Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

• Main Author: Ud Din, Salah
• Format: Thesis
• Language: English; English; English
• Published: 2020
• Subjects: QA Mathematics
• Online Access: http://eprints.uthm.edu.my/35/1/24p%20SALAH%20UD%20DIN.pdf; http://eprints.uthm.edu.my/35/3/SALAH%20UD%20DIN%20COPYRIGHT%20DECLARATION.pdf; http://eprints.uthm.edu.my/35/6/SALAH%20UD%20DIN%20WATERMARK.pdf; http://eprints.uthm.edu.my/35/

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.