Effect of Rotation on Couple Stress Ferromagnetic Micropolar Fluid Heated from Below in Porous Medium
DOI:
https://doi.org/10.55544/jrasb.4.1.23Keywords:
Convection, Micropolar fluid, Couple stress, Rotation, Porous medium, Ferromagnetic fluid, Linear stabilityAbstract
The linear stability analysis of heat convection in a rotating couple stress ferromagnetic micropolar fluid layer, heated from below and suspended within a porous medium, is the main focus of the current research. The work finds justification in understanding intricate convective processes in systems in which microstructural influence, rotation, magnetism, and porous media interaction occur together—typically occurring in geophysical, industrial, and biomedical processes. A general mathematical model is formulated by combining couple stress theory, Eringen's micropolar fluid theory, and the theory of magnetohydrodynamics. This multi-theory approach encompasses the classical and non-classical behavior of the fluid by incorporating micro-rotational effects, couple stress effects, and the influence of an external magnetic field. The porous medium is treated using Darcy's law, adding the Darcy number to include permeability effects. Rotation is included through the Coriolis force, which is described in terms of the Taylor number, and the magnetic field adds a body force term based on magnetic susceptibility and field direction. Linear stability analysis is performed through the normal mode method, and critical Rayleigh numbers are obtained analytically for different parameter ranges. The calculations show that both couple stresses and rotation effects result in higher critical Rayleigh numbers, meaning a stabilizing effect on the system. Micropolarity further increases this stabilization by opposing fluid motion through internal angular momentum. The magnetic field's function is discovered to be twofold in nature: it may either stabilize or destabilize the system based on its direction and interaction with the heat gradient. The results are useful in the design and optimization of complex fluid behavior systems, with applications in geophysical convection, advanced cooling systems, and processing of smart fluids in material science.
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