In order to investigate the dispersion of small particles in a turbulent shear flow, a new model based on accurate modelling of the directional dependence of the fluid Lagrangian time scales is proposed and tested against experimental data in a gas–solid channel flow. The continuum phase is described by a nonlinearlow-Reynolds k-ϵ model, thus allowing a fine description of turbulence anisotropy and near-wall effects. The dispersed phase is described by a Lagrangian stochastic method, which is formulated in order to take into account the nonhomogeneity and the anisotropy of turbulence. The fluid Lagrangian time scales in each direction are assessed following a recent proposal supported by channel flow DNS computations. The integral time scales of the fluid seen by the particles are then estimated in taking the inertia and crossing trajectory effects into account. The numerical predictions (particle and fluid statistical quantities) obtained by means of this time scale model and previously available time scale models are compared and confronted to recent experimental data from the literature about the motion of small solid particles in a turbulent vertical channel flow. It is shown that the new Lagrangian time scale formulation leads to very satisfactory results compared to the measurements.

This study presents a comprehensive 3D numerical analysis of thermal stratification, fluid dynamics, and heat transfer efficiency across six hot water storage tank configurations, identified as Tank-1 through Tank-6. The objective is to determine the most effective design for achieving uniform temperature distribution, stable stratification, and efficient heat retention in sensible heat storage systems, with potential for integration with phase change materials (PCMs). Using COMSOL Multiphysics 5.6, simulations were conducted to evaluate key performance indicators, including the Richardson number, capacity ratio, and exergy efficiency. Among the tanks, Tank-1 demonstrated the highest efficiency, with a capacity ratio of 84.6% and an exergy efficiency of 72.5%, while Tank-3, which achieved a capacity ratio of 70.2% and exergy efficiency of 50.5%, was identified as the most practical for real-world applications due to its balanced heat distribution and feasibility for PCM integration. Calculated dimensionless numbers (Reynolds number: 635, Prandtl number: 4.5, and Peclet number: 2858) indicated laminar flow and dominant convective heat transfer across all the configurations. These findings provide valuable insights into the design of efficient thermal storage systems, with Tank-3’s configuration offering a practical balance of thermal performance and operational feasibility. Future work will explore the inclusion of PCM containers within Tank-3, as well as applications for heat pump and solar water heaters, and high-temperature heat storage with various working fluids.