Convection in a ferrofluid layer of anisotropic and non-anisotropic porous medium

In this thesis, the stability convection in a ferrofluid layer with the internal heating effect is formulated mathematically. The linear and nonlinear stability analysis opt to the Marangoni-Benard convection and chaotic convection, respectively. Two objectives is discussed on the onset of Marangoni-Benard convection in a fluid layer system as well as an anisotropic saturated porous medium. For the linear stability analysis, the resulting eigenvalues are solved analytically using regular perturbation technique with wave number as a perturbation parameter with the rigid and upper free insulating boundaries. Another two objectives under a chaotic convection also considering two different medium which are fluid layer system and anisotropic porous medium. As for the nonlinear stability analysis, the Galerkin truncation method is used to obtain a Lorenz-like model concerning the lower and upper free isothermal boundary. The impact of internal heating, deformable, magnetic number, temperature­dependent viscosity, variable gravity, an anisotropic parameter with respect to the parameter of interest which are Marangoni number and Rayleigh number, are analyzed and presented graphically. Scrutinizing the effect of internal heating in all cases revealed that the thermal disturbance elevated proportionally making the system become unstable. This is due to a large deviation in the basic temperature distribution that enhances the thermal disturbances in the ferrofluid layer system. Moreover, an increase of magnetic number, magnetic Rayleigh number, Crispation value and temperature-dependent viscosity also will enhance the onset of convection in the system. Meanwhile, the increasing of a bond number will delay the convec­tion. As for the anisotropic porous medium, the result shows that the increment of anisotropic permeability will destabilize the system while the thermal anisotropy and ratio viscosity delay the Marangoni-Benard convection. The behavior of internal heating, magnetic number, anisotropic permeability, ther­mal anisotropy diffusivity and ratio viscosity are studied respected to the modified Rayleigh number. Chaotic convection can be strongly delayed under the influence of increasing thermal anisotropy diffusivity, ratio viscosity and also reducing the value of internal heating, magnetic number and anisotropic permeability.

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