The nonlinear stability analysis of a ferrofluid layer system is formulated mathematically. This system considered the upper and lower free isothermal boundary with the system heated from below. A mathematical formulation is produced to study the behaviour of the chaotic convection in a ferrofluid layer system using Galerkin truncated expansion. The Boussinesq approximation is opted with the existence of internal heating and the magnetic number. It is found that the transition to chaos in this present study is identical to the Lorenz attractor and thus validate the method and analysis of this study. The impact of elevating the internal heat generation is found to hasten the instability of the system and as for the magnetic number, at M1 = 2.5 the homoclinic bifurcation occurs and thus accelerates the convection process.
A linear stability assessment was performed to study the impact of internal heating and variable gravity in an anisotropic porous medium of a ferrofluid layer system on the onset of Benard-Marangoni convection. The system is heated from below with both the lower and upper limits are considered as completely insulated to the disturbance of the temperature. The eigenvalue problem is solved by using regular perturbation technique to obtain the critical Marangoni number and also the critical thermal Rayleigh number. It is noted that the increase of value anisotropic permeability, Darcy number and also magnetic number will enhance the convection of the system while the increasing values of anisotropic thermal diffusivity will help to stabilize the system.
A linear stability evaluation is conducted to explore the effect on the onset of Marangoni-Bénard convection in a ferrofluid layer system. The system is heated from below with treatment of both the lower and upper boundaries to completely insulate the temperature disturbance. The eigenvalue problem is solved by using regular perturbation technique to obtain the critical number of Marangoni and also the critical number of Rayleigh. It is observed that the increase in the value Crispation, the magnetic number of Rayleigh and also the magnetic number will destabilize the system while the increasing number of Bonds will delay the convection.
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