## 1 Introduction
In addition, a sufficient residence time in the high-temperature region is required for complex chemical reactions included in the complicated soot generation path, including gas-phase precursor formation, soot nucleation, soot surface growth, particle coalescence, agglomeration, and soot oxidation [21; 22]. The residence time can vary substantially depending on the flame height, which is affected by the fuel type and flow rate. Specifically, the residence time for soot formation in the buoyancy-controlled coflow flame is dependent on the flame height, which is proportional to QS, where QS is the volumetric flow rate of the fuel gas mixture, and S is the stoichiometric molar oxidizer-to-fuel ratio of the mixture [23; 24]. MLR, which is the mass flow rate of a gaseous substance that has been pyrolyzed in a cone calorimeter, increases with the external heat flux, while the flame height is linearly dependent on the 2/3 power of MLR [13]. The changes in MLR with respect to the external heat flux in a cone calorimeter may change the flame temperature owing to the changes in air entrainment, flame strain rate, and radiation. The residence time may also vary depending on the flame height [25; 26; 27; 28]. Consequently, the amount of soot, as well as the soot properties, can vary significantly depending on the external heat flux. Furthermore, quantitative changes in the soot yield with respect to external heat flux need to be examined sufficiently, considering the nonlinear nature of complicated chemical kinetics and various factors that are related to soot formation. Based on the principle of CO and soot generation, the changes in external heat flux in a cone calorimeter can be predicted to lead to changes in the MLR, flame height, flame temperature, and residence time, with a high possibility of ultimately inducing changes in CO and soot yields. However, the effects of the external heat flux are not sufficiently considered when measuring CO and soot yields in a cone calorimeter, where the measurement values at a specific external heat flux arbitrarily selected by researchers are recognized as unique combustion properties of each combustible [29]. In particular, the constant value of a specific fuel is applied for CO and soot yields, which are required as crucial input parameters in a fire risk analysis based on fire simulations [30]. As a result, a risk analysis based on fire simulations may produce quantitative errors that cannot be neglected. In studies conducted on the effects of the external heat flux on CO and soot yields in a cone calorimeter, [PERSON] [6] reported that the CO yield increases linearly, while no significant changes in CO\({}_{2}\) yield are observed as the external heat flux is increased (within the range of 25-75 kW/m\({}^{2}\)) for PMMA. On the other hand, [PERSON] et al. [31] reported that the CO yield decreases slightly, while the CO\({}_{2}\) yield increases slightly with the external heat flux (within the range of 15-60 kW/m\({}^{2}\)). When the measurement results were inspected in detail, however, the CO yield was 0.008 g/g when the external heat flux was 20 kW/m\({}^{2}\) or below, and the CO yield was constant at 0.006 g/g when the external heat flux was within the range of 25-60 kW/m\({}^{2}\). Despite the identical test methods and conditions such as the application of the cone calorimeter, PMMA, and spark ignition based on ISO 5660-1, the variation trends of the CO yield with respect to the changes in external heat flux differed; unfortunately, the soot yield was not measured in these studies. In a study that examined both CO and soot yields, [PERSON] et al. (2019) reported that CO and soot yields both increase linearly with the external heat flux (within the range of 25-75 kW/m\({}^{2}\)). There are fundamental limitations with respect to gaining a concrete understanding of CO and soot formation based on CO and soot yield measurements using a cone calorimeter.