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Coal consumption shares approximately 1/3 of a total global primary energy consumption, therefore this will mainly impact to global warming situation in the 21th century. For this reason, the natural resource such as coal should be processed in the most efficient way. Today, we have several combustion technologies to serve this purpose and oxy-fuel combustion is one of efficient method. In oxy-fuel technology, car-bon dioxide (CO2) will be captured in the liquid form for storaging into the ocean or injecting into the rock-sediment underground.CFD is an effective tool to analyse and approximate combustion gas species, temperature and heat transfer properties in oxy-fuel furnace. However, an insight into mathematical models for oxy-coal combustion is still restricted from many unknowns such as devolatilization rate, reaction mechanism of volatile reaction, turbulent gaseous combustion of volatile product, char heterogeneous reaction, radiation properties of gaseous mixture and heat transfer inside combustion chamber and through furnace’s wall. Therefore, this dissertation aims to study mathematical modeling of lignite combustion under oxy-fuel conditions and also create new correlations for weighted sum of gray gases (WSGG) model for predictions of radiation properties of oxy-coal gas mixture.