Through numerical solution of the dimensionless integral equations of the turbulent buoyant plume in stably linearly thermally stratified environments, the transportation laws of the buoyant flux, momentum flux and other parameters in the axial direction as well as the neutral buoyant force height and the maximum plume height are obtained. Measurements on the different fire smoke plumes in the medium-scale and big-scale experimental rooms indicate that the actual values of the maximum plume heights are consistent with both the numerical calculation results and the empirical formula in the available literatures, thus this work validates the integral model and provides a good foundation for the smoke transport research and fire detection technology development in big space buildings.