In this study, a sophisticated three-dimensional computational model was developed to investigate the kinetic and thermal characteristics of a bi-model slurry. This model utilized the Eulerian–Eulerian Re-Normalization Group k–ε turbulence approach in conjunction with the kinetic theory of granular flow. The slurry, composed of different combinations of silica sand and fly ash, was transported through a straight pipeline under varying Prandtl numbers. Five different mixture combinations were considered, ranging from 65% silica sand and 35% fly ash to 100% silica sand. The slurry was transported using four different Prandtl fluids with varying temperatures. The pipe wall was maintained at a constant temperature of 400 K. The computational results yielded significant findings. A mixture with a higher proportion of fly ash (65:35) exhibited superior flow characteristics when combined with a low-viscosity Prandtl fluid (Pr = 2.88), resulting in a minimal pressure gradient and specific energy consumption. Enhanced energy efficiency was observed at lower Reynolds numbers and reduced efflux concentrations. Additionally, the 95:05 mixture demonstrated the highest heat transfer coefficient, with further improvements as flow Reynolds numbers and efflux concentrations increased. These results provide valuable insight into optimizing the transportation of bi-model slurries for various industrial applications, emphasizing the importance of composition and Prandtl numbers.

The study establishes two mathematical formulations to predict the pressure drop in a solid–liquid slurry flowing through a straight pipe. Employing the Eulerian–Eulerian RNG k-ε model, the computational investigation uses water as the carrier fluid and glass beads as solid particles. The analysis spans various particle sizes (d₅₀ = 75–175 μm), volumetric concentrations (C_vf = 10–50%), and velocities (V_m = 1–5 m/s). The first model, developed using the MATLAB curve-fitting tool, is complemented by a second empirical equation derived through non-polynomial mathematical formulation. Results from both models are validated against existing experimental and computational data, demonstrating accurate predictions for d₅₀ = 75–175 µm particles within a Reynolds number range of 20,000 ≤ Re ≤ 320,000.