Weakly Non-Linear Stability of Maxwell Fluid in a Porous Layer with the Effect of Magnetic Field
DOI:
https://doi.org/10.12723/mjs.66.10Keywords:
Maxwell fluid, Magnetic effect, Porous media, ConvectionAbstract
The problem of magnetoconvection over a Maxwell fluid due to porous media with the Darcy–Brinkman model via magnetic field is studied. Analytical results of the critical Darcy–Rayleigh numbers at the onset of stationary convection and oscillatory convection are derived. The governing dimensionless equations are tackled through the normal mode
approach, resulting in an eigenvalue problem within the context of linear stability theory. Furthermore, we harness the power of the Galerkin first-order method in MATLAB R2020a to address and resolve this eigenvalue problem. The behaviour of various parameters, like the Q, Λ, Da, and Pm, has been analyzed. The neutral curves are obtained for different prescribed values of the other physical parameters. The Chandrasekhar and Darcy numbers stabilize the system, and the Critical oscillatory Rayleigh number is a non-monotonic function of Pm. In order to study the heat transport by convection, the well-known Ginzburg-Landau equation has been derived using weakly non-linear analysis.
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