In this paper, a numerical Harlow–Welch MAC (Marker and Cell) method is developed to investigate the unsteady free convection in lid-driven square cavity. The constant heat flux is considered over left wall and remaining walls are kept thermally insulated. The structure of thermal convection patterns analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermo-physical parameters, Reynolds number (Re), thermal Grashof number (Gr) Prandtl number (Pr) and Peclét number (Pe = PrRe), on these distributions are described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore, the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies. © 2018, Springer (India) Private Ltd., part of Springer Nature.