This study explains the impact of wall reabsorption on the steady movement of an incompressible Newtonian fluid through a permeable channel, considering the renal tubule as a physiological model. Such flow models are relevant to both biological and engineering applications, particularly in modeling filtration and transportation in biological tissues and artificial membranes. The Adomian decomposition method (ADM) is applied to calculate approximate analytical solutions to the non-dimensionalized governing equations under appropriate boundary conditions. The results exhibit that wall reabsorption significantly alters flow behavior-the axial and transverse velocities decrease along the channel length, the mean pressure drop reduces with increasing reabsorption, and the wall shear stress diminishes progressively downstream. Streamline plots further confirm that higher reabsorption weakens the overall flow intensity near the walls. To supplement the analytical results, an artificial neural network (ANN) trained by the Levenberg–Marquardt (LM) algorithm was used to model nonlinear relationships among the flow parameters. The network demonstrated exceptional predictive accuracy, exhibiting a near-perfect correlation between expected and real outputs, hence affirming the model's robust generalization capability. Early stopping was effectively engaged to prevent over-fitting, ensuring optimal model selection. The outcomes from both the ADM and ANN models showed strong consistency, validating the accuracy and robustness of the proposed approach. Overall, the study provides valuable insights into the influence of wall reabsorption on bio-fluid motion and signifies the efficiency of combining ADM with ANN–LM optimization for analyzing and predicting complex flow phenomena in a permeable channel. The methodology and findings can be extended to physiological systems with non-uniform geometries, such as real tubules and biomedical filtration devices.
Venkateshwarlu et al. (Thu,) studied this question.