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.