Dual Solutions in Unsteady Stagnation-Point Flow over a Shrinking Sheet

Abstract

An analysis is made to study the dual nature of solution of unsteady stagnation-point flow due to a shrinking sheet. Using similarity transformations, the governing boundary layer equations are transformed into the self-similar nonlinear ordinary differential equations. The transformed equations are solved numerically using a very efficient shooting method. The study reveals the conditions of existence, uniqueness and non-existence of unsteady similarity solution. The dual solutions for velocity distribution exist for certain values of velocity ratio parameter (c/a), and the increment in the unsteadiness parameter A increases the range of c/a where solution exists. Also, with increasing A, the skin friction coefficient increases for the first solution and decreases for the second.