This section will highlight some of the important aspects of heat transfer in industrial combustion, while the next section will discuss modeling of industrial combustors.

Hottel (1961) developed a relatively simple equation to calculate the heat transfer in a combustor. The model assumes the gas in the combustion space is isothermal and is referred to as a one-gas-zone furnace model. The wall and load temperatures are both assumed to be constant and the furnace walls are assumed to be radiatively adiabatic. A sketch of the combustion system is shown in Figure 35. The heat transfer to the load can be calculated as follows:

\[\label{eq5} q_1=\dfrac{\sigma\left(T_{\rm g}^4-T_1^4\right)}{\big[(1-\varepsilon_1)/A_1\varepsilon_{\rm g}\big]+(K_{\rm s}/4K_{\rm a}V)+\Big|1\big/\left\langle A_1\varepsilon_{\rm g}+\left\{1/\big[1/A_1F_{\rm 1w}(1-\varepsilon_{\rm g})\big]+(1/A_{\rm w}\varepsilon_{\rm g})\right\}\right\rangle\Big|}+h_1A_1\left(T_{\rm g}-T_1\right) \tag{5}\]

where σ is the Stefan-Boltzmann constant; T_g and T₁ are the absolute temperatures of the gas and load, respectively; ε₁ and ε_g are the emissivities of the load and the gas, respectively; A₁ and A_w are the surface areas of the load and the wall, respectively; K_s and K_a are the scattering and absorption coefficients for the gas, respectively; V is the volume of the gas; F_1w is the view factor to the wall from the load; and h₁ is the convection coefficient to the load. The equation is only valid when multiple scatter is negligible (K_sL << 1). An enthalpy balance on the gas can be written as follows: