Mathematical modelling and experimental study of the electric field control of combustion dynamics and development of exothermal combustion of volatiles downstream the swirling flame flow at biomass thermo chemical conversion are carried out with the aim to provide electric control of the combustion characteristics and to improve combustion conditions in the flame reaction zone. A mathematical model is developed for fuel combustion in a cylindrical pipe for an inviscid, compressible, axially symmetric swirling flow, which considers the development of the exothermic reaction of fuel combustion and approximation of the reaction rate by firstorder Arrhenius kinetics. The goal of the mathematical modelling is to illustrate the development of the flow velocity, temperature and composition fields and stream function provided the electric field is applied to the flame and considering its effects on development of the swirling flame reaction zone. The approximations of non-linear problems and development of fuel combustion are based on implicit finite-difference and alternating direction (ADI) methods.