Two-dimensional buoyant plume in porous media: higher-order effects

Abstract

The natural convection from a two-dimensional horizontal line source of heat embedded in a porous media has been studied by the method of matched asymptotic expansions at large Rayleigh numbers. The general case of a confined plume emerging from the apex of an insulated symmetric wedge with its axis coinciding with the direction of buoyant force vector is considered for arbitrary values of wedge angles. The first-order problem reduces to the boundary-layer approximation considered earlier by Wooding [ J. Fluid Mech. 15, 527–544 (1963)]. For the second-order boundary layer equations, representing the entrainment effect, a closed-form solution is given and for the third-order equations representing the effects of axial heat conduction and normal pressure gradiant the equations are integrated numerically. The results are displayed graphically and discussed critically.