SIMILARITY SOLUTIONS OF STEADY FLOWS IN A CHANNEL WITH ACCELERATING WALLS

We study the boundary layer equation F''' + R(F F '' = (F')(2)) + beta = 0 subject to conditions F(0) = F ''(0) = F(1) = F'(1) - i = 0 and F(-1) = F'(-1) = F(1) = F'(1) -1 = 0, respectively which arises from study of two-dimensional steady flows in a channel with two equally accelerating walls or one accelerating wall. The preliminary classification of possible solutions was introduced by Cox [1]. In this paper, we are able to verify the existence of families of solutions as indicated from the numerical computations. Moreover, multiple solutions for some positive R and local uniqueness are also obtained.