The flow of an elastico-viscous fluid past an infinite plate with time dependent suction

Abstract

An analysis of a two-dimensional flow of an elastico-viscous fluid past an infinite plate with time-dependant suction is carried out when the free stream velocity is i) constant ii) periodic. By expressing the velocity as a Fourier expansion, consisting of steady mean velocity superimposed by the unsteady part, solutions for coupled equations are derived and the expression for the mean velocity to 0(δ²) and 0(κ) is obtained, where δ is the non-dimensional amplitude of the suction velocity and κ is an elastic parameter. Due to the elastic property of the fluid, it is observed that the value of the mean wall shearing stress is affected by term of 0(δ²), and by the solution obtained when the free stream velocity is 90° out of phase with the suction velocity. Hence with increasing λ, the frequency parameter, the mean wall shearing stress decreases when both the free stream and suction velocity are in phase or directly out of phase, but it increases when the free stream is 90° out of phase with the suction velocity. Also the component arising due to term of 0(δ²) in the expression for the mean wall shearing stress increases with increasing λ.