Stationary Problem of the Flow of a Conductive Fluid Generated by the Rotation of a Circular Porous Disk Taking into Account the Magnetic Field

The paper studies the stationary problem of the flow generated by the rotation of a circular porous disk in an electrically conductive fluid, taking into account a uniform magnetic field for a constant value of the suction velocity of the same fluid in the disk. To study the problem, the method of successive approximations, known as the Green's function and the small parameter method, is used. In the considered case, the small parameter is the Reynolds number. The system of nonlinear differential equations with partial derivatives of the Navier-Stokes equation of the motion of an electrically conductive fluid in a magnetic field is reduced to a system of ordinary nonlinear differential equations using generalized Karman insertions, the solutions of which are sought in the form of infinite series for small values of the Reynolds number. The solution of the problem using the Green's function is reduced to the solution of integral-differential equations. The Green's function of the corresponding problem is constructed and recurrent formulas are obtained, by means of which it is possible to calculate solutions in any approximation. The first two approximations are calculated explicitly. The physical characteristics of the fluid flow are calculated and the expressions for the components of the fluid velocity are obtained, as well as the expression for the pressure distribution on the disk. The moment of resistance to the rotation of the plate is calculated.