Analytical Model of a Side-Heated Free Convection Loop Placed in a Transverse Magnetic Field

Abstract

The hydrodynamic characteristics of a buoyancy-driven convection loop containing an electrically-conducting fluid in a transverse magnetic field are investigated analytically using a one-dimensional model. One side of the loop is isothermally heated and the other side isothermally cooled, and the upper and lower sections are insulated. The model which is based on the use of the Hartmann Plane-Poiseuille flow solution for estimating loop shear stress, predicts the flow velocity and the induced current of the magnetohydrodynamic generator in terms of the flow and geometric parameters. The study covers ranges of Grashof number, Gr, from 102 to 106 , the Hartmann number, Ha, from 0 to 20, the Prandtl number, Pr, from .003 to 7, and loop height to thickness ratio, L/d, from 10 to 50. It is shown that at low Prandtl numbers, Pr ≪ 1, there exists an optimal Hartmann number, Haopt , that maximizes the induced electric current. This Haopt depends weakly on the Grashof number. The side-heated loop performance is also compared with the bottom heated loop model of Ghaddar, (1997a). It is found that at a low Prandtl number, side heated loop induces the higher velocity whereas at high Prandtl numbers the bottom heated loop induces higher velocity.