A two-dimensional coupled heat transfer model with Monte-Carlo ray tracing (MCRT) method is developed to analyze the heat transfer in windowed volumetric solar receiver. The local thermal non-equilibrium (LTNE) effects in ceramic foam absorber and spectral selectivity of quartz window are considered. With the solar absorption term calculated by the MCRT, the P-1-approximation for thermal radiative exchange in the foam absorber is examined by comparing with the MCRT. In the model based on P-1-approximation, net radiation method (NRM) and MCRT are applied to calculate the thermal radiative exchange between the window and absorber. The effects of porosity and cell size of the absorber foam on temperature distribution and thermal efficiency are investigated. The results show that for heat transfer in foam absorber at a highest temperature below 1727 K, the P-1-approximation underestimates the absorber temperature by about 27 K and overestimates the window temperature by 106-133 K. And the thermal efficiency is underestimated by about 2.1% using the P-1-approximation. There is small difference between the temperature in the absorber predicted by different models, but the NRM cannot predict the axial temperature gradient in the window. Under a constant air mass flow rate, within the absorber foam with the cell size range of 2-4 mm and porosity range of 0.7-0.9, a higher thermal efficiency can be reached at a larger cell size or a lower porosity.