Non-Darcy Natural Convection Heat Transfer Along a Vertical Cylinder Filled by a Porous Media with Variable Porosity.

Theoretical and numerical study of the phenomenon of natural convection in a cylindrical enclosure filled by a non-Darcy porous media and saturated by a Newtonian fluid. The porosity of the media considered is variable and approximated by an exponential function based on an empirical law and equal to the unity near the walls due to the effects of the walls. The hydrodynamic flow in the porous medium is governed by Forchheimer-Brinkman extension of Darcy model (EBFD) with non-uniform porosity. The dimensionless equations reveal some important dimensionless numbers controlling this phenomenon such as the thermal Rayleigh number, Ra, the number of Darcy, Da, the number of Prandtl, Pr, the aspect ratio, RA, and the porosity, ε. The results are discussed graphically. The heat exchange traduced by Nusselt number is also considered in the study. The results obtained under the limiting conditions were found to be in good agreement with the existing ones. The established numerical code can also be used in various other industrial applications. [ABSTRACT FROM AUTHOR]