Small parameter method for determining motion of a viscous incompressible fluid in a thrust bearing

Abstract

We consider the plane stationary motion of a viscous incompressible fluid between two surfaces. The fixed surface is given by the equation y=h[1+εf(x/h)], where the functionf(x/h=h) characterizes the deviation of the fixed surface from the plane y=h(h and ε, are constants). The moving surface is a plane which moves with constant velocity along the x axis and remains parallel to the plane y=h. The small parameter method is used to solve the problem. The problem formulation is presented in the first section, the solvability of the linear equations obtained using the small parameter method is investigated in the second section, and the third section studies the convergence of the method and finds the radius of convergence of the constructed series.