Everyone recognizes the mathematic simulation as a powerful research tool, but only few in number have vigour to master its complicated equations and methods. Unlike many manuals, this monograph contains a detailed description of advanced stable algorithms, which adequacy is strictly proved. Algorithm SAMPLE is able to exclude the pressure-correction equation out of the mathematic model. A new configurational parameter in Van Driest's exponential factor ascertains values of Prandtl's mixing length near a wall. An easy differential algorithm SMART was elaborated for radiative transfer in selective gases. New computing modes were suggested for absorption coefficients of triatomic gases and for transforming them into a local selective-absorption coefficient within concept of an anti-gray spectrum. Boundary conditions for the heat transfer in rotary kilns are stated, accounting for bed reemission and transitional heat conduction through walls. A variety of horizontal and downward diffusion flames of the natural gas were researched. The book is intended for postgraduates, engineers and scientists concerned themselves with numerical researching the mass and heat transfer in furnaces.