This research explores the creeping flow of a Jeffrey fluid through a narrow permeable slit with an application of blood flow through a planer hemodialyzer. The fluid motion of Jeffrey fluid in a two-dimensional conduit with nonhomogeneous boundary conditions due to constant reabsorption on the wall is a complicated problem. The viscous effect of Jeffrey fluid in a cross-sectional area of a narrow slit is computed with the help of continuity and momentum equation. The stress component, velocity profile, stream function, and pressure gradient show the behavior of creeping flow of Jeffrey fluid in a narrow slit. To find the explicit expression of velocity, pressure, stream function, and flux, recursive (Langlois) approach is adopted. Maximum velocity, shear stress, leakage flux, and fractional absorption on the wall are also calculated in this research. The mathematical results of this research are very helpful to study the blood flow through planer hemodialyzer; therefore, this theoretical model has significant importance in the field of renal physiology.