Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative magnetic field and thermal radiation effects
Yakubu D.G. Abdulhameed M. Tahiru A.G. Roslan R. Issakhov A. Rahimi-Gorji M. Bakouri M.
October 2021SAGE Publications Ltd
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering
2021#235Issue 51618 - 1627 pp.
We consider the unsteady flow of Burger fluid within a circular cylindrical tube, driven by a time-dependent pressure gradient, a body acceleration and a magnetic field acting normal to the flow direction. The solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow through arterial walls were obtained via the Laplace transform and the finite Hankel transform. The effects of magnetic field on parameters such as blood temperature and velocity were studied by Caputo time-fractional derivatives. We note that the solutions of many particular models such as fractional Oldroyd-B fluid, fractional Maxwell fluid, fractional second grade fluid and fractional Newtonian fluid models can be recovered from the solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow by particularizing the material coefficients (i.e. special and limiting cases of the earlier Burger’s fluid model). The numerical computations have been carried out to analyze the effects of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R0 and material parameter λ2 on the blood velocity and temperature. Some interesting flow and temperature characteristics are presented graphically and discussed. The study reveals that blood velocity, temperature and fractional parameters are reduced in the presence of magnetic field. The importance of this study can be found in the application fields of magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering, medicine, etc.
Cylindrical blood vessel , fractional relaxation time derivative , fractional retardation time derivative , magnetic heat source , thermal radiations
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Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria
School of Science and Technology, The Federal Polytechnic Bauchi, Bauchi, Nigeria
Department of Mathematical Sciences, Bauchi State University, Bauchi, Nigeria
Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Malaysia
Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematical and Computer Modelling, Kazakh-British Technical University, Almaty, Kazakhstan
Faculty of Medicine and Health Sciences, Ghent University, Ghent, Belgium
Department of Medical Equipment Technology, College of Applied Medical Science, Majmaah University, Majmaah, Majmaah City, Saudi Arabia
Department of Physics, College of Arts, Fezzan University, Traghen, Libya
Department of Mathematical Sciences
School of Science and Technology
Department of Mathematical Sciences
Faculty of Applied Sciences and Technology
Department of Mathematical and Computer Modelling
Department of Mathematical and Computer Modelling
Faculty of Medicine and Health Sciences
Department of Medical Equipment Technology
Department of Physics
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