The College of Education for Pure Sciences, Department of Mathematics, University of Basra, discussed a doctoral thesis on the analysis of linear instability and non-linear stability of convection in mediums of dual porosity and Poiseuille flow
The thesis that was managed by the researcher (Alaa Jabbar Biday) included
This thesis consists of three main parts. In the first part, the stability and instability of saturated fluids for a bi-porous medium is studied and in three issues, namely: the effect of the chemical reaction on the load in a bi-porous medium, the effects of the chemical reaction and the magnetic field on the diffuse double load in a medium. Dual porosity, dual diffusion convection in bi-porous media with cycling effect and general type boundary conditions for both heat and concentration equations.
In the second part, three models of double diffusion convection of saturated fluid in porous media are analyzed. It was assumed that the concentrations of solute in the fluid have a linear relationship with respect to temperature in three models. In the first model, we studied the stability of the Darcy model of double diffusion convection in a bi-porous medium with chemical reaction. In the second embodiment, the issue of double-diffusion load in a Brinkman porous medium with chemical reaction and slip boundary conditions is adopted. At the end of this section, the issue of double-diffusion load in a bi-porous medium is studied with Brinkman's model for micro-media and Darcy's model for micro-media, where the effects of chemical reaction and slip boundary conditions in relatively large pores are investigated.
In the third part, the issue of flow called Poiseuille in a porous medium with slip boundary conditions is studied in two issues. In the first issue, the effect of uniform vertical flow on the stability of flow in a channel with a porous medium saturated with a Newtonian fluid was investigated and the Brinkman model was adopted. Moreover, in the second issue, the linear instability of pressure-driven flow in a porous and saturated material channel is studied using the Brinkman model also, with the presence of the effects of the uniform magnetic field and the conditions of the slip boundary

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