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Two-dimensional upward flame spread and subsequent steady burning of a vertical PMMA surface was studied using CFD methodology. Both the turbulent combustion of the gas phase and the pyrolysis of the solid fuel were numerically simulated. The transpired wall function was used to calculate the convection heat transfer with the blowing effect considered. Radiation was considered by using the discrete transfer method. A fast narrowband computer model, FASTNB, which predicts the radiation properties of the combustion products in a general, non-isothermal and non-homogeneous combustion environment, was implemented for the solution of the radiation equation along every ray. An efficient, simple and practical pyrolysis model was adopted to describe the pyrolysis of the solid fuel. The sensitivity of the prediction to grid, time step interval and ray number was analyzed. The calculated flame spread velocity, heat fluxes, and the steady burning rate, etc. were analyzed and compared with experimental measurements. Good agreement was obtained.