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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).

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.

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.

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.

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.

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.

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.

The purpose of this paper is to investigate the unsteady flow past through a permeable diamond-shaped cylinder and to study the effects of the aspect ratios and Darcy numbers of the cylinder.

The lattice Boltzmann method with D2Q9 lattice model was used to simulate the unsteady flow through permeable diamond-shaped cylinders. The present numerical method is validated against the available data.

The key findings are that increasing the permeability enhances the suppression of vortex shedding, and that the Strouhal number is directly proportion to the Darcy number, Reynolds number and the aspect ratio of the porous cylinder.

The present study considers unsteady laminar flow past through single permeable diamond-shaped cylinder. According to the authors’ knowledge, very few studies have been found in this field. The present findings are novel and original, which in turn can attract wide attention and citations.