Natural convection in a porous medium saturated with supercritical carbon dioxide (CO 2) which is bounded by square cavity is studied numerically by solving the governing Darcy equation using finite-differences method. The side walls of cavity were assumed to be isotherm with fixed temperature difference of 0.0152 K, while the upper and lower sides are assumed to be thermally insulated, the aspect ratio is chosen to be one, with cavity height of 0.01 m, the Darcy number adopted is 5 10  , usually these values lead to very small modified Rayleigh number. Despite all of this, the state of supercritical takes the fluid (CO 2) to a huge changes in its properties (

This numerical study documents the phenomena of heat transfer by natural convection in thermally non-equilibrium porous cavity for Darcy flow model. The cavity is heated from below at constant temperature   h T with keeping the upper plate isothermal   c T. The side walls were assumed to be thermally insulated. Finite difference 100 1. 0   r K. The non-equilibrium is found to be affected by scaled heat transfer coefficient more than being affected by the thermal conductivity ratio. So It had been noticed that all Nusselt numbers are affected by the thermal conductivity ratio, while the effect of scaled heat transfer coefficient was confined to a solid phase Nusselt number.

Fluid mixtures in real life exist in two forms: miscible and immiscible. Separation of these mixtures using chemical agents or thermal energy has both environmental and economic disadvantages. The high cost and the environmental damage caused by I am extremely grateful to my adviser Dr. Tretheway for his valuable guidance, unparalleled support, and for introducing me to Lattice Boltzmann Method and passive separation. I would like to extend my sincere thanks to Professor Weislogel for his fruitful discussions and practical suggestions that made me indebted to him. I also wish to thank Dr. Recktenwald for his invaluable mentoring about parallel processing programming using the message passing interface. Special thanks to Professor Daescu for serving in my dissertation committee and for inspiring me to expand my knowledge in applied mathematics. My great thanks to the Higher Committee of Education Development in Iraq (HCEDIRAQ) for their support during this long trip. I am deeply indebted to my parents for their priceless care and love during my entire life. Words are not enough to describe my acknowledgement to my beloved family starting from my amazing wife Makarim for providing me with encouragement and patience throughout the duration of the Ph.D study, my kids: Sarah, Anas, and Sama for filling my life with pleasure and happiness.