Entropy generation during the mixed convection process have been studied in a square enclosure for various moving horizontal (cases 1a-1d) or vertical wall(s) (cases 2a-2c) where the bottom wall of the cavity is isothermally hot, side walls are cold, and the top wall is adiabatic. Simulations have been performed for Prandtl number Pr=0.026 and 7.2, Reynolds number Re=10-100, and Grashof number Gr=103-105. Results show that, in the case of the horizontally moving wall(s) (cases 1a-1d), the overall heat transfer rate Nub- and total entropy generation (Stotal) are identical for cases 1a-1d and the cup-mixing temperature (θcup) is high for case 1b at Pr=0.026, Re=100, and Gr=105. Similarly, in the case of the vertically moving wall(s) (cases 2a-2c), Nub- and Stotal are identical for cases 2a-2c with the maximum θcup occurring for the case 2a. At Pr=7.2, Gr=105, and Re=10, case 1a and case 1c are preferable for horizontally moving wall(s) and either of case 2a-2c is preferable for vertically moving wall(s). At Pr=7.2, Gr=105, and Re=100, case 1d may be preferable for the horizontally moving wall(s) and case 2a may be preferable for the vertically moving wall(s). © 2015 Elsevier Ltd.