Analytical Study of Viscous Fluid Movement in a Rectangular Pipe using Diffusion Magnetic Resonance Equation

Abstract

Silicene, a two-dimensional material analogous to graphene, has garnered Diffusion Magnetic Resonance Imaging (DMRI) equation is used in this research work to examine the flow of fluid in a rectangular. Having previously considered flow in cylindrical and spherical coordinates, this study explores the rectangular channel of a three dimensional - (3D) flow using DMRI equation evolved and solved analytically using the method of separation of variables (MSV) with appropriate boundary conditions applied. Relaxation times of three viscous fluids were used - crude oil, oil wax and black oil in the simulation and the values of magnetization registered by each fluid recorded. The results obtained showed that oil wax has the highest value of magnetization followed by crude oil and then black oil. The study underscores the multivarious ways diffusion MRI can be applied and its use in the analysis of flow of viscous fluid through different geometrical channels.