Similarity solutions of steady flows in a channel with accelerating walls

We study the boundary layer equation F + R(FF″ − (F′)2) + β = 0 subject to the conditions F(0) = F″(0) = F(1) = F′(1) - 1 = 0 and F(−1) = F′(−1) = F(1) = F′(1) − 1 = 0, respectively, which arises from the 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.