Hemodialysis is a crucial procedure for removing toxins and waste from the body when kidneys fail to perform this function effectively. This study addresses the need to improve the efficiency and biocompatibility of membranes used in dialyzers. We simulate fluid flow through two types of membranes, Cuprophan (cellulosic) and AN69ST (synthetic), to understand the complex mechanisms involved and quantify key variables such as pressure, concentration, and flow. This study presents a detailed model that applies mass conservation equations and Navier-Stokes principles adapted for porous media, along with heat and mass transfer considerations. The results revealed significant differences in the flow behavior and filtration efficiency between the two membranes, highlighting the superiority of the AN69ST membrane in terms of flow rate and toxin removal. This model serves as a valuable tool for characterizing new porous membranes in dialysis applications, enabling the prediction of the temperature, pressure, and concentration profiles. By providing this information without requiring extensive experimentation, the model complements the design and evaluation of new membranes and, optimizes their development. The ability to predict these profiles is crucial because they directly influence the parameters that determine treatment effectiveness. Moreover, this study underscores the importance of continued innovation in membrane materials and designs, contributing to improved clinical outcomes and treatment efficiency, representing a significant advancement in healthcare.