A burner sub-system, a furnace comprising the same, a fuel combustion process and steam cracking process carried out in the furnace. The burner sub-system comprises a barrier wall segment between the burner tip and the flue-gas recirculation (“FGR”) duct, effectively blocking direct gas flow between the burner tip and the FGR duct opening, but without encircling the whole burner tip. The presence of the partial barrier wall has the advantage of preventing the temperature inside the FGR duct from becoming too high, while achieving low NOx emissions from the combustion process without overheating the burner tip because of reduced amount of heat reflection to the burner tip compared to an annular barrier wall. The invention is particularly useful in furnaces where hydrogen-rich fuel gas is combusted.