Natural Convection From a Buried Pipe With a Superimposed Fluid Layer Available to Purchase

Heat transfer induced by buoyancy from a pipe buried in a semi-infinite porous medium with a superimposed fluid layer has been numerically examined in this study. Due to the complexity involved, finite difference method along with body-fitted coordinate systems has been employed. The Brinkman-extended Darcy equations are used to model flow in the porous medium while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the fluid and porous layers are the continuity of temperature, heat flux, normal and tangential velocity, shear stress and pressure. A parametric study has been performed to investigate the effects of Rayleigh number, Prandtl number, Darcy number, and fluid layer thickness on the flow patterns and heat transfer rates. The results show that heat transfer increases with the Rayleigh number, but the convective strength decreases with the Darcy number. The heat transfer rate is smaller when the superimposed fluid is air instead of water. For a porous layer with Da ≤ 0.0005 and an overlaying fluid layer thickness of L/r_i ≥ 1, convection is initiated in the fluid layer and it may develop into multiple recirculating cells at a moderate Rayleigh number (i.e., Ra ≤ 10⁴), and may further develop into a single cell at a higher Rayleigh number of 10⁵.