Multiple solutions of the steady flows in a rectangular channel with slip effect on two equally porous walls

摘要

We study the boundary layer equation f″'(η)+R((f′(η)) ~2-f(η)f″(η)) = K, subjects to the boundary conditions f(0) = f″ (0) = 0, f(1) = 1 and f′ (1) + phisf″ (1) = 0. The given problem arises from the study of steady laminar flows in channels with two equally porous walls, where R relates to the Reynold's number, and K is an integration constant. We are able to obtain the homogeneity property and classify all types of solutions for the prescribed positive slip coef-ficient. In particular, the existence of the continuums in the R - K plane has been verified, and this leads to the existence of multiple solutions for large R.