The present work provides a simulation of control and filtration process of hydromagnetic blood flow with Hall current under the effect of heat source or sink through a vertical conduit (pipe). This work meets other engineering applications, such as nuclear reactors cooled during emergency shutdown, geophysical transport in electrically conducting and heat exchangers at low velocity conditions. The problem is modeled by a system of partial differential equations taking the effect of viscous dissipation, and these equations are simplified and solved analytically as a series solution using the Differential Transformation Method (DTM). The velocities and temperature profiles of the flow are plotted and discussed. Moreover, the conduit wall shear stress and heat flux are deduced and explained.