Impact of Vertical Magnetic Field on Onset of Instability of a Casson Fluid Saturated Porous Layer: A Nonlinear Theory

S. Suresh Kumar Raju, Fatemah H. H. Al Mukahal, Hasan Mulki and Saleh Mahmoud ()
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S. Suresh Kumar Raju: Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Fatemah H. H. Al Mukahal: Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Hasan Mulki: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
Saleh Mahmoud: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait

Mathematics, 2025, vol. 13, issue 21, 1-12

Abstract: This study examines the stability and instability of a Casson fluid in a horizontal porous medium with magnetic effect using linear and global theories. Both linear and nonlinear analyses are conducted using the normal modes. The study proves that the linear and nonlinear stability thresholds coincide. Two different methodologies were used to solve the system of equations. The eigenvalue problem for linear and global theories were solved using a Galerkin scheme and bvp4c routine in MATLAB. The results show that the Casson parameter destabilizes the flow, while the solutal Rayleigh number and Darcy number stabilize it.

Keywords: nonlinear stability; Casson fluid; porous medium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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