. The lithium blanket is thus a very important reactor component. On other hand, the blanket will be acted upon by an extremely strong magnetic field. Consequently, to calculate the flow of liquid metal in channels or pipes situated at different angles to the magnetic field, and to determine the required pressure drop, heat transfer, etc., a knowledge of the appropriate MHD relationships will be necessary. Magnetohydrodynamics (MHD) has been studied since the 19th century, but extensive investigations in this field accelerated only at the beginning of the 20th century. The first theoretical and laboratory studies of MHD flows in pipes and ducts were carried out in the 1930s. Williams published results of experiments with electrolytes flowing in insulated tubes. The tubes were placed between the poles of a magnet, and the potential difference across the flow was measured using wires passed through the walls. Hartmann and Lazarus made some very comprehensive theoretical and experimental studies of this subject. They performed their experiments with mercury which has an electrical conductivity 100,000 times greater than that of an electrolyte. This made it possible to observe a wider range of phenomena than in the experiments by Williams. In particular, Hartmann and Lazarus were 17