Magneto-Fluid-Dynamics of Joukowski Thin Airfoils in Oblique Fields

The problem to be considered in the case of steady motion of a fluid which is incompressible inviscid and perfect electrically conducting,past a cylindrical body whose cross-section represents a Joukowski thin,non-conducting,airfoil in the presence of a magnetic field which when undisturbed is uniform and oriented in an arbitrary direction. The problem is studied with the usual model in which the fluid variables obey the Lundquist equations linearized about a constant unperturbed flow. All the flow and magnetic field variables are assumed to differ by small amounts from their undisturbed values due to the presence of the thin airfoil. The main purposes in this problem are to illustrate the effect of the Joukowski thin airfoils on the general motion of the fluids as well as to throw further light on the flow pattern due to the change in the direction of magnetic field with respect to the flow direction. Flow and magnetic field quantities,at the body surface,such as speed,pressure coefficient,lift force,and drag force are obtained in terms of the inclination angle of the magnetic field and the number "m",which measures the ratio of the undisturbed speed of the fluid to the speed of the Alfven waves. The effect of the thin airfoil,the number "m" and the inclination angle "X" on the flow and magnetic field quantities have illustrated and discussed.