Highly Viscous Pipe Flow with Least Entropy Generation under Magnetic Field Effect in Low Stokes Number

Abstract

This study aims to express an optimize temperature profile with the most heat transfer and least work loss by minimizing the total entropy generation of a pipeline under external magnetic field. This study has investigated in low Stokes number and low Reynolds number conditions. It shows that, the fluid’s shear stress increases around the wall (r* > 0.8), due to presence of magnetic field. As a consequence, the magnetic field boosts the dissipation term. However, the velocity gradient over a wide range of radius 0 < r∗ < 0.8 decreases and hence the mean flow velocity increases. Our goal is to use this analysis to manage our magnetic energy better. The entropy generation for fluid flow is minimized in the circular tube with a fix wall temperature under constant magnetic field effect and considering heat dissipation, by applying the calculus of variations. By solving the normalized energy and momentum equations with added source terms due to magnetic field, the real temperature distribution is obtained. Taking the variational of the entropy generation function in the integral form, a nonlinear differential equation with respect to temperature is obtained, which is difficult to be solved analytically. However, series method used to obtain approximate optimize temperature profile.