## 1 Introduction  
Reaction-to-fire (flammability), which indicates how combustibles respond to fire or heating, is often considered for quantitatively evaluating fire risks and hazards through various fire test standards, in addition to fire endurance (or resistance) [1]. In particular, cone calorimeters that are based on ISO 5660-1 [2] and ASTM E1354 [3] are commonly used for assessing the flame-retardant nature of solid combustibles in an open space, and for measuring combustion properties; further, they have been recognized as the most critical bench-scale apparatus in the fire safety field [4, 5]. Specifically, simulated fire environments can be embodied by controlling the incident radiant heat flux on the surface of a solid combustible using a cone calorimeter. The ignition time, mass loss rate (MLR), heat release rate (HRR), effective heat of combustion (EHC), and combustion products, including toxic gases and smoke, can also be measured [6]. These data are used to evaluate the various fire risk factors such as the pyrolysis, flammability, and fire spread rate of solid combustibles. Clearly, caution is needed when directly associating the results of a bench-scale cone calorimeter experiment conducted using a specimen of limited size (10 mm square) with the complicated fire behaviors in full-scale models [1, 7, 8]. However, the experimental results of a cone calorimeter can be useful in understanding thermal and chemical characteristics per unit area of combustibles in the thermal environment of a controlled fire. Furthermore, information on various physical input parameters is provided to enable the numerical prediction of the risk of a full-scale fire. Numerous reports on the cone calorimeter apparatus, test data, and engineering applications are systematically explained in Ref. [9]. The effective heat flux on the specimen surface of a cone calorimeter can be determined by the thermal balance of the irradiance (external heat flux), flame heat flux, and re-radiated heat flux. Among these heat fluxes, the external heat flux supplied by a cone heater is the most fundamental and important control variable in a cone calorimeter. In general, an external heat flux value below 20 kW/m\({}^{2}\) is applied to examine the ignition and flammability, and a range of 25-30 kW/m\({}^{2}\) may be applied for the fire spread. In addition, a higher external heat flux of 50 kW/m\({}^{2}\) is applied to discuss compartment fires after flashover, as well as to measure combustion properties. In practice, an external heat flux of 35 or 50 kW/m\({}^{2}\), which has a higher reproducibility of measurement results, has commonly been applied in previous studies [10; 11]. Considering the degree to which the thermal conditions of combustible surfaces in compartment fires have a quantitatively very large scale or vary significantly over time, applications of an appropriate external heat flux should be examined, which accurately correspond to each of the fire growth stages of ignition (incipient)-growth-fully developed-decay or the considered fire scenario. In studies that examined the effects of external heat flux on pyrolysis and the fire behaviors of solid combustibles, [PERSON] et al. [12] verified that the transformed ignition time \(\left(1/t_{ig}\right)^{0.55}\) or \(1/t_{ig}\) linearly increases, and this was considered to identify thermally thick or thermally thin materials with respect to the changes in external heat flux for commercial flame retardant materials within the range of 20-60 kW/m\({}^{2}\). Moreover, the peak and average MLR, as well as the HRR, all increased linearly with respect to the heat flux. On the contrary, the thermal thickness, which indicates the thermal penetration depth of the material at ignition, decreased with heat flux. [PERSON] et al. [13] confirmed that the MLR increases linearly with respect to the external heat flux for polymethyl methacrylate (PMMA) flames, and that the flame height is linearly dependent on the 2/3 power of MLR. [PERSON] et al.