An annular combustion system includes a fuel nozzle, a panel fuel injector including a fuel plenum and at least one premixing channel therein, an inner liner having a hot side surface and a cool side surface and an outer liner having a hot side surface and a cool side surface. The inner liner, the outer liner and the panel fuel injector partially define a hot gas path downstream from the fuel nozzle. The inner liner and/or the outer liner define a plurality of micro-channel cooling passages which is disposed between the hot side surface and cool side surface of the inner liner. Each micro-channel cooling passage of the first plurality of micro-channel cooling passages is in fluid communication with an inlet hole defined along the cool side surface of the respective liner and an outlet hole.