A Comparative Study of Fluid Flow in Hemodialyzer using Differential Transform Method

Abstract

AbstractIn this paper, a series‐based method called differential transform method (DTM) is used (which is relatively simple and high accurate) for solving the differential equations in biofluid problems. Diffusion equation governed during laminar flow of blood in hemodialysis is solved under the view of this method. The problem formulation of the present paper is modeled under the situation where patients are suffering from renal diseases due to the blockage of semi‐permeable membrane in hemodialysis. The problem is modeled as a half channel model of a hemodialyzer (i.e., artificial kidney) and the wall of inner channel model is a semi‐permeable membrane in which impure blood of the body loses waste products. In other words, it is described by a diffusion equation along with boundary conditions and angular displacement. Eigenvalues is obtained after the simplification of diffusion equation with different Sharewood number, Peclet number, and angular displacement using DTM. A significant impact on the concentration of unwanted materials found in the blood is observed . The obtained results show that the angular displacement is an important parameter that may be treated as an indicator for the purity (in medical terms) of the blood. Moreover, such solutions are illustrated by tables and figures.