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It is shown that the standard method of design of boiler furnaces is not suitable for nonstandard operating conditions. A physicomathematical model of the furnace process is suggested for design studies of promising furnace devices and of conditions of flame extinction. An example of engineering design of a furnace with controlled process is presented.The theory and design of heat exchange in furnaces presented in [1,2] have been developed for the most part by professors A. M. Gurvich and V. V. Mitor. For many years these norms have played a determining role in the creation and maintenance of boiler units in Russia. In 1998 the furnace part of the standard method was amended in the third edition [3].Under conditions of unsteady supply of fuel to power generating units, of the need for changing (or, on the contrary, for preservation of) their operating parameters and for raising the flexibility of operation, and of increasingly stringent economical and ecological requirements, it has became necessary to control the processes of combustion and heat exchange in the furnace chambers of boilers. It is obvious that the zero-dimensional standard methods of furnace design developed for traditional furnace and burner devices have limited possibilities as applied to novel technologies of firing, especially for solid fuel. This circumstance makes it necessary to develop a zonal engineering method of furnace design, which will consider simultaneously the processes of mixing, combustion, and heat exchange in the furnace.Unfortunately, the procedure for computation of radiant heat exchange recommended in [3] does not involve the concepts of the degree of flame blackness a fl and of the reduced degree of furnace blackness a f widely used in scientific literature. This has led to discrepancies in methodological recommendations on design of furnace devices issued jointly by the Central Boiler and Turbine Institute (TsKTI) and the All-Russia Thermal Engineering Institute (VTI) [4].Considering the computation of heat exchange in furnaces we should not neglect the discussion in [5] concerning the reliability of the values of the coefficient of thermal efficiency of waterwalls ø recommended in [2, 3], which is determined as the ratio of the radiant heat flows taken up by a waterwall (q t ) and incident on it (q i ). This inevitably involves conditional evaluation of the coefficients ø and a f and of the effective radiant temperature of the flame T eff that enter the equation for computing the specific heat taken up by the waterwalls [2], i.e.,Since the value of the heat flow q t is measured quite reliably, for the specified the temperature T eff it is fully determined by the product y a f . This gives some leeway for choosing the factors ø and a f individually. Numerous experimental data show that the gas temperature at the outlet from boiler furnaces computed by the method of [2] is usually lower than the actual temperature [5]. This means that the computed values of the degree of blackness a f (or of the coefficient ø) have been ov...