## 3 Results and Discussions
### Non-Monotonicity in Radiation-Induced Thermal Runaway  
It should be noted that although Cell 2 receives radiation heat flux from Cell 1, it also emits radiation to the ambient. Therefore, at a certain state, the net radiation heat flux may become zero, even before thermal runaway occurs. In this scenario, the net radiation heat flux on Cell 2 can actually be negative, which may counteract the occurrence of thermal runaway. Figure 8 shows the evolution of net radiation heat flux q over the surface of Cell 2. It can be seen that for cases with T\({}_{1}\) = 602 K, q transitions to a negative value much earlier than the onset of thermal runaway, defined as the instant with maximum temperature rise rate. Therefore, in this case, radiation facilitates thermal runaway in the early stage before net radiation flux vanishes, and it actually mitigates thermal runaway in the later stage when net radiation flux becomes negative. With elevated temperature--when T\({}_{1}\) reaches close to 650 K--the cross-over state of q occurs very close to the onset of thermal runaway, indicating the constant promotion effects of radiation during thermal runaway at higher triggering temperatures.  
Figure 8: Evolution of net radiation heat flux q during thermal runaway with different T\({}_{1}\). Solid line is for net radiation heat flux over Cell 2 surface, dash dot is for the max temperature of Cell 2, green dash indicates the crossover of radiation heat flux.  
Figure 7: Evolution of average dimensionless concentration and temperature with thermal runaway triggering temperature of T\({}_{1}\) = 900 K.  
To further characterize the role of radiative heat transfer at different triggering temperatures, a time-integrated radiative heat flux is calculated by integrating the net radiation flux \(q\) over the surface of Cell 2 from the initial condition to the instant of when the net radiation heat flux in Cell 2 vanishes. This provides a basis to evaluate the maximum facilitation effect of radiation on the triggering of thermal runaway. Interestingly, as shown in Figure 9, the time-integrated radiative heat flux as so defined exhibits a counter-intuitive non-monotonic dependence on temperature. On the high temperature branch, the integrated radiative heat flux decreases with increase in the triggering temperature, as expected. However, the peak-integrated radiative heat flux does not occur at the lowest temperature, as one might expect. Instead, it occurs at an intermediate temperature, around 700 K in this case. One possible explanation of such a non-monotonic trend may be offered by considering the time duration for the integral: higher triggering temperature T\({}_{1}\) leads to higher radiative heat flux, which nevertheless leads to a much shorter time scale to cancel out net radiation flux \(q\). On the other hand, lower triggering temperature T\({}_{1}\) leads to lower radiative heat flux which, however, elongates the time scale to cancel out net radiation. This nevertheless only partially explains the role of radiation with varying triggering temperature, in that heat release from the exothermic thermal runaway reactions will also facilitate the temperature increment. With longer thermal runaway delay time at low temperatures, it allows longer residence time for the chemical reaction progress and heat release to accumulate internally within the cell.