Fluid Model using Recursive approach: Application to Permeable Slit with Uniform Reabsorption and Velocity Slip

Abstract The present mathematical study discussed the two-dimensional slow flow of linear Phan Thien Tanner (LPTT) fluid by taking into account the permeable slit with slippage walls and reabsorption undergoes uniformly through slit walls. Mathematical modeling of the two-dimensional flow situation is carried out in Cartesian coordinates and as result, a system of nonlinear PDEs along with nonhomogeneous boundary conditions are solved analytically using the recursive approach. The explicit expressions for velocity components in axial and radial directions along with stream function, pressure fields, normal stresses difference, and shear stress are obtained which are strongly dependent on the elongation parameter, Weissenberg number, slip parameter, and porosity parameter. The leakage flux and axial flow rate are calculated. The points are identified for maximum velocity. Graphical analysis is also established and found that an increment in the fluid elasticity enhances the magnitude of axial velocity and a significant change is noticed in the profile of axial velocity due to the extensional characteristic of the LPTT fluid. This theoretical study helps to understand the physical phenomena that describe the 2-dimensional flow through the permeable slit and have significant importance in industry and biosciences.