The aim of this paper is to develop a line by line model for CO2 vibrational nonequilibrium radiation and to investigate nonequilibrium effects in the case of some applications involving high temperature expanding flows. A vibrational specific collisional relaxation model is developed and is incorporated in a multi- temperature thermodynamic description of the gas mixture, in order to compute vibrational level populations along the flow. The HITEMP-2010 spectroscopic database is employed with a model for level energy splitting to provide line by line absorption and emission total and per-vibrational mode specific spectra. The specific spectra allow us to derive the radiative source terms to be used in the multi-temperature model if a coupled approach is required. The model is applied first to a simple conical nozzle flow and then to the plume of a high altitude solid propellant rocket engine. It is shown that, for the considered applications, the partial freeze of vibrational excitation in the expanding flow increases significantly the radiative intensity escaping from the mixture.