In most of the systems where heat or mass transfer occur geometrical symmetries are often present. In this paper, we wish to know if the global flux transferred to cylindrical particles in motion (sedimentation, etc.) could be influenced when introducing some geometrical disturbance breaking the general symmetry of the system. To answer this question, we numerically investigate the simple configuration of a single cylindrical particle moving at constant speed between two parallel walls when the particle is off the symmetry plane and when the thermal boundary conditions are of the Dirichlet or Neumann type. When the geometrical disturbance of the system increases, the results show that the backflow that appears in such confined situations yields a non-intuitive evolution of the transfer in convective regimes. In this case a minimum of the flux appears off the symmetry plane. However, in purely diffusive regimes, we find a monotonical evolution of the transfer. (C) 2008 Elsevier Ltd. All rights reserved.