In this paper, a numerical investigation is performed to study the heat transfer characteristics and the mixed convective flow past a square cylinder oscillating at different inclinations. The computations are carried out for a fluid with a Prandlt number of 0.7 at low Reynolds number ranging from 40 to 220. The tilt angle is varied from 0 (inline oscillation) to pi/2 (transverse oscillation). The governing equations were solved using a finite-volume technique. The validity of the simulations is established by comparison with the available data from literature. The flow and heat transfer features are analyzed for different angles of oscillations. A critical oscillation angle at which the flow structure changes from inline oscillation mode to transverse oscillation mode has been determined. The effects of blockage ratio (beta = h/H, the ratio between the side length of the cylinder and the height of the channel), Reynolds number Re, oscillating amplitude A(m) and oscillating frequency F-c on the heat transfer characteristics are examined. The results show that the heat transfer is enhanced remarkably, when these parameters are increased. Furthermore, the rate of heat transfer from the cylinder increases when the angle of oscillation tends to pi/2. For engineering applications, appropriate correlations have been proposed between the average Nusselt number and the different parameters. Finally, the interest of using the inclined oscillation is discussed. This approach has the advantage of widening the range of the oscillation amplitude. The results show that the heat transfer rate has been at least doubled. (C) 2018 Elsevier Ltd. All rights reserved.