A new analytical solution branch for the Blasius equation with a shrinking sheet

A similarity equation of the momentum boundary layer is analytically studied for a moving flat plate with mass transfer in a stationary fluid by a newly developed technique namely homotopy analysis method (HAM). The equation shows its significance for the practical problem of a shrinking sheet with a constant velocity, and only admits the existence of the solution with mass suction at the wall surface. The present work provides analytically new solution branch of the Blasius equation with a shrinking sheet in different solution areas, including both multiple solutions and unique solution with the aid of an introduced auxiliary function. The analytical results show that quite complicated behavior with three different solution areas controlled by two critical mass transfer parameters exists, which agrees well with the numerical techniques and greatly differs from the continuously stretching surface problem and the Blasius problem with a free stream. The new analytical solution branch of the Blasius equation with a shrinking sheet enriches the solution family of the Blasius equation, and helps to deeply understand the Blasius equation.