Purpose The purpose of this paper is to propose an effective numerical approach for solving the natural convection in a two-dimensional square enclosure by using the single relaxation time-Bhatnagar, Gross and Krook (SRT-BGK) model (D2Q9) and lattice Boltzmann method (LBM). Design/methodology/approach Navier–Stroke equation is replaced by lattice Boltzmann method, and the numerical approach was simulated using LBM. LBM is a linear equation so, it reduces the computational time. The governing equations are solved using the SRT-BGK model. To achieve better numerical stability and accuracy, the momentum and energy equations are solved using two-dimensional nine-directional (D2Q9) lattice arrangement. Findings The results are presented at different convection mechanism with constant Prandtl number = 0.71, and the result is validated with reported literature. Numerical investigation is performed and accurate results are obtained; the range of Pr = 0.71, various Rayleigh number, phase change, periodicity parameter and amplitude ratio with three different blockage ratios. The present study is performed using LBM. Research limitations/implications To extend this work, the influence of natural convection, various selections of Prandtl number and Rayleigh number, periodicity and the effect of aspect ratio with mounted number of blockages could be included. Practical implications This research article will be useful for the study of fluid flow and heat transfer in hot and cold fluid interaction over the solid object. Like gear hardening with various sizes of gear blocks, material processing with hot and cold fluid interactions inside the furnace wall, solar panels high and low density fluid variation, indoor hot and cold fluid thermal environments, inside nuclear reactors heat and heavy water fluid interaction, cooling of electronic equipments and various chemical engineering applications. Social implications This paper will be useful for studying fluid flow and heat transfer within a square enclosure, and it gives practical information in engineering and heat transfer applications. Originality/value The present work is the first to investigate using LBM for selected parameters to apply a natural convection with imposed sinusoidal wave for different convection mechanisms.