Semi-Analytical Study of Transient Magnetohydrodynamic (MHD) Axial Flow in a Permeable Annulus

Jibrin Danjuma Yahaya; Raji Muhammed; Agbata Benedict Celestine; Adaji Isaac; Ibrahim Aminu; Abraham Ayegba Alfa; Jacob Funsho Omonile

doi:10.5281/zenodo.21396565

Jibrin Danjuma Yahaya Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Raji Muhammed Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Agbata Benedict Celestine Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Adaji Isaac Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Ibrahim Aminu Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Abraham Ayegba Alfa Department of Computer Science, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Jacob Funsho Omonile Department of Physics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria

DOI: https://doi.org/10.5281/zenodo.21396565

Keywords: Magnetohydrodynamics; porous annulus; transient axial flow; Darcy number; Hartmann number; Laplace transform; Riemann-sum approximation; skin friction; annular flow.

Abstract

This study investigates transient magnetohydrodynamic axial flow of an incompressible, viscous, electrically conducting Newtonian fluid through a porous annulus bounded by two stationary concentric cylinders. The flow is driven by a constant axial pressure gradient and subjected to a uniform transverse magnetic field. Darcy resistance is used to represent porous-medium drag, while the Lorentz-force term accounts for magnetic damping under the low-magnetic-Reynolds-number approximation. The governing momentum equation is non-dimensionalized and solved using the Laplace transform method, with numerical inversion performed by the Riemann-sum approximation. Steady-state expressions for velocity and wall shear stress are also obtained for comparison with the large-time behaviour of the transient solution. The results show that magnetic and porous resistances combine through . Increasing the Hartmann number reduces the axial velocity, while increasing the Darcy number enhances the flow by reducing porous resistance. The transient velocity and skin friction approach their steady-state limits as time increases. The formulation may be useful for idealized studies of hydromagnetic transport in porous annular systems.

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References

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