Effect of thermal radiation on non-darcy natural convection from a vertical cylinder embedded in a nanofluid porous media

The objective of the present work is to investigate theoretically the effects of thermal radiation and the nonlinear Forchheimer terms on boundary-layer flow and heat transfer by non-Darcy natural convection from a vertical cylinder embedded in a porous medium saturated with nanofluids. A model is developed to analyze the behavior of nanofluids taking into account the solid volume fraction parameter. The cylinder surface is maintained at a constant temperature and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved numerically by an efficient implicit finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature profiles, and the local Nusselt number is illustrated graphically to show interesting features of the solutions.