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.

目前的数学研究通过考虑具有滑移壁的可渗透缝隙和通过缝隙壁均匀地进行再吸收，讨论了线性Phan Thien Tanner（LPTT）流体的二维缓慢流动。在笛卡尔坐标系中对二维流动情况进行数学建模，结果，使用递归方法分析了非线性PDE以及非均匀边界条件的系统。获得了轴向和径向速度分量以及流函数，压力场，法向应力差和剪切应力的明确表达式，这些表达式在很大程度上取决于伸长率参数，Weissenberg数，滑移参数和孔隙率参数。计算泄漏通量和轴向流量。确定这些点以获得最大速度。还建立了图形分析，发现流体弹性的增加增强了轴向速度的大小，并且由于LPTT流体的延伸特性，轴向速度的分布出现了显着变化。这项理论研究有助于理解描述二维流过可渗透缝的物理现象，这些物理现象在工业和生物科学中具有重要意义。