Abstract
The present work introduces a fully resolved three-dimensional thermal Lattice Boltzmann framework developed to investigate the impact of freely moving, finite-size spherical particles on natural convection within a cubic enclosure. The fluid-phase momentum and energy fields are resolved using coupled double-distribution function kinetic approach, while the solid phase is governed by explicitly coupled linear, angular, and thermal conservation equations. To accurately map the moving spherical surfaces onto the Eulerian lattice grid, a second-order linear interpolated bounce-back scheme is implemented. The conjugate heat transfer between the phases is simplified via a lumped capacitance model, assuming negligible internal thermal resistance within the solid spheres. Short-range particle–particle and particle–wall interactions are handled using Glowinski’s repulsive force model. The spatial accuracy of the framework is validated using a circular Taylor–Couette flow benchmark—demonstrating second-order spatial convergence and a differentially heated natural convection in a cubic cavity benchmark, yielding bulk Nusselt numbers within 1% of established literature data. This validated tool is subsequently used to analyze the complex interplay between particulate motion and bulk thermal transport efficiency. Analysis of the temperature fields reveals that the overall thermal structure is governed primarily by the Rayleigh number, while the low particle concentration produces only minor modifications to the convective heat transfer. In contrast, the particle distribution exhibits a strong dependence on the flow intensity.