Wang, Jiahao; Zanoni, Marco AB; Rashwan, Tarek L; Torero, José L; Gerhard, Jason I; (2026) Approximating local thermal non-equilibrium in water-sand-gas phases within wet smoldering processes via a two-energy equation model. International Journal of Heat and Mass Transfer , 255 (Part 1) , Article 127723. 10.1016/j.ijheatmasstransfer.2025.127723.

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Abstract

Smoldering combustion offers a robust solution for treating high-moisture porous materials, but accurately modeling the heat transfer processes, especially during intense water phase changes, remains challenging due to local thermal non-equilibrium (LTNE) among water, sand, and gas phases. Traditional two-energy equations often assume local thermal equilibrium (LTE), which fails to capture the rapid and spatially variable heat transfer dynamics in wet smoldering environments. This study introduces a novel approach to approximate LTNE by redefining the thermal coefficient (γ) in two-energy equation models. Experimental data from four wet smoldering tests were used to calibrate and validate γ values under different conditions. The results demonstrate that γ varies systematically with the rate of water phase change, and a new correlation γ = 1.83m˙ w ʹʹʹ +1 (m˙ w ʹʹʹ is in kg m-3 s -1, 0< γ ≤ 5) is proposed. This approach eliminates the need for explicit modeling of interfacial areas or heat transfer coefficients. Simulations using the revised γ captured both evaporation and condensation fronts, improved smoldering propagation predictions, and closely matched experimental temperature profiles. Results show that LTNE effects are most pronounced during rapid phase change, where LTE-based models significantly underestimate heat transfer. The proposed method enhances the predictive capability of smoldering models and may be extended to other high-moisture thermal systems such as those for remediation, drying, and energy recovery.

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