This article illustrates the fundamental features of lateral penetration of natural convection into a horizontal porous layer in lateral communication with a heat reservoir. It is found that the important group governing the fluid mechanics of the phenomenon is the Darcy-modified Rayleigh number Ra based on longitudinal (horizontal) permeability and on transversal (vertical) thermal diffusivity. It is shown that the buoyancy-driven flow has flattened C-shaped streamlines and isotherms. The flow penetrates laterally to a distance of order H Ra1/2, where H is the height of the porous layer. The net heat exchange between the porous structure and the lateral heat reservoir is described by a Nusselt number result of the type Nu ∼ Ra1/2. The effect of horizontal wall temperature gradient on penetration length and heat transfer is discussed. The engineering importance of these findings is illustrated by examples related to the conceptual design of porous winding structures for rotating superconducting electric machines.