To determine the response of a convective atmosphere to non-uniform heating, a fully Lagrangian N-body computational scheme (smoothed particle hydrodynamics) is adapted to follow convective motions within the two-dimensional Roche geometry of close binary systems. Fluid motions are computed for two similar problems: first, energy transfer within the common convective envelope of a contact binary with unequal component masses heated asymmetrically at the base, and secondly, irradiation of the secondary star in a cataclysmic variable system. For the contact binary system the circulation patterns generated under the action of the Coriolis force show fluid rising and sinking away from the line of centres, a motion not encountered in previous discussions of circulation. It is suggested that the energy transfer scheme put forward by Robertson may be viable. An asymmetric flow pattern is also produced within the cataclysmic variable system when the Coriolis terms are included in the equations of motion, with the numerical results predicting flow velocities ~1 km s^-1 for a temperature increase of 1000K.