Boundary layer development on a continuous moving surface with a parallel free stream due to impulsive motion

Abstract

The development of the momentum and thermal boundary layers over a semi-infinite flat plate has been studied when the external stream as well as the plate are impulsively moved with constant velocities. At the same time the temperature of the wall is suddenly raised from T_∞, the temperature of the surrounding fluid, to T_w and maintained at this temperature. The problem has been formulated in a new system of scaled coordinates such that for t^∗=0 it reduces to Rayleigh type of equation and for t^∗→∞ it reduces to Blasius or Sakiadis type of equation. A new scale of time has been used which reduces the region of integration from an infinite region to a finite region which reduces the computational time considerably. The governing singular parabolic partial differential equations have been solved numerically using an implicit finite difference scheme. For some particular cases, analytical solutions have been obtained. The results show that there is a smooth transition from Rayleigh solution to Blasius or Sakiadis solution as the dimensionless time ξ increases from zero to one. The shear stress at the wall is negative for the friction parameter λ<0.5, positive for λ>0.5 and zero for λ=0.5. The zero shear stress at the wall does not imply separation but corresponds to the parallel flow. The surface heat transfer is strongly dependent on the Prandtl number Pr and increases with it. Also for Pr<Pr₀, the surface heat transfer is enhanced as the friction parameter λ increases, but for Pr>Pr₀ it get reduced.