Heat flow between the particle and the environment due to convection and radiation.

$$T_{env} = \begin{cases} T_{init} + t \left( \frac{T_{fin} - T_{init}}{\Delta t_{heat}} \right) &t \le \Delta t_{heat} \\\ T_{fin} &t > \Delta t_{heat} \end{cases}$$ $$S = \pi R_{p}^{2}$$ $$\dot{Q}_{conv} = h S \left( T_{env} - T_{p} \right)$$ $$\dot{Q}_{rad} = \varepsilon S \left( T_{env}^{4} - T_{p}^{4} \right)$$ $$\dot{Q}_{p} = k \left( \dot{Q}_{conv} + \dot{Q}_{rad} \right)$$

Integration of heat is done as:

$$T_{p} = T_{p} + \frac{\dot{Q}_{p}}{C_{p} m_{p}} \Delta t_{sim}$$

Symbol	Parameter name	Description
$\varepsilon$	SURFACE_EMISSIVITY	Surface emissivity [-]
$C_{p}$		Heat capacity of the particle from materials editor [J/kg/K]
$h$	HEAT_TRANSFER_COEFFICIENT	Heat transfer coefficient [W/m2/K]
$k$	SCALING_FACTOR	Scaling factor [-]
$m_{p}$		Particle mass [kg]
$\dot{Q}_{p}$		Total particle heat flow [W]
$\dot{Q}_{conv}$		Heat flow due to convection [W]
$\dot{Q}_{rad}$		Heat flow due to radiation [W]
$R_{p}$		Particle radius [m]
$S$		Heat exchange surface [m2]
$t$		Current simulation time [s]
$\Delta t_{heat}$	HEATING_TIME	Time for heating from $T_{init}$ to $T_{fin}$ [s]
$\Delta t_{sim}$		Simulation time step [s]
$T_{env}$		Environment temperature [K]
$T_{fin}$	AIR_TEMPERATURE_FINAL	Final environment temperature [K]
$T_{init}$	AIR_TEMPERATURE_INIT	Initial environment temperature [K]
$T_{p}$		Particle temperature [K]