Convective plumes in porous media: the effect of asymmetrically placed boundaries

A boundary layer analysis is performed for free convective plume induced by a uniform line source which is placed at the intersection of two semi-infinite planes. Particular emphasis is placed on how the presence of the planes, which are not placed symmetrically with respect to the vertical affects the direction of the plume. To this end, a two-term boundary layer expansion together and a one-term approximation of the flow in the outer regions either side of the plume are performed using the method of matched asymptotic expansions. A closed-form solution is deduced which determines the orientation of the plume in terms of the inclinations of the bounding planes. We find that asymmetrically placed planes result in a vertical plume, but that the plume is aligned differently otherwise.