Simulations of non-Oberbeck–Boussinesq thermal convection in an inclined square cavity

This study presents a detailed comparative analysis of natural convection in an inclined differentially heated square cavity under Non-Oberbeck–Boussinesq (NOB) and OB assumptions at moderate Rayleigh numbers. The simulations are done using the discrete unified gas kinetic Scheme based on a total energy kinetic model, from which the fully compressible Navier–Stokes–Fourier equations are recovered. To investigate the NOB effects in an inclined square cavity, simulations are performed for a range of Rayleigh numbers 106≤Ra≤107 with a fixed temperature difference of ε=0.7 and inclination angles 0°≤θ≤90°. The results show that, with the increase in the inclined angle, the flow undergoes a transition from steady to unsteady and the NOB effect has a significant effect on the overall flow structure, flow instability mechanism, and heat transfer rate. With the inclination of the cavity, the flow pattern evolves from two vortices near the isothermal wall to a single-roll state. The NOB effect accelerates this transition at a lower inclination angle. At Ra=107, the NOB and OB conditions share the same critical inclination angle (θcr=35°±5°) for the transition to the unsteady flow regime. Beyond the critical angle, the fluctuations of the temperature and velocity field exhibit strong symmetry with relatively small fluctuation amplitudes for OB convection. In contrast, under the NOB condition, the flow field manifests asymmetric fluctuations characterized by larger fluctuation amplitudes. Moreover, in NOB scenarios, the local Nusselt number distribution is asymmetric for isothermal walls, and the NOB effect weakens the heat transfer.