Effects of novel nonlinear flow channels inspired by classical mathematical function on the output performance and low-grade heat recovery efficiency of thermally regenerative ammonia-based flow battery

In addressing the challenges of enhancing the output performance and low-grade waste heat recovery efficiency of thermally regenerative ammonia-based flow battery (TRAFB), this study introduces four novel nonlinear flow channels: the Hyperbolic tangent function flow channel (HTF-FC), Elliptic function flow channel (EF-FC) Quadratic function flow channel (QF-FC), and Exponential function flow channel (ExF-FC). These flow channel designs are inspired by classical mathematical function curves, enabling more targeted mass transfer enhancement based on species distribution. Multiple quantitative metrics are employed to evaluate the effects of these nonlinear structures on cross-scale mass transfer, reactant distribution, power output, and thermoelectric conversion efficiency under both Forward Flow mode (FF mode) and Reverse Flow mode (RF mode). The findings reveal that optimizing mass transfer at the electrode interface of the channel end is more critical for enhancing performance in TRAFB. The overall performance of the nonlinear flow channels in FF mode is superior to that in RF mode, yet both outperform the conventional straight channel (S-FC), with the ExF-FC showing the best performance and the HTF-FC the least. The ExF-FC exhibits the highest overall mass transfer efficiency and uniformity of active species in the electrode region, and its nonlinear contraction zone at the channel tail induces a significant acceleration effect, increasing the Cu²⁺ flux by ∼39.13 times in the reactant-starved region. When the inlet flow rate is 1 mL/min, the HTF-FC, QF-FC, EF-FC, and ExF-FC can enhance the peak power density by up to ∼1.30 %, ∼11.52 %, ∼54.67 %, and ∼ 80.65 %, respectively, compared to the S-FC, and when the inlet flow rate is increased to 3.8 mL/min, these enhancements reach ∼1.62 %, ∼42.60 %, ∼101.38 %, and ∼ 142.84 %, respectively. Moreover, the nonlinear channels significantly improve the energy storage capacity and waste heat recovery performance of TRAFB, particularly at high current densities. When the current density is 350 A/m², at an inlet flow rate of 1 mL/min, the ExF-FC can enhance the electrical capacity and thermoelectric conversion efficiency by ∼2.81 times and ∼ 5.41 times, respectively, compared to the S-FC, and at an inlet flow rate of 3.8 mL/min, these increases are ∼1.11 times and ∼ 2.98 times, respectively.