Galerkin finite element analysis of Darcy–Brinkman–Forchheimer natural convective flow in conical annular enclosure with discrete heat sources

Abstract

This numerical study is intended for the analysis of thermal convection induced by buoyancy forces generated within a conical annular porous gap. The annulus was vertically positioned, it contains a discrete heat source and is filled with a Single-Walled Carbon Nanotubes-Water (SWCNT-H2O) nanoliquid exposed to a Lorentz force. To describe the porous medium in question, we have adopted the Darcy–Forchheimer model. Galerkin Finite Element Method (GFEM) has been used in this study to predict both thermal and hydrodynamic fields in the physical model. An extensive range of parameters are explored, i.e., the Rayleigh number (103 to 106), Hartman number Ha (1 to 100), and the volume fraction of nanoparticles (0 ≤ϕ≤0.08). For the purpose of exterminating the effects of heat source location on thermal and hydrodynamic fields, three locations (bottom, middle and upper) have been considered. Findings include current lines, isotherms, and Nusselt number evolution according to the previously stated variables. Predictably, our findings prove that heat transfer rate exhibits a decreasing function of Ha and an increasing function of Da and ϕ. Also, it was revealed that the convective regime is preponderant when the heat source was located in the bottom wall.

Keywords

• Conical annular space
• Natural convection
• Discrete heating source
• Porous medium
• Magnetic field
• Galerkin finite element technique