Mathematical model of generalized heat transfer inside boiler unit furnace - heat exchange paradigm

Based on the energy conservation law the balance of heat flows in the divergent form for the two dispersion and dossipative heat transfer mechanisms is formulated. Dispersion heat entrance into the furnace is determined by the physical heat of gas flow from the area of intense burning and the chemical energy of the unburned fuel. Dissipative use of heat is determined by a variety of gradient transfer mechanisms, similar to the Fourier and Fick laws. When determining the transfer coefficients for each of the mechanisms one needs to set a generalized equation of energy conservation, which is a second order differential equation in partial derivatives, allowing for the solution with separation of variables. The application of boundary conditions of the third kind and constant initial temperature in space lets us determine the constants of integration and separation of variables and set a generalized temperature field equation in the integral form, including the dimensionless form. The set of physical and mathematical methods that put the fundamental law of energy conservation to a specific form of the temperature field from is defined as a paradigm of heat in the furnace of a boiler unit. The result of the solution for spatial temperature field characterizes the intensity of the heat in the furnace and depends on the generalized Nusselt number and then is adapted to the furnaces with the different cross-sectional area.