Abstract
We consider the linearized Euler and Maxwell equations and Ohm’s law. We calculate the fundamental matrix and give integral representations for the velocity, magnetic induction and pressure. We use the boundary (slip) condition to obtain an integral equation for the jump of the pressure. We give some graphic representations of the velocity and magnetic induction for the case of the flat plate.
Highlights
In papers dedicated to the motion of a wing in an electro-conductive fluid, the lift, drag and moment coefficients were calculated
In order to obtain the integral representations for the velocity, the magnetic induction and the pressure fields, we perform the convolution of the components of the fundamental matrix with the simple layer distributions determined by the jump of the functions we are looking for
We notice that every integral representation has an elliptic as well as a hyperbolic part, this last one being determined by the presence of simple waves bounded by straight characteristics
Summary
In papers dedicated to the motion of a wing in an electro-conductive fluid, the lift, drag and moment coefficients were calculated. In order to obtain the integral representations for the velocity, the magnetic induction and the pressure fields (which represent the original result of this work), we perform the convolution of the components of the fundamental matrix with the simple layer distributions determined by the jump of the functions we are looking for. From the integral representation of the velocity and the boundary conditions (linearized slipping condition and the continuity of the magnetic induction), we rediscover the singular integral equation for the jump of the pressure across the airfoil. Fundamental matrix of the linearized equations for the two-dimensional incompressible flow of perfectly conducting fluids Let v, b and p designate the nondimensional perturbations of the velocity, magnetic induction and pressure, respectively, determined by the presence of a thin insulating airfoil whose equation is y = h±(x), x ∈ [ , ], h±(x) , h±(x).
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