The effects of classical and irregular streaming motion on convective heat transfer in air-filled shallow enclosures carrying a standing sound wave are investigated. The fluid motion is driven by the periodic vibration of the enclosure left wall. The vertical walls of the enclosure are adiabatic while the horizontal walls are heated differentially. The fully compressible form of the Navier-Stokes equations are considered to compute the oscillatory and mean flow fields. A control-volume method based, explicit time-marching Flux-Corrected Transport (FCT) Algorithm is used to simulate the transport phenomena in the enclosure. The simulation results of a test case for an unheated enclosure are compared with the existing literature for code validation. Transverse temperature gradient strongly affects the acoustic streaming structures and velocities. The streaming motion significantly enhances overall heat transfer from the bottom wall compared to pure conduction. Enhancement is more pronounced in the presence of irregular streaming. (C) 2010 Elsevier Ltd. All rights reserved.