Unsteady Generalized Couette Flow in a Horizontal Channel with Sudden Application or Removal of a Porous Material

Abstract

The role of sudden application or removal of a porous material on generalized Couette flow in a horizontal channel is carried out. The governing momentum equation is obtained and solved with the necessary initial and boundary conditions. The well-known Laplace transform technique is employed to transform the PDEs into ODEs and then solved exactly in the Laplace domain. A numerical approximation based on the Riemann-sum is employed to transform the solutions obtained from the Laplace domain to the time domain. Based on the simulated results, it is found that the time taken to attain steady-state skin-friction and volumetric flow rate is strictly affected by the sudden application/withdrawal of porous medium. Also, despite the sudden application/withdrawal of porous medium, the velocities, skin-friction and volumetric flow-rates still attain steady state values.