Combined convective heat transfer from a horizontal cylinder in a porous medium to a vertical flow

摘要

The flow over a circular cylinder embedded with its axis in a horizontal plane in a saturated porous medium has been considered. There is a vertical forced flow over the cylinder, this flow being uniform across a horizontal surface which is relatively close to the cylinder. There is also a vertical impermeable surface near the cylinder, this surface being adiabatic. The cylinder is assumed to be kept at a uniform temperature, which is either lower or higher than the temperature of the flowing fluid. The conditions considered are such that the buoyancy forces resulting from the temperature differences have an effect on the flow and consequently on the heat transfer rate from the cylinder despite the presence of the forced velocity, i.e. mixed- or combined convection has been considered. The study is based on the Darcy type assumptions with the buoyancy terms being treated using the Boussinesq approximation. The flow has been assumed to be steady and two-dimensional. The governing equations, written in dimensionless form, have been solved using the finite element method. THe solution has as parameters the dimensionless distance, W, of the cylinder from the horizontal surface, the dimensionless distance, H, of the cylinder from the vertical impermeable surface, the Peclet number Pe, a buoyancy parameter, B, and depends on whether the buoyancy forces act in the same or in the opposite direction to the direction of the forced flow (i.e. on whether there is assisting or opposing flow). Results have been obtained for a range of values of the parameters for both assisting and opposing flows. The results of the present study have been used to deduce the conditions under which the buoyancy force effects can be neglected and to derive equations that can be used to calculate heat transfer rates for the flow situation considered. The results indicate that the distance of the cylinder from the surface only has an effect on the heat transfer rate from the cylinder when the cylinder is very close to the surface or when the Peclet number is low.