Finite Integral Transform Based Solution of Second Grade Fluid Flow between Two Parallel Plates

The importance of the slip flow over the no-slip condition is widely accepted in microscopic scaled domains with the direct impact on microfluidic and nanofluidic systems. The popular Navier Stoke’s (N-S) flow model is largely utilized with the slip flow phenomenon. In the present study, the finite integral transform scheme along with the shift of variables is implemented to solve the equation of motion of second grade fluid having third-order mixed partial derivative term. The velocity over the flow regime is studied with both the slip and no-slip boundary conditions for Newtonian and non-Newtonian characteristics by considering the generalized Couette flow. The impact of the pressure gradient and flow time on the velocity is investigated analytically. The output of the present research reveals that due to the slip flow velocity randomly varies at the vicinity of wall surface and such nature hasn’t been found for the no-slip condition. The validation of the present work was done by comparison with the published work and the numerical values, and it shows well verified.

Keywords:

Second grade fluid , Exact solution , Couette flow , Slip condition , Non-Newtonian fluid