A new branch of solutions of boundary-layer flows over an impermeable stretched plate

The boundary-layer flows over a stretched impermeable wall are solved by means of an analytic technique, namely the homotopy analysis method. Two branches of solutions are found. The first agrees well with numerical results given by Banks in 1983. The second branch of solutions can be divided into two parts. One is mathematically equivalent to a branch of solutions of Cheng and Minkowycz’s equation reported by Ingham and Brown in 1986, the other is new and has never been reported. Different from the first branch of solutions, the second branch of solutions shows reversed velocity flows. It is found that the difference of skin frictions of the two branches of solutions is rather small, even when the corresponding profiles of velocity are clearly distinct. Thus, from a practical point of view, we need not worry about large variations of the skin friction on the wall when the profile of the velocity changes from one to the other.