This thesis investigates analytically the magnetohydrodynamics (MHD) transport of
Newtonian and non-Newtonian fluids flows inside a circular channel. The flow
was subjected to an external electric field for the Newtonian model and a uniform
transverse magnetic field for all models. Pressure gradient or oscillating boundary
condition was employed to drive the flow. In the first model Newtonian fluid flow
without stenotic porous tube was considered and in the second model stenotic porous
tube was taken into account. The third model is concerned with the temperature
distribution and Nusselt number. The fourth model investigates the non-Newtonian
second grade fluid velocity affected by the heat distribution and oscillating walls. Last
model study the velocity, acceleration and flow rate of third grade non-Newtonian
fluid flow in the porous tube. The non-linear governing equations were solved
using the Caputo-Fabrizio time fractional order model without singular kernel. The
analytical solutions were obtained using Laplace transform, finite Hankel transforms
and Robotnov and Hartley’s functions. The velocity profiles obtained from various
physiological parameters were graphically analyzed using Mathematica. Results were
compared with those reported in the previous studies and good agreement were found.
Fractional derivative and electric field are in direct relation whereas magnetic field and
porosity are in inverse relation with respect to the velocity profile in Newtonian flow
case. Meanwhile, fractional derivative and Womersely number are in direct relation
whereas magnetic field, third grade parameter, frequency ratio and porosity are in
inverse relation in third grade non-Newtonian flow case. In the case of second grade
fluid, Prandtl number, fractional derivative and Grashof number are in direct relation
whereas second grade parameter and magnetic field are in inverse relation. The fluid
flow model can be regulated by applying a sufficiently strong magnetic field
