The Brinkman model for the mixed convection boundary layer flow past a horizontal circular cylinder in a porous medium

Abstract

The Brinkman model is used for the theoretical study of the mixed convection boundary layer flow past a horizontal circular cylinder with a constant surface temperature and embedded in a fluid-saturated porous medium in a stream flowing vertically upwards. Both the cases of a heated (assisting flow) and a cooled (opposing flow) cylinder are considered. It is shown that there are two governing dimensionless parameters, which are related to thermal and viscous effects. These are the Darcy–Brinkman parameter Γ and the mixed convection parameter λ. It is shown that for Γ=0 the problem reduces to the similarity Darcy’s model, while for Γ≠0 the governing equations are non-similar and they have been solved numerically using the Keller-box method. It is found that heating the cylinder ( λ>0) delays separation of the boundary layer and can, if the cylinder is warm enough (large values of λ>0), suppress it completely. On the other hand, cooling the cylinder ( λ<0) brings the boundary layer separation point nearer to the lower stagnation point and for sufficiently cold cylinder (large values of λ<0) there will not be a boundary layer on the cylinder. A complete physical description of the problem is presented throughout the analysis. Some results were given in the form of tables. Such tables are very important and they can serve as a reference against which other exact or approximate solutions can be compared in the future.